Package 'CDM'

Description

Functions for cognitive diagnosis modeling and multidimensional item response modeling for dichotomous and polytomous item responses. This package enables the estimation of the DINA and DINO model (Junker & Sijtsma, 2001, <doi:10.1177/01466210122032064>), the multiple group (polytomous) GDINA model (de la Torre, 2011, <doi:10.1007/s11336-011-9207-7>), the multiple choice DINA model (de la Torre, 2009, <doi:10.1177/0146621608320523>), the general diagnostic model (GDM; von Davier, 2008, <doi:10.1348/000711007X193957>), the structured latent class model (SLCA; Formann, 1992, <doi:10.1080/01621459.1992.10475229>) and regularized latent class analysis (Chen, Li, Liu, & Ying, 2017, <doi:10.1007/s11336-016-9545-6>). See George, Robitzsch, Kiefer, Gross, and Uenlue (2017) <doi:10.18637/jss.v074.i02> or Robitzsch and George (2019, <doi:10.1007/978-3-030-05584-4_26>) for further details on estimation and the package structure. For tutorials on how to use the CDM package see George and Robitzsch (2015, <doi:10.20982/tqmp.11.3.p189>) as well as Ravand and Robitzsch (2015).

Details

Cognitive diagnosis models (CDMs) are restricted latent class models. They represent model-based classification approaches, which aim at assigning respondents to different attribute profile groups. The latent classes correspond to the possible attribute profiles, and the conditional item parameters model atypical response behavior in the sense of slipping and guessing errors. The core CDMs in particular differ in the utilized condensation rule, conjunctive / non-compensatory versus disjunctive / compensatory, where in the model structure these two types of response error parameters enter and what restrictions are imposed on them. The confirmatory character of CDMs is apparent in the Q-matrix, which can be seen as an operationalization of the latent concepts of an underlying theory. The Q-matrix allows incorporating qualitative prior knowledge and typically has as its rows the items and as the columns the attributes, with entries 1 or 0, depending on whether an attribute is measured by an item or not, respectively.

CDMs as compared to common psychometric models (e.g., IRT) contain categorical instead of continuous latent variables. The results of analyses using CDMs differ from the results obtained under continuous latent variable models. CDMs estimate in a direct manner the probabilistic attribute profile of a respondent, that is, the multivariate vector of the conditional probabilities for possessing the individual attributes, given her / his response pattern. Based on these probabilities, simplified deterministic attribute profiles can be derived, showing whether an individual attribute is essentially possessed or not by a respondent. As compared to alternative two-step discretization approaches, which estimate continuous scores and discretize the continua based on cut scores, with CDMs the classification error can generally be reduced.

The package CDM implements parameter estimation procedures for the DINA and DINO model (e.g.,de la Torre & Douglas, 2004; Junker & Sijtsma, 2001; Templin & Henson, 2006; the generalized DINA model for dichotomous attributes (GDINA, de la Torre, 2011) and for polytomous attributes (pGDINA, Chen & de la Torre, 2013); the general diagnostic model (GDM, von Davier, 2008) and its extension to the multidimensional latent class IRT model (Bartolucci, 2007), the structure latent class model (Formann, 1992), and tools for analyzing data under the models. These and related concepts are explained in detail in the book about diagnostic measurement and CDMs by Rupp, Templin and Henson (2010), and in such survey articles as DiBello, Roussos and Stout (2007) and Rupp and Templin (2008).

The package CDM is implemented based on the S3 system. It comes with a namespace and consists of several external functions (functions the package exports). The package contains a utility method for the simulation of artificial data based on a CDM model (sim.din). It also contains seven internal functions (functions not exported by the package): this are plot, print, and summary methods for objects of the class din (plot.din, print.din, summary.din), a print method for objects of the class summary.din (print.summary.din), and three functions for checking the input format and computing intermediate information. The features of the package CDM are illustrated with an accompanying real dataset and Q-matrix (fraction.subtraction.data and fraction.subtraction.qmatrix) and artificial examples (Data-sim).

See George et al. (2016) and Robitzsch and George (2019) for an overview and some computational details of the CDM package.

Author(s)

Alexander Robitzsch [aut, cre], Thomas Kiefer [aut], Ann Cathrice George [aut], Ali Uenlue [aut]

Maintainer: Alexander Robitzsch <[email protected]>

References

Bartolucci, F. (2007). A class of multidimensional IRT models for testing unidimensionality and clustering items. Psychometrika, 72, 141-157.

Chen, J., & de la Torre, J. (2013). A general cognitive diagnosis model for expert-defined polytomous attributes. Applied Psychological Measurement, 37, 419-437.

Chen, Y., Li, X., Liu, J., & Ying, Z. (2017). Regularized latent class analysis with application in cognitive diagnosis. Psychometrika, 82, 660-692.

de la Torre, J., & Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333–353.

de la Torre, J. (2009). A cognitive diagnosis model for cognitively based multiple-choice options. Applied Psychological Measurement, 33, 163-183.

de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179–199.

DiBello, L. V., Roussos, L. A., & Stout, W. F. (2007). Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao and S. Sinharay (Eds.), Handbook of Statistics, Vol. 26 (pp. 979–1030). Amsterdam: Elsevier.

Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data. Journal of the American Statistical Association, 87, 476-486.

George, A. C., & Robitzsch, A. (2015) Cognitive diagnosis models in R: A didactic. The Quantitative Methods for Psychology, 11, 189-205. doi:10.20982/tqmp.11.3.p189

George, A. C., Robitzsch, A., Kiefer, T., Gross, J., & Uenlue, A. (2016). The R package CDM for cognitive diagnosis models. Journal of Statistical Software, 74(2), 1-24.

Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258–272.

Ravand, H., & Robitzsch, A.(2015). Cognitive diagnostic modeling using R. Practical Assessment, Research & Evaluation, 20(11). Available online: http://pareonline.net/getvn.asp?v=20&n=11

Robitzsch, A., & George, A. C. (2019). The R package CDM. In M. von Davier & Y.-S. Lee (Eds.). Handbook of diagnostic classification models (pp. 549-572). Cham: Springer. doi:10.1007/978-3-030-05584-4_26

Rupp, A. A., & Templin, J. (2008). Unique characteristics of diagnostic classification models: A comprehensive review of the current state-of-the-art. Measurement: Interdisciplinary Research and Perspectives, 6, 219–262.

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Templin, J., & Henson, R. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287–305.

von Davier, M. (2008). A general diagnostic model applied to language testing data. British Journal of Mathematical and Statistical Psychology, 61, 287-307.

See Also

See the GDINA package for comprehensive functions for the GDINA model.

See also the ACTCD and NPCD packages for nonparametric cognitive diagnostic models.

See the dina package for estimating the DINA model with a Gibbs sampler.

Examples

##
##   **********************************
##   ** CDM 2.5-16 (2013-11-29)      **
##   ** Cognitive Diagnostic Models  **
##   **********************************
##

Description

This function compares two models estimated with din, gdina or gdm using a likelihood ratio test.

Usage

## S3 method for class 'din'
anova(object,...)

## S3 method for class 'gdina'
anova(object,...)

## S3 method for class 'gdm'
anova(object,...)

## S3 method for class 'mcdina'
anova(object,...)

## S3 method for class 'reglca'
anova(object,...)

## S3 method for class 'slca'
anova(object,...)

Arguments

Note

This function is based on IRT.anova.

See Also

din, gdina, gdm, mcdina, slca

Examples

#############################################################################
# EXAMPLE 1: anova with din objects
#############################################################################

# Model 1
d1 <- CDM::din(sim.dina, q.matr=sim.qmatrix )
# Model 2 with equal guessing and slipping parameters
d2 <- CDM::din(sim.dina, q.matr=sim.qmatrix, guess.equal=TRUE, slip.equal=TRUE)
# model comparison
anova(d1,d2)
  ##     Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2    d2 -2176.482 4352.963     9 4370.963 4406.886 268.2071 16  0
  ##   1    d1 -2042.378 4084.756    25 4134.756 4234.543       NA NA NA

## Not run: 
#############################################################################
# EXAMPLE 2: anova with gdina objects
#############################################################################

# Model 3: GDINA model
d3 <- CDM::gdina( sim.dina, q.matr=sim.qmatrix )

# Model 4: DINA model
d4 <- CDM::gdina( sim.dina, q.matr=sim.qmatrix, rule="DINA")

# model comparison
anova(d3,d4)
  ##     Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
  ##   2    d4 -2042.293 4084.586    25 4134.586 4234.373 31.31995 16 0.01224
  ##   1    d3 -2026.633 4053.267    41 4135.266 4298.917       NA NA      NA

## End(Not run)

Description

This function computes several cognitive diagnostic indices grounded on the Kullback-Leibler information (Rupp, Henson & Templin, 2009, Ch. 13) at the test, item, attribute and item-attribute level. See Henson and Douglas (2005) and Henson, Roussos, Douglas and He (2008) for more details.

Usage

cdi.kli(object)

## S3 method for class 'cdi.kli'
summary(object, digits=2,  ...)

Arguments

Value

A list with following entries

References

Henson, R., DiBello, L., & Stout, B. (2018). A generalized approach to defining item discrimination for DCMs. Measurement: Interdisciplinary Research and Perspectives, 16(1), 18-29. http://dx.doi.org/10.1080/15366367.2018.1436855

Henson, R., & Douglas, J. (2005). Test construction for cognitive diagnosis. Applied Psychological Measurement, 29, 262-277. http://dx.doi.org/10.1177/0146621604272623

Henson, R., Roussos, L., Douglas, J., & He, X. (2008). Cognitive diagnostic attribute-level discrimination indices. Applied Psychological Measurement, 32, 275-288. http://dx.doi.org/10.1177/0146621607302478

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

See Also

See discrim.index for computing discrimination indices at the probability metric.

See Henson, DiBello and Stout (2018) for an overview of different discrimination indices.

Examples

#############################################################################
# EXAMPLE 1: Examples based on CDM::sim.dina
#############################################################################

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")

mod <- CDM::din( sim.dina, q.matrix=sim.qmatrix )
summary(mod)
  ##  Item parameters
  ##         item guess  slip   IDI rmsea
  ##  Item1 Item1 0.086 0.210 0.704 0.014
  ##  Item2 Item2 0.109 0.239 0.652 0.034
  ##  Item3 Item3 0.129 0.185 0.686 0.028
  ##  Item4 Item4 0.226 0.218 0.556 0.019
  ##  Item5 Item5 0.059 0.000 0.941 0.002
  ##  Item6 Item6 0.248 0.500 0.252 0.036
  ##  Item7 Item7 0.243 0.489 0.268 0.041
  ##  Item8 Item8 0.278 0.125 0.597 0.109
  ##  Item9 Item9 0.317 0.027 0.656 0.065

cmod <- CDM::cdi.kli( mod )

# attribute discrimination indices
round( cmod$attr_disc, 3 )
  ##      V1     V2     V3
  ##   1.966  2.506 11.169

# look at global item discrimination indices
round( cmod$glob_item_disc, 3 )
  ##  > round( cmod$glob_item_disc, 3 )
  ##  Item1 Item2 Item3 Item4 Item5 Item6 Item7 Item8 Item9
  ##  0.594 0.486 0.533 0.465 5.913 0.093 0.040 0.397 0.656

# correlation of IDI and global item discrimination
stats::cor( cmod$glob_item_disc, mod$IDI )
  ##  [1] 0.6927274

# attribute-specific item indices
round( cmod$attr_item_disc, 3 )
  ##           V1    V2    V3
  ##  Item1 0.648 0.648 0.000
  ##  Item2 0.000 0.530 0.530
  ##  Item3 0.581 0.000 0.581
  ##  Item4 0.697 0.000 0.000
  ##  Item5 0.000 0.000 8.870
  ##  Item6 0.000 0.140 0.000
  ##  Item7 0.040 0.040 0.040
  ##  Item8 0.000 0.433 0.433
  ##  Item9 0.000 0.715 0.715

## Note that attributes with a zero entry for an item
## do not differ from zero for the attribute specific item index

Description

Utility functions in CDM.

Usage

## requireNamespace with package message for needed installation
CDM_require_namespace(pkg)
## attach internal function in a package
cdm_attach_internal_function(pack, fun)

## print function in summary
cdm_print_summary_data_frame(obji, from=NULL, to=NULL, digits=3, rownames_null=FALSE)
## print summary call
cdm_print_summary_call(object, call_name="call")
## print computation time
cdm_print_summary_computation_time(object, time_name="time", time_start="s1",
         time_end="s2")

## string vector of matrix entries
cdm_matrixstring( matr, string )

## mvtnorm::rmvnorm with vector conversion for n=1
CDM_rmvnorm(n, mean=NULL, sigma, ...)
## fit univariate and multivariate normal distribution
cdm_fit_normal(x, w)

## fit unidimensional factor analysis by unweighted least squares
cdm_fa1(Sigma, method=1, maxit=50, conv=1E-5)

## another rbind.fill implementation
CDM_rbind_fill( x, y )
## fills a vector row-wise into a matrix
cdm_matrix2( x, nrow )
## fills a vector column-wise into a matrix
cdm_matrix1( x, ncol )

## SCAD thresholding operator
cdm_penalty_threshold_scad(beta, lambda, a=3.7)
## lasso thresholding operator
cdm_penalty_threshold_lasso(val, eta )
## ridge thresholding operator
cdm_penalty_threshold_ridge(beta, lambda)
## elastic net threshold operator
cdm_penalty_threshold_elnet( beta, lambda, alpha )
## SCAD-L2 thresholding operator
cdm_penalty_threshold_scadL2(beta, lambda, alpha, a=3.7)
## truncated L1 penalty thresholding operator
cdm_penalty_threshold_tlp( beta, tau, lambda )
## MCP thresholding operator
cdm_penalty_threshold_mcp(beta, lambda, a=3.7)

## general thresholding operator for regularization
cdm_parameter_regularization(x, regular_type, regular_lam, regular_alpha=NULL,
         regular_tau=NULL )
## values of penalty function
cdm_penalty_values(x, regular_type, regular_lam, regular_tau=NULL,
       regular_alpha=NULL)
## thresholding operators regularization
cdm_parameter_regularization(x, regular_type, regular_lam, regular_alpha=NULL,
       regular_tau=NULL)

## utility functions for P-EM acceleration
cdm_pem_inits(parmlist)
cdm_pem_inits_assign_parmlist(pem_pars, envir)
cdm_pem_acceleration( iter, pem_parameter_index, pem_parameter_sequence, pem_pars,
      PEM_itermax, parmlist, ll_fct, ll_args, deviance.history=NULL )
cdm_pem_acceleration_assign_output_parameters(res_ll_fct, vars, envir, update)

## approximation of absolute value function and its derivative
abs_approx(x, eps=1e-05)
abs_approx_D1(x, eps=1e-05)

## information criteria
cdm_calc_information_criteria(ic)
cdm_print_summary_information_criteria(object, digits_crit=0, digits_penalty=2)

## string pasting
cat_paste(...)

Arguments

Description

This function computes the classification accuracy and consistency originally proposed by Cui, Gierl and Chang (2012; see also Wang et al., 2015). The function computes both statistics by estimators of Johnson and Sinharay (2018; see also Sinharay & Johnson, 2019) and simulation based estimation.

Usage

cdm.est.class.accuracy(cdmobj, n.sims=0, version=2)

Arguments

Details

The item parameters and the probability distribution of latent classes is used as the basis of the simulation. Accuracy and consistency is estimated for both MLE and MAP classification estimators. In addition, classification accuracy measures are available for the separate classification of all skills.

Value

A data frame for MLE, MAP and MAP (Skill 1, ..., Skill $K$) classification reliability for the whole latent class pattern and marginal skill classification with following columns:

References

Cui, Y., Gierl, M. J., & Chang, H.-H. (2012). Estimating classification consistency and accuracy for cognitive diagnostic assessment. Journal of Educational Measurement, 49, 19-38. doi:10.1111/j.1745-3984.2011.00158.x

Johnson, M. S., & Sinharay, S. (2018). Measures of agreement to assess attribute-level classification accuracy and consistency for cognitive diagnostic assessments. Journal of Educational Measurement, 45(4), 635-664. doi:10.1111/jedm.12196

Sinharay, S., & Johnson, M. S. (2019). Measures of agreement: Reliability, classification accuracy, and classification consistency. In M. von Davier & Y.-S. Lee (Eds.). Handbook of diagnostic classification models (pp. 359-377). Cham: Springer. doi:10.1007/978-3-030-05584-4_17

Wang, W., Song, L., Chen, P., Meng, Y., & Ding, S. (2015). Attribute-level and pattern-level classification consistency and accuracy indices for cognitive diagnostic assessment. Journal of Educational Measurement, 52(4), 457-476. doi:10.1111/jedm.12096

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: DINO data example
#############################################################################

data(sim.dino, package="CDM")
data(sim.qmatrix, package="CDM")

#***
# Model 1: estimate DINO model with din
mod1 <- CDM::din( sim.dino, q.matrix=sim.qmatrix, rule="DINO")
# estimate classification reliability
cdm.est.class.accuracy( mod1, n.sims=5000)

#***
# Model 2: estimate DINO model with gdina
mod2 <- CDM::gdina( sim.dino, q.matrix=sim.qmatrix, rule="DINO")
# estimate classification reliability
cdm.est.class.accuracy( mod2 )

m1 <- mod1$coef[, c("guess", "slip" ) ]
m2 <- mod2$coef
m2 <- cbind( m1, m2[ seq(1,18,2), "est" ],
          1 - m2[ seq(1,18,2), "est" ]  - m2[ seq(2,18,2), "est" ]  )
colnames(m2) <- c("g.M1", "s.M1", "g.M2", "s.M2" )
  ##   > round( m2, 3 )
  ##          g.M1  s.M1  g.M2  s.M2
  ##   Item1 0.109 0.192 0.109 0.191
  ##   Item2 0.073 0.234 0.072 0.234
  ##   Item3 0.139 0.238 0.146 0.238
  ##   Item4 0.124 0.065 0.124 0.009
  ##   Item5 0.125 0.035 0.125 0.037
  ##   Item6 0.214 0.523 0.214 0.529
  ##   Item7 0.193 0.514 0.192 0.514
  ##   Item8 0.246 0.100 0.246 0.100
  ##   Item9 0.201 0.032 0.195 0.032
# Note that s (the slipping parameter) substantially differs for Item4
# for DINO estimation in 'din' and 'gdina'

## End(Not run)

Description

Extracts the estimated parameters from either din, gdina, gdina or gdm objects.

Usage

## S3 method for class 'din'
coef(object, ...)

## S3 method for class 'gdina'
coef(object, ...)

## S3 method for class 'mcdina'
coef(object, ...)

## S3 method for class 'gdm'
coef(object, ...)

## S3 method for class 'slca'
coef(object, ...)

Arguments

Value

A vector, a matrix or a data frame of the estimated parameters for the fitted model.

See Also

din, gdina, gdm, mcdina, slca

Examples

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")

# DINA model
d1 <- CDM::din( sim.dina, q.matrix=sim.qmatrix)
coef(d1)

## Not run: 
# GDINA model
d2 <- CDM::gdina( sim.dina, q.matrix=sim.qmatrix)
coef(d2)

# GDM model
theta.k <- seq(-4,4,len=11)
d3 <- CDM::gdm( sim.dina, irtmodel="2PL", theta.k=theta.k,
            Qmatrix=as.matrix(sim.qmatrix),  centered.latent=TRUE)
coef(d3)

## End(Not run)

Description

Artificial data: dichotomously coded fictitious answers of 400 respondents to 9 items assuming 3 underlying attributes.

Usage

data(sim.dina)
  data(sim.dino)
  data(sim.qmatrix)

Format

The sim.dina and sim.dino data sets include dichotomous answers of $N=400$ respondents to $J=9$ items, thus they are $400 \times 9$ data matrices. For both data sets $K=3$ attributes are assumed to underlie the process of responding, stored in sim.qmatrix.

The sim.dina data set is simulated according to the DINA condensation rule, whereas the sim.dino data set is simulated according to the DINO condensation rule. The slipping errors for the items 1 to 9 in both data sets are 0.20, 0.20, 0.20, 0.20, 0.00, 0.50, 0.50, 0.10, 0.03 and the guessing errors are 0.10, 0.125, 0.15, 0.175, 0.2, 0.225, 0.25, 0.275, 0.3. The attributes are assumed to be mastered with expected probabilities of -0.4, 0.2, 0.6, respectively. The correlation of the attributes is 0.3 for attributes 1 and 2, 0.4 for attributes 1 and 3 and 0.1 for attributes 2 and 3.

Example Index

Dataset sim.dina

anova (Examples 1, 2), cdi.kli (Example 1), din (Examples 2, 4, 5), gdina (Example 1), itemfit.sx2 (Example 2), modelfit.cor.din (Example 1)

Dataset sim.dino

cdm.est.class.accuracy (Example 1), din (Example 3), gdina (Examples 2, 3, 4),

References

Rupp, A. A., Templin, J. L., & Henson, R. A. (2010) Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Description

Several datasets for the CDM package

Usage

data(data.cdm01)
data(data.cdm02)
data(data.cdm03)
data(data.cdm04)
data(data.cdm05)
data(data.cdm06)
data(data.cdm07)
data(data.cdm08)
data(data.cdm09)
data(data.cdm10)

Format

• Dataset data.cdm01

  This dataset is a multiple choice dataset and used in the mcdina function. The format is:

  List of 3
$ data :'data.frame':
..$ I1 : int [1:5003] 3 3 4 1 1 1 1 1 1 1 ...
..$ I2 : int [1:5003] 1 1 3 1 1 2 1 1 2 1 ...
..$ I3 : int [1:5003] 4 3 2 3 2 2 2 2 1 2 ...
..$ I4 : int [1:5003] 3 3 3 2 2 2 2 3 3 1 ...
..$ I5 : int [1:5003] 2 2 2 3 1 1 2 3 2 1 ...
..$ I6 : int [1:5003] 3 1 1 1 1 2 1 1 1 1 ...
..$ I7 : int [1:5003] 1 1 2 2 1 3 1 1 1 3 ...
..$ I8 : int [1:5003] 1 1 1 1 1 2 1 4 3 3 ...
..$ I9 : int [1:5003] 3 2 1 1 1 1 3 3 1 3 ...
..$ I10: int [1:5003] 2 1 2 1 1 2 2 2 2 1 ...
..$ I11: int [1:5003] 2 2 2 2 1 2 1 2 1 1 ...
..$ I12: int [1:5003] 1 2 1 1 2 1 1 1 1 2 ...
..$ I13: int [1:5003] 2 1 1 1 2 1 2 2 1 1 ...
..$ I14: int [1:5003] 1 1 1 1 1 2 1 1 2 1 ...
..$ I15: int [1:5003] 1 2 1 1 1 1 1 1 1 1 ...
..$ I16: int [1:5003] 1 2 2 1 2 2 2 1 1 1 ...
..$ I17: int [1:5003] 1 1 1 1 1 1 1 1 1 1 ...
$ group : int [1:5003] 1 1 1 1 1 1 1 1 1 1 ...
$ q.matrix:'data.frame':
..$ item : int [1:52] 1 1 1 1 2 2 2 2 3 3 ...
..$ categ: int [1:52] 1 2 3 4 1 2 3 4 1 2 ...
..$ A1 : int [1:52] 0 1 0 1 0 1 1 1 0 0 ...
..$ A2 : int [1:52] 0 0 1 1 0 0 0 1 0 0 ...
..$ A3 : int [1:52] 0 0 0 0 0 0 0 0 0 0 ...
  

• Dataset data.cdm02

  Multiple choice dataset with a Q-matrix designed for polytomous attributes.

  List of 2
$ data :'data.frame':
..$ I1 : int [1:3000] 3 3 4 1 1 1 1 1 1 1 ...
..$ I2 : int [1:3000] 1 1 3 1 1 2 1 1 2 1 ...
..$ I3 : int [1:3000] 4 3 2 3 2 2 2 2 1 2 ...
[...]
..$ B17: num [1:3000] 1 1 1 1 1 1 1 1 1 1 ...
..$ B18: num [1:3000] 1 1 1 1 2 2 2 2 2 2 ...
$ q.matrix:'data.frame':
..$ item : int [1:100] 1 1 1 1 2 2 2 2 3 3 ...
..$ categ: int [1:100] 1 2 3 4 1 2 3 4 1 2 ...
..$ A1 : num [1:100] 0 1 0 1 0 1 1 1 0 0 ...
..$ A2 : num [1:100] 0 0 1 1 0 0 0 1 0 0 ...
..$ A3 : num [1:100] 0 0 0 0 0 0 0 0 0 0 ...
..$ B1 : num [1:100] 0 0 0 0 0 0 0 0 0 0 ...
  

• Dataset data.cdm03:

  This is a resimulated dataset from Chiu, Koehn and Wu (2016) where the data generating model is a reduced RUM model. See Example 1.

  List of 2
$ data : num [1:725, 1:16] 0 1 1 1 1 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:16] "I01" "I02" "I03" "I04" ...
$ qmatrix:'data.frame': 16 obs. of 6 variables:
..$ item: Factor w/ 16 levels "I01","I02","I03",..: 1 2 3 4 5 6 7 8 9 10 ...
..$ A1 : int [1:16] 1 0 0 0 0 0 0 0 1 1 ...
..$ A2 : int [1:16] 0 1 0 0 1 1 0 0 0 0 ...
..$ A3 : int [1:16] 0 0 1 1 1 1 0 0 0 0 ...
..$ A4 : int [1:16] 0 0 0 0 0 0 1 1 1 1 ...
..$ A5 : int [1:16] 0 0 0 0 0 0 0 0 0 0 ...
  

• Dataset data.cdm04:

  Simulated dataset for the sequential DINA model (as described in Ma & de la Torre, 2016). The dataset contains 1000 persons and 12 items which measure 2 skills.

  List of 3
$ data : num [1:1000, 1:12] 0 0 0 1 1 0 0 0 0 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:12] "I1" "I2" "I3" "I4" ...
$ q.matrix1:'data.frame': 18 obs. of 4 variables:
..$ Item: chr [1:18] "I1" "I2" "I3" "I4" ...
..$ Cat : int [1:18] 1 1 1 1 1 1 1 2 1 2 ...
..$ A1 : int [1:18] 1 1 1 0 0 0 1 1 1 1 ...
..$ A2 : int [1:18] 0 0 0 1 1 1 0 0 0 0 ...
$ q.matrix2:'data.frame': 18 obs. of 4 variables:
..$ Item: chr [1:18] "I1" "I2" "I3" "I4" ...
..$ Cat : int [1:18] 1 1 1 1 1 1 1 2 1 2 ...
..$ A1 : num [1:18] 1 1 1 0 0 0 1 1 1 1 ...
..$ A2 : num [1:18] 0 0 0 1 1 1 0 0 0 0 ...
  

• Dataset data.cdm05:

  Example dataset used in Philipp, Strobl, de la Torre and Zeileis (2018). This dataset is a sub-dataset of the probability dataset in the pks package (Heller & Wickelmaier, 2013).

  List of 3
$ data :'data.frame': 504 obs. of 12 variables:
..$ b101: num [1:504] 1 1 1 1 1 1 1 1 1 1 ...
..$ b102: num [1:504] 1 1 1 1 1 1 1 1 1 1 ...
..$ b103: num [1:504] 1 1 1 1 1 1 1 1 1 1 ...
..$ b104: num [1:504] 1 1 1 1 0 1 0 0 0 1 ...
..$ b105: num [1:504] 1 0 1 1 1 1 0 1 1 1 ...
..$ b106: num [1:504] 1 1 1 1 1 1 1 1 1 1 ...
..$ b107: num [1:504] 1 1 1 1 1 1 1 1 1 1 ...
..$ b108: num [1:504] 1 1 1 1 1 1 0 1 1 1 ...
..$ b109: num [1:504] 1 1 0 1 1 0 0 1 1 0 ...
..$ b110: num [1:504] 0 0 0 1 0 0 0 0 0 1 ...
..$ b111: num [1:504] 0 1 0 0 0 1 0 0 0 0 ...
..$ b112: num [1:504] 1 1 0 1 0 1 0 1 0 0 ...
$ q.matrix:'data.frame': 12 obs. of 4 variables:
..$ pb: num [1:12] 1 0 0 0 1 1 1 1 1 0 ...
..$ cp: num [1:12] 0 1 0 0 1 1 0 0 0 1 ...
..$ un: num [1:12] 0 0 1 0 0 0 1 1 0 0 ...
..$ id: num [1:12] 0 0 0 1 0 0 0 0 1 1 ...
$ skills : Named chr [1:4] "how to calculate the classic probability "
..- attr(*, "names")=chr [1:4] "pb" "cp" "un" "id"
  

• Dataset data.cdm06:

  Resimulated example dataset from Chen and Chen (2017).

  List of 3
$ data :'data.frame': 2733 obs. of 15 variables:
..$ I01: num [1:2733] 1 0 0 1 0 0 0 1 1 1 ...
..$ I02: num [1:2733] 1 0 0 1 1 0 1 0 0 1 ...
..$ I03: num [1:2733] 0 0 0 1 1 0 1 0 1 0 ...
..$ I04: num [1:2733] 1 1 0 0 0 0 1 1 1 0 ...
..$ I05: num [1:2733] 1 0 1 1 0 1 1 1 1 1 ...
..$ I06: num [1:2733] 0 0 0 1 1 0 0 0 1 1 ...
..$ I07: num [1:2733] 1 1 1 0 0 1 1 0 1 1 ...
..$ I08: num [1:2733] 0 0 0 0 0 0 0 0 1 1 ...
..$ I09: num [1:2733] 1 0 0 1 1 1 0 1 0 1 ...
..$ I10: num [1:2733] 0 0 0 1 0 1 1 0 1 1 ...
..$ I11: num [1:2733] 0 1 0 1 1 1 1 0 1 1 ...
..$ I12: num [1:2733] 0 1 0 1 0 0 0 1 1 1 ...
..$ I13: num [1:2733] 0 0 1 1 0 1 0 0 0 1 ...
..$ I14: num [1:2733] 0 0 0 1 1 0 1 1 0 0 ...
..$ I15: num [1:2733] 0 0 0 1 0 0 1 0 1 1 ...
$ q.matrix:'data.frame': 15 obs. of 5 variables:
..$ RI: num [1:15] 1 1 1 0 1 1 1 1 0 0 ...
..$ JS: num [1:15] 1 0 0 1 0 0 0 0 0 1 ...
..$ GI: num [1:15] 0 1 0 1 0 0 1 1 1 1 ...
..$ II: num [1:15] 0 1 1 0 1 0 1 0 0 0 ...
..$ MI: num [1:15] 0 0 1 0 0 0 0 0 1 0 ...
$ skills : chr [1:5, 1:2] "Retrieving explicit information " ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:5] "RI" "JS" "GI" "II" ...
.. ..$ : chr [1:2] "skill" "description"
  

• Dataset data.cdm07:

  This is a resimulated dataset from the social anxiety disorder data concerning social phobia which involve 13 dichotomous questions (Fang, Liu & Ling, 2017). The simulation was based on a latent class model with five classes. The dataset was also used in Chen, Li, Liu and Ying (2017).

  $ data : num [1:863, 1:13] 1 0 1 1 1 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:13] "I1" "I2" "I3" "I4" ...
$ q.matrix: num [1:13, 1:3] 1 1 1 1 0 0 0 0 0 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:13] "I1" "I2" "I3" "I4" ...
.. ..$ : chr [1:3] "A1" "A2" "A3"
$ items : atomic [1:13] 1 speaking in front of other people? ...
..- attr(*, "stem")=chr "Have you ever had a strong fear or avoidance of ..."
  

• Dataset data.cdm08:

  This is a simulated dataset involving four skills and three misconceptions for the model for simultaneously identifying skills and misconceptions (SISM; Kuo, Chen & de la Torre, 2018). The Q-matrix follows the specification in their simulation study.

  List of 2
$ data :'data.frame': 1300 obs. of 20 variables:
..$ I01: num [1:1300] 1 0 0 1 1 1 1 1 1 1 ...
..$ I02: num [1:1300] 0 0 0 0 1 1 1 1 1 1 ...
..$ I03: num [1:1300] 0 0 0 0 1 1 1 1 1 1 ...
..$ I04: num [1:1300] 1 1 0 1 0 1 1 0 1 1 ...
..$ I05: num [1:1300] 1 1 1 0 1 1 0 1 1 1 ...
..[...]
..$ I18: num [1:1300] 0 1 0 0 0 0 0 0 0 1 ...
..$ I19: num [1:1300] 1 1 0 0 0 0 0 1 1 1 ...
..$ I20: num [1:1300] 1 1 0 0 0 1 0 1 0 1 ...
$ q.matrix:'data.frame': 20 obs. of 7 variables:
..$ S1: num [1:20] 1 0 0 0 0 0 0 1 0 0 ...
..$ S2: num [1:20] 0 1 0 0 0 0 0 0 1 0 ...
..$ S3: num [1:20] 0 0 1 0 0 0 0 0 0 1 ...
..$ S4: num [1:20] 0 0 0 1 0 0 0 0 0 0 ...
..$ B1: num [1:20] 0 0 0 0 1 0 0 1 1 0 ...
..$ B2: num [1:20] 0 0 0 0 0 1 0 0 0 0 ...
..$ B3: num [1:20] 0 0 0 0 0 0 1 0 0 1 ...
  

• Dataset data.cdm09: This is a simulated dataset involving polytomous skills which is adapted from the empirical example (proportional reasoning data) of Chen and de la Torre (2013).

  List of 2
$ data : num [1:500, 1:15] 1 0 1 1 0 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:15] "I1" "I2" "I3" "I4" ...
$ q.matrix:'data.frame': 15 obs. of 4 variables:
..$ A1: int [1:15] 0 0 0 0 2 0 0 2 1 1 ...
..$ A2: int [1:15] 1 0 2 0 0 1 2 0 1 1 ...
..$ A3: int [1:15] 0 0 0 1 0 0 0 0 0 0 ...
..$ A4: int [1:15] 0 1 1 0 0 0 0 0 0 0 ...
  

• Dataset data.cdm10: This is a simulated dataset involving a hierarchical skill structure. Skill A has four levels, skill B possesses two levels and skill C has three levels.

  List of 2
$ data : num [1:1500, 1:15] 1 1 0 0 0 1 1 0 0 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:15] "I1" "I2" "I3" "I4" ...
$ q.matrix: num [1:15, 1:6] 1 1 1 1 1 1 0 0 0 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:15] "I1" "I2" "I3" "I4" ...
.. ..$ : chr [1:6] "A1" "A2" "A3" "B1" ...
  

References

Chen, H., & Chen, J. (2017). Cognitive diagnostic research on chinese students' English listening skills and implications on skill training. English Language Teaching, 10(12), 107-115. http://dx.doi.org/10.5539/elt.v10n12p107

Chen, J., & de la Torre, J. (2013). A general cognitive diagnosis model for expert-defined polytomous attributes. Applied Psychological Measurement, 37, 419-437. http://dx.doi.org/10.1177/0146621613479818

Chen, Y., Li, X., Liu, J., & Ying, Z. (2017). Regularized latent class analysis with application in cognitive diagnosis. Psychometrika, 82, 660-692. http://dx.doi.org/10.1007/s11336-016-9545-6

Chiu, C.-Y., Koehn, H.-F., & Wu, H.-M. (2016). Fitting the reduced RUM with Mplus: A tutorial. International Journal of Testing, 16(4), 331-351. http://dx.doi.org/10.1080/15305058.2016.1148038

Fang, G., Liu, J., & Ying, Z. (2017). On the identifiability of diagnostic classification models. arXiv, 1706.01240. https://arxiv.org/abs/1706.01240

Heller, J. and Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49-56.
http://dx.doi.org/10.1016/j.endm.2013.05.145

Kuo, B.-C., Chen, C.-H., & de la Torre, J. (2018). A cognitive diagnosis model for identifying coexisting skills and misconceptions. Applied Psychological Measurement, 42(3), 179-191. http://dx.doi.org/10.1177/0146621617722791

Ma, W., & de la Torre, J. (2016). A sequential cognitive diagnosis model for polytomous responses. British Journal of Mathematical and Statistical Psychology, 69(3), 253-275.
https://doi.org/10.1111/bmsp.12070

Philipp, M., Strobl, C., de la Torre, J., & Zeileis, A. (2018). On the estimation of standard errors in cognitive diagnosis models. Journal of Educational and Behavioral Statistics, 43(1), 88-115. http://dx.doi.org/10.3102/1076998617719728

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Reduced RUM model, Chiu et al. (2016)
#############################################################################

data(data.cdm03, package="CDM")
dat <- data.cdm03$data
qmatrix <- data.cdm03$qmatrix

#*** Model 1: Reduced RUM
mod1 <- CDM::gdina( dat, q.matrix=qmatrix[,-1], rule="RRUM" )
summary(mod1)

#*** Model 2: Additive model with identity link function
mod2 <- CDM::gdina( dat, q.matrix=qmatrix[,-1], rule="ACDM" )
summary(mod2)

#*** Model 3: Additive model with logit link function
mod3 <- CDM::gdina( dat, q.matrix=qmatrix[,-1], rule="ACDM", linkfct="logit")
summary(mod3)

#############################################################################
# EXAMPLE 2: GDINA model - probability dataset from the pks package
#############################################################################

data(data.cdm05, package="CDM")
dat <- data.cdm05$data
Q <- data.cdm05$q.matrix

#* estimate model
mod1 <- CDM::gdina( dat, q.matrix=Q )
summary(mod1)

## End(Not run)

Description

Dataset from Chapter 9 of the book 'Diagnostic Measurement' (Rupp, Templin & Henson, 2010).

Usage

data(data.dcm)

Format

The format of the data is a list containing the dichotomous item response data data (10000 persons at 7 items) and the Q-matrix q.matrix (7 items and 3 skills):

List of 2
$ data :'data.frame':
..$ id: int [1:10000] 1 2 3 4 5 6 7 8 9 10 ...
..$ D1: num [1:10000] 0 0 0 0 1 0 1 0 0 1 ...
..$ D2: num [1:10000] 0 0 0 0 0 1 1 1 0 1 ...
..$ D3: num [1:10000] 1 0 1 0 1 1 0 0 0 1 ...
..$ D4: num [1:10000] 0 0 1 0 0 1 1 1 0 0 ...
..$ D5: num [1:10000] 1 0 0 0 1 1 1 0 1 0 ...
..$ D6: num [1:10000] 0 0 0 0 1 1 1 0 0 1 ...
..$ D7: num [1:10000] 0 0 0 0 0 1 1 0 1 1 ...
$ q.matrix: num [1:7, 1:3] 1 0 0 1 1 0 1 0 1 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:7] "D1" "D2" "D3" "D4" ...
.. ..$ : chr [1:3] "skill1" "skill2" "skill3"

Source

For supplementary material of the Rupp, Templin and Henson book (2010) see http://dcm.coe.uga.edu/.

The dataset was downloaded from http://dcm.coe.uga.edu/supplemental/chapter9.html.

References

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Examples

## Not run: 
data(data.dcm, package="CDM")

dat <- data.dcm$data[,-1]
Q <- data.dcm$q.matrix

#*****************************************************
# Model 1: DINA model
#*****************************************************
mod1 <- CDM::din( dat, q.matrix=Q )
summary(mod1)

#--------
# Model 1m: estimate model in mirt package
library(mirt)
library(sirt)

  #** define theta grid of skills
  # use the function skillspace.hierarchy just for convenience
hier <- "skill1 > skill2"
skillspace <- CDM::skillspace.hierarchy( hier, skill.names=colnames(Q) )
Theta <- as.matrix(skillspace$skillspace.complete)
  #** create mirt model
mirtmodel <- mirt::mirt.model("
      skill1=1
      skill2=2
      skill3=3
      (skill1*skill2)=4
      (skill1*skill3)=5
      (skill2*skill3)=6
      (skill1*skill2*skill3)=7
          " )
  #** mirt parameter table
mod.pars <- mirt::mirt( dat, mirtmodel, pars="values")
  # use starting values of .20 for guessing parameter
ind <- which( mod.pars$name=="d" )
mod.pars[ind,"value"] <- stats::qlogis(.20) # guessing parameter on the logit metric
  # use starting values of .80 for anti-slipping parameter
ind <- which( ( mod.pars$name %in% paste0("a",1:20 ) ) & (mod.pars$est) )
mod.pars[ind,"value"] <- stats::qlogis(.80) - stats::qlogis(.20)
mod.pars
  #** prior for the skill space distribution
I <- ncol(dat)
lca_prior <- function(Theta,Etable){
  TP <- nrow(Theta)
  if ( is.null(Etable) ){ prior <- rep( 1/TP, TP ) }
  if ( ! is.null(Etable) ){
    prior <- ( rowSums(Etable[, seq(1,2*I,2)]) + rowSums(Etable[,seq(2,2*I,2)]) )/I
  }
  prior <- prior / sum(prior)
  return(prior)
 }

 #** estimate model in mirt
mod1m <- mirt::mirt(dat, mirtmodel, pars=mod.pars, verbose=TRUE,
            technical=list( customTheta=Theta, customPriorFun=lca_prior) )
  # The number of estimated parameters is incorrect because mirt does not correctly count
  # estimated parameters from the user customized  prior distribution.
mod1m@nest <- as.integer(sum(mod.pars$est) + nrow(Theta) - 1)
  # extract log-likelihood
mod1m@logLik
  # compute AIC and BIC
( AIC <- -2*mod1m@logLik+2*mod1m@nest )
( BIC <- -2*mod1m@logLik+log(mod1m@Data$N)*mod1m@nest )
  #** extract item parameters
cmod1m <- sirt::mirt.wrapper.coef(mod1m)$coef
# compare estimated guessing and slipping parameters
dfr <- data.frame(    "din.guess"=mod1$guess$est,
                  "mirt.guess"=plogis(cmod1m$d), "din.slip"=mod1$slip$est,
                  "mirt.slip"=1-plogis( rowSums( cmod1m[, c("d", paste0("a",1:7) ) ] ) )
                    )
round(t(dfr),3)
  ##               [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]
  ##   din.guess  0.217 0.193 0.189 0.135 0.143 0.135 0.162
  ##   mirt.guess 0.226 0.189 0.184 0.132 0.142 0.132 0.158
  ##   din.slip   0.338 0.331 0.334 0.220 0.222 0.211 0.042
  ##   mirt.slip  0.339 0.333 0.336 0.223 0.225 0.214 0.044

# compare estimated skill class distribution
dfr <- data.frame("din"=mod1$attribute.patt$class.prob,
                    "mirt"=mod1m@Prior[[1]] )
round(t(dfr),3)
  ##         [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]
  ##   din  0.113 0.083 0.094 0.092 0.064 0.059 0.065 0.429
  ##   mirt 0.116 0.074 0.095 0.064 0.095 0.058 0.066 0.433

#** extract estimated classifications
fsc1m <- sirt::mirt.wrapper.fscores( mod1m )
#- estimated reliabilities
fsc1m$EAP.rel
  ##      skill1    skill2    skill3
  ##   0.5479942 0.5362595 0.5357961
#- estimated classfications: EAPs, MLEs and MAPs
head( round(fsc1m$person,3) )
  ##     case     M EAP.skill1 SE.EAP.skill1 EAP.skill2 SE.EAP.skill2 EAP.skill3 SE.EAP.skill3
  ##   1    1 0.286      0.508         0.500      0.067         0.251      0.820         0.384
  ##   2    2 0.000      0.162         0.369      0.191         0.393      0.190         0.392
  ##   3    3 0.286      0.200         0.400      0.211         0.408      0.607         0.489
  ##   4    4 0.000      0.162         0.369      0.191         0.393      0.190         0.392
  ##   5    5 0.571      0.802         0.398      0.267         0.443      0.928         0.258
  ##   6    6 0.857      0.998         0.045      1.000         0.019      1.000         0.020
  ##     MLE.skill1 MLE.skill2 MLE.skill3 MAP.skill1 MAP.skill2 MAP.skill3
  ##   1          1          0          1          1          0          1
  ##   2          0          0          0          0          0          0
  ##   3          0          0          1          0          0          1
  ##   4          0          0          0          0          0          0
  ##   5          1          0          1          1          0          1
  ##   6          1          1          1          1          1          1

#** estimate model fit in mirt
( fit1m <- mirt::M2( mod1m ) )

#*****************************************************
# Model 2: DINO model
#*****************************************************
mod2 <- CDM::din( dat, q.matrix=Q, rule="DINO")
summary(mod2)

#*****************************************************
# Model 3: log-linear model (LCDM): this model is the GDINA model with the
#    logit link function
#*****************************************************
mod3 <- CDM::gdina( dat, q.matrix=Q, link="logit")
summary(mod3)

#*****************************************************
# Model 4: GDINA model with identity link function
#*****************************************************
mod4 <- CDM::gdina( dat, q.matrix=Q )
summary(mod4)

#*****************************************************
# Model 5: GDINA additive model identity link function
#*****************************************************
mod5 <- CDM::gdina( dat, q.matrix=Q, rule="ACDM")
summary(mod5)

#*****************************************************
# Model 6: GDINA additive model logit link function
#*****************************************************
mod6 <- CDM::gdina( dat, q.matrix=Q, link="logit", rule="ACDM")
summary(mod6)

#--------
# Model 6m: GDINA additive model in mirt package
# use data specifications from Model 1m)
  #** create mirt model
mirtmodel <- mirt::mirt.model("
      skill1=1,4,5,7
      skill2=2,4,6,7
      skill3=3,5,6,7
          " )
  #** mirt parameter table
mod.pars <- mirt::mirt( dat, mirtmodel, pars="values")
 #** estimate model in mirt
 # Theta and lca_prior as defined as in Model 1m
mod6m <- mirt::mirt(dat, mirtmodel, pars=mod.pars, verbose=TRUE,
            technical=list( customTheta=Theta, customPriorFun=lca_prior) )
mod6m@nest <- as.integer(sum(mod.pars$est) + nrow(Theta) - 1)
  # extract log-likelihood
mod6m@logLik
  # compute AIC and BIC
( AIC <- -2*mod6m@logLik+2*mod6m@nest )
( BIC <- -2*mod6m@logLik+log(mod6m@Data$N)*mod6m@nest )
  #** skill distribution
  mod6m@Prior[[1]]
  #** extract item parameters
cmod6m <- mirt.wrapper.coef(mod6m)$coef
print(cmod6m,digits=4)
  ##     item    a1    a2    a3       d g u
  ##   1   D1 1.882 0.000 0.000 -0.9330 0 1
  ##   2   D2 0.000 2.049 0.000 -1.0430 0 1
  ##   3   D3 0.000 0.000 2.028 -0.9915 0 1
  ##   4   D4 2.697 2.525 0.000 -2.9925 0 1
  ##   5   D5 2.524 0.000 2.478 -2.7863 0 1
  ##   6   D6 0.000 2.818 2.791 -3.1324 0 1
  ##   7   D7 3.113 2.918 2.785 -4.2794 0 1

#*****************************************************
# Model 7: Reduced RUM model
#*****************************************************
mod7 <- CDM::gdina( dat, q.matrix=Q, rule="RRUM")
summary(mod7)

#*****************************************************
# Model 8: latent class model with 3 classes and 4 sets of starting values
#*****************************************************

#-- Model 8a: randomLCA package
library(randomLCA)
mod8a <- randomLCA::randomLCA( dat, nclass=3, verbose=TRUE, notrials=4)

#-- Model8b: rasch.mirtlc function in sirt package
library(sirt)
mod8b <- sirt::rasch.mirtlc( dat, Nclasses=3, nstarts=4 )
summary(mod8a)
summary(mod8b)

## End(Not run)

Description

This is a simulated dataset of the DTMR fraction data described in Bradshaw, Izsak, Templin and Jacobson (2014).

Usage

data(data.dtmr)

Format

The format is:

List of 5
$ data : num [1:5000, 1:27] 0 0 0 0 0 1 0 0 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:27] "M1" "M2" "M3" "M4" ...
$ q.matrix :'data.frame': 27 obs. of 4 variables:
..$ RU : int [1:27] 1 0 0 1 1 0 1 0 0 0 ...
..$ PI : int [1:27] 0 0 1 0 0 1 0 0 0 0 ...
..$ APP: int [1:27] 0 1 0 0 0 0 0 1 1 1 ...
..$ MC : int [1:27] 0 0 0 0 0 0 0 0 0 0 ...
$ skill.distribution:'data.frame': 16 obs. of 5 variables:
..$ RU : int [1:16] 0 0 0 0 0 0 0 0 1 1 ...
..$ PI : int [1:16] 0 0 0 0 1 1 1 1 0 0 ...
..$ APP : int [1:16] 0 0 1 1 0 0 1 1 0 0 ...
..$ MC : int [1:16] 0 1 0 1 0 1 0 1 0 1 ...
..$ freq: int [1:16] 1064 350 280 406 196 126 238 770 14 28 ...
$ itempars :'data.frame': 27 obs. of 7 variables:
..$ item : chr [1:27] "M1" "M2" "M3" "M4" ...
..$ lam0 : num [1:27] -1.12 0.59 -2.07 -1.19 -1.67 -3.81 -0.73 -0.62 -0.09 0.28 ...
..$ RU : num [1:27] 2.24 0 0 0.65 1.52 0 1.2 0 0 0 ...
..$ PI : num [1:27] 0 0 1.7 0 0 2.08 0 0 0 0 ...
..$ APP : num [1:27] 0 1.27 0 0 0 0 0 4.25 2.16 0.87 ...
..$ MC : num [1:27] 0 0 0 0 0 0 0 0 0 0 ...
..$ RU.PI: num [1:27] 0 0 0 0 0 0 0 0 0 0 ...
$ sim_data :function (N, skill.distribution, itempars)
..- attr(*, "srcref")='srcref' int [1:8] 1 13 20 1 13 1 1 20
.. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x00000000298a8ed0>

The attribute definition are as follows

RU: Referent units

PI: Partitioning and iterating attribute

APP: Appropriateness attribute

MC: Multiplicative Comparison attribute

Source

Simulated dataset according to Bradshaw et al. (2014).

References

Bradshaw, L., Izsak, A., Templin, J., & Jacobson, E. (2014). Diagnosing teachers' understandings of rational numbers: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practice, 33, 2-14.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Model comparisons data.dtmr
#############################################################################

data(data.dtmr, package="CDM")
data <- data.dtmr$data
q.matrix <- data.dtmr$q.matrix
I <- ncol(data)

#*** Model 1: LCDM
# define item wise rules
rule <- rep( "ACDM", I )
names(rule) <- colnames(data)
rule[ c("M14","M17") ] <- "GDINA2"
# estimate model
mod1 <- CDM::gdina( data, q.matrix, linkfct="logit", rule=rule)
summary(mod1)

#*** Model 2: DINA model
mod2 <- CDM::gdina( data, q.matrix, rule="DINA" )
summary(mod2)

#*** Model 3: RRUM model
mod3 <- CDM::gdina( data, q.matrix, rule="RRUM" )
summary(mod3)

#--- model comparisons

# LCDM vs. DINA
anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -76570.89 153141.8    69 153279.8 153729.5 1726.645 10  0
  ##   1 Model 1 -75707.57 151415.1    79 151573.1 152088.0       NA NA NA

# LCDM vs. RRUM
anova(mod1,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -75746.13 151492.3    77 151646.3 152148.1 77.10994  2  0
  ##   1 Model 1 -75707.57 151415.1    79 151573.1 152088.0       NA NA NA

#--- model fit
summary( CDM::modelfit.cor.din( mod1 ) )
  ##   Test of Global Model Fit
  ##          type   value       p
  ##   1   max(X2) 7.74382 1.00000
  ##   2 abs(fcor) 0.04056 0.72707
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.00959
  ##   SRMSR           0.01217
  ##   MX2             0.75696
  ##   100*MADRESIDCOV 0.20283
  ##   MADQ3           0.02220

#############################################################################
# EXAMPLE 2: Simulating data of structure data.dtmr
#############################################################################

data(data.dtmr, package="CDM")

# draw sample of N=200
set.seed(87)
data.dtmr$sim_data(N=200, skill.distribution=data.dtmr$skill.distribution,
             itempars=data.dtmr$itempars)

## End(Not run)

Description

ECPE dataset from the Templin and Hoffman (2013) tutorial of specifying cognitive diagnostic models in Mplus.

Usage

data(data.ecpe)

Format

The format of the data is a list containing the dichotomous item response data data (2922 persons at 28 items) and the Q-matrix q.matrix (28 items and 3 skills):

List of 2
$ data :'data.frame':
..$ id : int [1:2922] 1 2 3 4 5 6 7 8 9 10 ...
..$ E1 : int [1:2922] 1 1 1 1 1 1 1 0 1 1 ...
..$ E2 : int [1:2922] 1 1 1 1 1 1 1 1 1 1 ...
..$ E3 : int [1:2922] 1 1 1 1 1 1 1 1 1 1 ...
..$ E4 : int [1:2922] 0 1 1 1 1 1 1 1 1 1 ...
[...]
..$ E27: int [1:2922] 1 1 1 1 1 1 1 0 1 1 ...
..$ E28: int [1:2922] 1 1 1 1 1 1 1 1 1 1 ...
$ q.matrix:'data.frame':
..$ skill1: int [1:28] 1 0 1 0 0 0 1 0 0 1 ...
..$ skill2: int [1:28] 1 1 0 0 0 0 0 1 0 0 ...
..$ skill3: int [1:28] 0 0 1 1 1 1 1 0 1 0 ...

The skills are

skill1: Morphosyntactic rules

skill2: Cohesive rules

skill3: Lexical rules.

Details

The dataset has been used in Templin and Hoffman (2013), and Templin and Bradshaw (2014).

Source

The dataset was downloaded from http://psych.unl.edu/jtemplin/teaching/dcm/dcm12ncme/.

References

Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79, 317-339.

Templin, J., & Hoffman, L. (2013). Obtaining diagnostic classification model estimates using Mplus. Educational Measurement: Issues and Practice, 32, 37-50.

See Also

GDINA::ecpe

Examples

## Not run: 
data(data.ecpe, package="CDM")

dat <- data.ecpe$data[,-1]
Q <- data.ecpe$q.matrix

#*** Model 1: LCDM model
mod1 <- CDM::gdina( dat, q.matrix=Q, link="logit")
summary(mod1)

#*** Model 2: DINA model
mod2 <- CDM::gdina( dat, q.matrix=Q, rule="DINA")
summary(mod2)

# Model comparison using likelihood ratio test
anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -42841.61 85683.23    63 85809.23 86185.97 206.0359 18  0
  ##   1 Model 1 -42738.60 85477.19    81 85639.19 86123.57       NA NA NA

#*** Model 3: Hierarchical LCDM (HLCDM) | Templin and Bradshaw (2014)
#      Testing a linear hierarchy
hier <- "skill3 > skill2 > skill1"
skill.names <- colnames(Q)
# define skill space with hierarchy
skillspace <- CDM::skillspace.hierarchy( hier, skill.names=skill.names )
skillspace$skillspace.reduced
  ##        skill1 skill2 skill3
  ##   A000      0      0      0
  ##   A001      0      0      1
  ##   A011      0      1      1
  ##   A111      1      1      1
zeroprob.skillclasses <- skillspace$zeroprob.skillclasses

# define user-defined parameters in LCDM: hierarchical LCDM (HLCDM)
Mj.user <- mod1$Mj
# select items with require two attributes
items <- which( rowSums(Q) > 1 )
# modify design matrix for item parameters
for (ii in items){
    m1 <- Mj.user[[ii]]
    Mj.user[[ii]][[1]] <- (m1[[1]])[,-2]
    Mj.user[[ii]][[2]] <- (m1[[2]])[-2]
}

# estimate model
#    note that avoid.zeroprobs is set to TRUE to avoid algorithmic instabilities
mod3 <- CDM::gdina( dat, q.matrix=Q, link="logit",
            zeroprob.skillclasses=zeroprob.skillclasses, Mj=Mj.user,
            avoid.zeroprobs=TRUE )
summary(mod3)

#*****************************************
#** estimate further models

#*** Model 4: RRUM model
mod4 <- CDM::gdina( dat, q.matrix=Q, rule="RRUM")
summary(mod4)
# compare some models
IRT.compareModels(mod1, mod2, mod3, mod4 )

#*** Model 5a: GDINA model with identity link
mod5a <- CDM::gdina( dat, q.matrix=Q, link="identity")
summary(mod5a)
#*** Model 5b: GDINA model with logit link
mod5b <- CDM::gdina( dat, q.matrix=Q, link="logit")
summary(mod5b)
#*** Model 5c: GDINA model with log link
mod5c <- CDM::gdina( dat, q.matrix=Q, link="log")
summary(mod5c)
# compare models
IRT.compareModels(mod5a, mod5b, mod5c)

## End(Not run)

Description

Contains different sub-datasets of the fraction subtraction data of Tatsuoka with different Q-matrix specifications.

Usage

data(data.fraction1)
data(data.fraction2)
data(data.fraction3)
data(data.fraction4)
data(data.fraction5)

Format

• The dataset data.fraction1 is the fraction subtraction data set with 536 students and 15 items. The Q-matrix was defined in de la Torre (2009). This dataset is a list with the dataset (data) and the Q-matrix as entries.

  The format is:

  List of 2
$ data :'data.frame':
..$ T01: int [1:536] 0 1 1 1 0 0 0 0 0 0 ...
..$ T02: int [1:536] 1 1 1 1 1 0 0 1 0 0 ...
..$ T03: int [1:536] 0 1 1 1 1 1 0 0 0 0 ...
..$ T04: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ T05: int [1:536] 0 1 0 0 0 1 1 0 1 1 ...
..$ T06: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ T07: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ T08: int [1:536] 1 1 0 1 1 0 0 0 1 1 ...
..$ T09: int [1:536] 1 1 1 1 0 1 0 0 1 0 ...
..$ T10: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ T11: int [1:536] 1 1 1 1 0 0 0 0 0 0 ...
..$ T12: int [1:536] 0 1 0 0 0 0 0 0 0 0 ...
..$ T13: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ T14: int [1:536] 1 1 0 0 0 0 0 0 0 0 ...
..$ T15: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
$ q.matrix: int [1:15, 1:5] 1 1 1 1 0 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:15] "T01" "T02" "T03" "T04" ...
.. ..$ : chr [1:5] "QT1" "QT2" "QT3" "QT4" ...
  

• The dataset data.fraction2 is the fraction subtraction data set with 536 students and 11 items. For this data set, several $Q$ matrices are available. The data is a list. The first entry data contains the data frame. The entry q.matrix1 contains the Q-matrix of Henson, Templin and Willse (2009). The third entry q.matrix2 is an alternative Q-matrix of de la Torre (2009). The fourth entry is a modified Q-matrix of q.matrix1.

  The format is:

  $ data :'data.frame':
..$ H01: int [1:536] 1 1 1 1 1 0 0 1 0 0 ...
..$ H02: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ H03: int [1:536] 0 1 0 0 0 1 1 0 1 1 ...
..$ H04: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ H05: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ H06: int [1:536] 1 1 0 1 1 0 0 0 1 1 ...
..$ H08: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ H09: int [1:536] 1 1 1 1 0 0 0 0 0 0 ...
..$ H10: int [1:536] 0 1 0 0 0 0 0 0 0 0 ...
..$ H11: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ H13: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
$ q.matrix1: int [1:11, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:11] "H01" "H02" "H03" "H04" ...
.. ..$ : chr [1:3] "QH1" "QH2" "QH3"
$ q.matrix2: int [1:11, 1:5] 1 1 0 1 1 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:11] "H01" "H02" "H03" "H04" ...
.. ..$ : chr [1:5] "QT1" "QT2" "QT3" "QT4" ...
$ q.matrix3: num [1:11, 1:3] 0 0 0 1 0 0 0 0 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:11] "H01" "H02" "H03" "H04" ...
.. ..$ : chr [1:3] "Dim1" "Dim2" "Dim3"
  

• The dataset data.fraction3 contains 12 items and was used in de la Torre (2011).

  List of 2
$ data :'data.frame': 536 obs. of 12 variables:
..$ B01: int [1:536] 0 1 1 1 0 0 0 0 0 0 ...
..$ B02: int [1:536] 1 1 1 1 1 0 0 1 0 0 ...
..$ B03: int [1:536] 0 1 1 1 1 1 0 0 0 0 ...
..$ B04: int [1:536] 0 1 0 0 0 1 1 0 1 1 ...
..$ B05: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ B06: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ B07: int [1:536] 1 1 0 1 1 0 0 0 1 1 ...
..$ B08: int [1:536] 1 1 1 1 0 1 0 0 1 0 ...
..$ B09: int [1:536] 1 1 1 1 0 0 0 0 0 0 ...
..$ B10: int [1:536] 0 1 0 0 0 0 0 0 0 0 ...
..$ B11: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ B12: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
$ q.matrix:'data.frame': 12 obs. of 5 variables:
..$ item: Factor w/ 13 levels "","B01","B02",..: 2 3 4 5 6 7 8 9 10 11 ...
..$ QA1 : int [1:12] 1 1 1 1 1 1 1 1 1 1 ...
..$ QA2 : int [1:12] 0 1 0 0 1 1 1 0 0 0 ...
..$ QA3 : int [1:12] 0 1 0 1 1 1 0 1 1 1 ...
..$ QA4 : int [1:12] 0 1 0 0 1 1 0 0 0 1 ...
  

• The dataset data.fraction4 contains 17 items and was used in de la Torre and Douglas (2004) and Chen, Liu, Xu and Ying (2015).

  List of 2
$ data :'data.frame': 536 obs. of 17 variables:
..$ A01: int [1:536] 0 0 0 1 0 0 0 0 0 0 ...
..$ A02: int [1:536] 0 1 1 1 0 0 0 0 0 0 ...
..$ A03: int [1:536] 0 1 1 1 0 0 0 0 0 0 ...
..$ A04: int [1:536] 1 1 1 1 1 0 0 1 0 0 ...
..$ A05: int [1:536] 1 1 0 1 1 0 0 0 1 1 ...
..$ A06: int [1:536] 1 1 1 1 0 1 0 0 1 0 ...
..$ A07: int [1:536] 1 1 1 1 0 0 0 0 0 0 ...
..$ A08: int [1:536] 0 0 0 1 0 0 0 0 0 1 ...
..$ A09: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ A10: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ A11: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ A12: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ A13: int [1:536] 0 1 0 0 0 0 0 0 0 0 ...
..$ A14: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ A15: int [1:536] 1 1 0 0 0 0 0 0 0 0 ...
..$ A16: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ A17: int [1:536] 0 1 0 0 0 0 0 0 0 0 ...
$ q.matrix:'data.frame': 17 obs. of 9 variables:
..$ item: Factor w/ 18 levels "","A01","A02",..: 2 3 4 5 6 7 8 9 10 11 ...
..$ QA1 : int [1:17] 0 0 0 0 0 0 0 0 1 0 ...
..$ QA2 : int [1:17] 0 0 0 1 0 1 1 1 1 1 ...
..$ QA3 : int [1:17] 0 0 0 1 0 0 0 0 0 0 ...
..$ QA4 : int [1:17] 1 1 1 0 0 0 0 1 0 0 ...
..$ QA5 : int [1:17] 0 0 0 1 0 0 1 0 0 1 ...
..$ QA6 : int [1:17] 1 0 0 0 0 0 1 0 0 0 ...
..$ QA7 : int [1:17] 1 1 1 1 1 1 1 1 1 1 ...
..$ QA8 : int [1:17] 0 0 0 0 1 0 0 1 0 0 ...
  

• The dataset data.fraction5 contains 15 items and was used as an example for the multiple strategy DINA model in de la Torre and Douglas (2008) and Hou and de la Torre (2014). The two Q-matrices for coding the multiple strategies are contained in one matrix q.matrix by joining the columns of both matrices.

  List of 2
$ data :'data.frame': 536 obs. of 15 variables:
..$ T01: int [1:536] 0 1 1 1 0 0 0 0 0 0 ...
..$ T02: int [1:536] 1 1 1 1 1 0 0 1 0 0 ...
..$ T03: int [1:536] 0 1 1 1 1 1 0 0 0 0 ...
..$ T04: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ T05: int [1:536] 0 1 0 0 0 1 1 0 1 1 ...
..$ T06: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ T07: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ T08: int [1:536] 1 1 0 1 1 0 0 0 1 1 ...
..$ T09: int [1:536] 1 1 1 1 0 1 0 0 1 0 ...
..$ T10: int [1:536] 1 1 1 0 0 0 0 0 0 0 ...
..$ T11: int [1:536] 1 1 1 1 0 0 0 0 0 0 ...
..$ T12: int [1:536] 0 1 0 0 0 0 0 0 0 0 ...
..$ T13: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
..$ T14: int [1:536] 1 1 0 0 0 0 0 0 0 0 ...
..$ T15: int [1:536] 1 1 0 1 0 0 0 0 0 0 ...
$ q.matrix:'data.frame': 15 obs. of 15 variables:
..$ item: Factor w/ 16 levels "","T01","T02",..: 2 3 4 5 6 7 8 9 10 11 ...
..$ SA1 : int [1:15] 0 1 1 1 0 1 1 1 1 1 ...
..$ SA2 : int [1:15] 0 1 0 1 0 1 1 1 0 0 ...
..$ SA3 : int [1:15] 0 1 0 1 1 1 1 0 1 1 ...
..$ SA4 : int [1:15] 0 1 0 1 0 1 1 0 0 1 ...
..$ SA5 : int [1:15] 0 0 0 1 0 0 0 0 0 1 ...
..$ SA6 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ...
..$ SA7 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ...
..$ SB1 : int [1:15] 0 1 1 1 0 1 1 1 1 1 ...
..$ SB2 : int [1:15] 0 0 0 0 1 1 1 1 0 1 ...
..$ SB3 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ...
..$ SB4 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ...
..$ SB5 : int [1:15] 0 0 0 1 1 0 0 0 0 1 ...
..$ SB6 : int [1:15] 0 1 0 1 1 1 1 0 1 0 ...
..$ SB7 : int [1:15] 0 0 0 0 1 0 0 0 0 0 ...
  

Source

See fraction.subtraction.data for more information about the data source.

References

Chen, Y., Liu, J., Xu, G. and Ying, Z. (2015). Statistical analysis of Q-matrix based diagnostic classification models. Journal of the American Statistical Association, 110(510), 850-866.

de la Torre, J. (2009). DINA model parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.

de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.

de la Torre, J., & Douglas, J. A. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333-353.

de la Torre, J., & Douglas, J. A. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595-624.

Henson, R. A., Templin, J. T., & Willse, J. T. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74, 191-210.

Huo, Y., & de la Torre, J. (2014). Estimating a cognitive diagnostic model for multiple strategies via the EM algorithm. Applied Psychological Measurement, 38, 464-485.

See Also

GDINA::frac20

Description

Dataset data.hr used for illustrating some functionalities of the CDM package (Ravand, Barati, & Widhiarso, 2013).

Usage

data(data.hr)

Format

The format of the dataset is:

List of 2
$ data : num [1:1550, 1:35] 1 0 1 1 1 0 1 1 1 0 ...
$ q.matrix:'data.frame':
..$ Skill1: int [1:35] 0 0 0 0 0 0 1 0 0 0 ...
..$ Skill2: int [1:35] 0 0 0 0 1 0 0 0 0 0 ...
..$ Skill3: int [1:35] 0 1 1 1 1 0 0 1 0 0 ...
..$ Skill4: int [1:35] 1 0 0 0 0 0 0 0 1 1 ...
..$ Skill5: int [1:35] 0 0 0 0 0 1 0 0 1 1 ...

Source

Simulated data according to Ravand et al. (2013).

References

Ravand, H., Barati, H., & Widhiarso, W. (2013). Exploring diagnostic capacity of a high stakes reading comprehension test: A pedagogical demonstration. Iranian Journal of Language Testing, 3(1), 1-27.

Examples

## Not run: 
data(data.hr, package="CDM")

dat <- data.hr$data
Q <- data.hr$q.matrix

#*************
# Model 1: DINA model
mod1 <- CDM::din( dat, q.matrix=Q )
summary(mod1)       # summary

# plot results
plot(mod1)

# inspect coefficients
coef(mod1)

# posterior distribution
posterior <- mod1$posterior
round( posterior[ 1:5, ], 4 )  # first 5 entries

# estimate class probabilities
mod1$attribute.patt

# individual classifications
mod1$pattern[1:5,]   # first 5 entries

#*************
# Model 2: GDINA model
mod2 <- CDM::gdina( dat, q.matrix=Q)
summary(mod2)

#*************
# Model 3: Reduced RUM model
mod3 <- CDM::gdina( dat, q.matrix=Q, rule="RRUM" )
summary(mod3)

#--------
# model comparisons

# DINA vs GDINA
anova( mod1, mod2 )
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   1 Model 1 -31391.27 62782.54   101 62984.54 63524.49 195.9099 20  0
  ##   2 Model 2 -31293.32 62586.63   121 62828.63 63475.50       NA NA NA

# RRUM vs. GDINA
anova( mod2, mod3 )
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -31356.22 62712.43   105 62922.43 63483.76 125.7924 16  0
  ##   1 Model 1 -31293.32 62586.64   121 62828.64 63475.50       NA NA NA

# DINA vs. RRUM
anova(mod1,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   1 Model 1 -31391.27 62782.54   101 62984.54 63524.49 70.11246  4  0
  ##   2 Model 2 -31356.22 62712.43   105 62922.43 63483.76       NA NA NA

#-------
# model fit

# DINA
fmod1 <- CDM::modelfit.cor.din( mod1, jkunits=0)
summary(fmod1)
  ##   Test of Global Model Fit
  ##          type    value       p
  ##   1   max(X2) 16.35495 0.03125
  ##   2 abs(fcor)  0.10341 0.01416
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01911
  ##   SRMSR           0.02445
  ##   MX2             0.93157
  ##   100*MADRESIDCOV 0.39100
  ##   MADQ3           0.02373

# GDINA
fmod2 <- CDM::modelfit.cor.din( mod2, jkunits=0)
summary(fmod2)
  ##   Test of Global Model Fit
  ##          type   value p
  ##   1   max(X2) 7.73670 1
  ##   2 abs(fcor) 0.07215 1
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01830
  ##   SRMSR           0.02300
  ##   MX2             0.82584
  ##   100*MADRESIDCOV 0.37390
  ##   MADQ3           0.02383

# RRUM
fmod3 <- CDM::modelfit.cor.din( mod3, jkunits=0)
summary(fmod3)
  ##   Test of Global Model Fit
  ##          type    value       p
  ##   1   max(X2) 15.49369 0.04925
  ##   2 abs(fcor)  0.10076 0.02201
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01868
  ##   SRMSR           0.02374
  ##   MX2             0.87999
  ##   100*MADRESIDCOV 0.38409
  ##   MADQ3           0.02416

## End(Not run)

Description

Simulated dataset according to the Jang (2005) L2 reading comprehension study.

Usage

data(data.jang)

Format

The format is:

List of 2
$ data : num [1:1500, 1:37] 1 1 1 1 1 1 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:37] "I1" "I2" "I3" "I4" ...
$ q.matrix:'data.frame':
..$ CDV: int [1:37] 1 0 0 1 0 0 0 0 0 0 ...
..$ CIV: int [1:37] 0 0 1 0 0 0 1 0 1 1 ...
..$ SSL: int [1:37] 1 1 1 1 0 0 0 0 0 0 ...
..$ TEI: int [1:37] 0 0 0 0 0 0 0 1 0 0 ...
..$ TIM: int [1:37] 0 0 0 1 1 1 0 0 0 0 ...
..$ INF: int [1:37] 0 1 0 0 0 0 1 0 0 0 ...
..$ NEG: int [1:37] 0 0 0 0 1 0 1 0 0 0 ...
..$ SUM: int [1:37] 0 0 0 0 1 0 0 0 0 0 ...
..$ MCF: int [1:37] 0 0 0 0 0 0 0 0 0 0 ...

Source

Simulated dataset.

References

Jang, E. E. (2009). Cognitive diagnostic assessment of L2 reading comprehension ability: Validity arguments for Fusion Model application to LanguEdge assessment. Language Testing, 26, 31-73.

Examples

## Not run: 
data(data.jang, package="CDM")

data <- data.jang$data
q.matrix <- data.jang$q.matrix

#*** Model 1: Reduced RUM model
mod1 <- CDM::gdina( data, q.matrix, rule="RRUM", conv.crit=.001, increment.factor=1.025 )
summary(mod1)

#*** Model 2: Additive model (identity link)
mod2 <- CDM::gdina( data, q.matrix, rule="ACDM", conv.crit=.001, linkfct="identity" )
summary(mod2)

#*** Model 3: DINA model
mod3 <- CDM::gdina( data, q.matrix, rule="DINA", conv.crit=.001 )
summary(mod3)

anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   1 Model 1 -30315.03 60630.06   153 60936.06 61748.98 88.29627  0  0
  ##   2 Model 2 -30270.88 60541.76   153 60847.76 61660.68       NA NA NA
anova(mod1,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -30373.99 60747.97   129 61005.97 61691.38 117.9128 24  0
  ##   1 Model 1 -30315.03 60630.06   153 60936.06 61748.98       NA NA NA

# RRUM
summary( CDM::modelfit.cor.din( mod1, jkunits=0) )
  ##          type    value       p
  ##   1   max(X2) 11.79073 0.39645
  ##   2 abs(fcor)  0.09541 0.07422
  ##                       est
  ##   MADcor          0.01834
  ##   SRMSR           0.02300
  ##   MX2             0.86718
  ##   100*MADRESIDCOV 0.38690
  ##   MADQ3           0.02413

# additive model (identity)
summary( CDM::modelfit.cor.din( mod2, jkunits=0) )
  ##          type   value       p
  ##   1   max(X2) 9.78958 1.00000
  ##   2 abs(fcor) 0.08770 0.22993
  ##                       est
  ##   MADcor          0.01721
  ##   SRMSR           0.02158
  ##   MX2             0.69163
  ##   100*MADRESIDCOV 0.36343
  ##   MADQ3           0.02423

# DINA model
summary( CDM::modelfit.cor.din( mod3, jkunits=0) )
  ##          type    value       p
  ##   1   max(X2) 13.48449 0.16020
  ##   2 abs(fcor)  0.10651 0.01256
  ##                       est
  ##   MADcor          0.01999
  ##   SRMSR           0.02495
  ##   MX2             0.92820
  ##   100*MADRESIDCOV 0.42226
  ##   MADQ3           0.02258

## End(Not run)

Description

This is a simulated dataset according to the MELAB reading study (Li, 2011; Li & Suen, 2013). Li (2011) investigated the Fusion model (RUM model) for calibrating this dataset. The dataset in this package is simulated assuming the reduced RUM model (RRUM).

Usage

data(data.melab)

Format

The format of the dataset is:

List of 3
$ data : num [1:2019, 1:20] 0 1 0 1 1 0 0 0 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:20] "I1" "I2" "I3" "I4" ...
$ q.matrix :'data.frame':
..$ skill1: int [1:20] 1 1 0 0 1 1 0 1 0 1 ...
..$ skill2: int [1:20] 0 0 0 0 0 0 0 0 0 0 ...
..$ skill3: int [1:20] 0 0 0 1 0 1 1 0 1 0 ...
..$ skill4: int [1:20] 1 0 1 0 1 0 0 1 0 1 ...
$ skill.labels:'data.frame':
..$ skill : Factor w/ 4 levels "skill1","skill2",..: 1 2 3 4
..$ skill.label: Factor w/ 4 levels "connecting and synthesizing",..: 4 3 2 1

Source

Simulated data according to Li (2011).

References

Li, H. (2011). A cognitive diagnostic analysis of the MELAB reading test. Spaan Fellow, 9, 17-46.

Li, H., & Suen, H. K. (2013). Constructing and validating a Q-matrix for cognitive diagnostic analyses of a reading test. Educational Assessment, 18, 1-25.

Examples

## Not run: 
data(data.melab, package="CDM")

data <- data.melab$data
q.matrix <- data.melab$q.matrix

#*** Model 1: Reduced RUM model
mod1 <- CDM::gdina( data, q.matrix, rule="RRUM" )
summary(mod1)

#*** Model 2: GDINA model
mod2 <- CDM::gdina( data, q.matrix, rule="GDINA" )
summary(mod2)

#*** Model 3: DINA model
mod3 <- CDM::gdina( data, q.matrix, rule="DINA" )
summary(mod3)

#*** Model 4: 2PL model
mod4 <- CDM::gdm( data, theta.k=seq(-6,6,len=21), center )
summary(mod4)

#----
# Model comparisons

#*** RRUM vs. GDINA
anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
  ##   1 Model 1 -20252.74 40505.48    69 40643.48 41030.60 30.88801 18 0.02966
  ##   2 Model 2 -20237.30 40474.59    87 40648.59 41136.69       NA NA      NA

  ##  -> GDINA is not superior to RRUM (according to AIC and BIC)

#*** DINA vs. RRUM
anova(mod1,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -20332.52 40665.04    55 40775.04 41083.61 159.5566 14  0
  ##   1 Model 1 -20252.74 40505.48    69 40643.48 41030.60       NA NA NA

  ##  -> RRUM fits the data significantly better than the DINA model

#*** RRUM vs. 2PL (use only AIC and BIC for comparison)
anova(mod1,mod4)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -20390.19 40780.38    43 40866.38 41107.62 274.8962 26  0
  ##   1 Model 1 -20252.74 40505.48    69 40643.48 41030.60       NA NA NA

  ## -> RRUM fits the data better than 2PL

#----
# Model fit statistics

# RRUM
fmod1 <- CDM::modelfit.cor.din( mod1, jkunits=0)
summary(fmod1)
  ##   Test of Global Model Fit
  ##          type    value       p
  ##   1   max(X2) 10.10408 0.28109
  ##   2 abs(fcor)  0.06726 0.24023
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01708
  ##   SRMSR           0.02158
  ##   MX2             0.96590
  ##   100*MADRESIDCOV 0.27269
  ##   MADQ3           0.02781

  ##  -> not a significant misfit of the RRUM model

# GDINA
fmod2 <- CDM::modelfit.cor.din( mod2, jkunits=0)
summary(fmod2)
  ##   Test of Global Model Fit
  ##          type    value       p
  ##   1   max(X2) 10.40294 0.23905
  ##   2 abs(fcor)  0.06817 0.20964
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01703
  ##   SRMSR           0.02151
  ##   MX2             0.94468
  ##   100*MADRESIDCOV 0.27105
  ##   MADQ3           0.02713

## End(Not run)

Description

Large-scale dataset with multiple groups, survey weights and 11 polytomous items.

Usage

data(data.mg)

Format

A data frame with 38243 observations on the following 14 variables.

idstud

Student identifier

group

Group identifier

weight

Survey weight

I1

Item 1

I2

Item 2

I3

Item 3

I4

Item 4

I5

Item 5

I6

Item 6

I7

Item 7

I8

Item 8

I9

Item 9

I10

Item 10

I11

Item 11

Source

Subsample of a large-scale dataset of 11 survey questions.

Examples

## Not run: 
library(psych)
data(dat.mg, package="CDM")
psych::describe( data.mg )
  ##   > psych::describe(data.mg)
  ##          var     n       mean       sd     median    trimmed      mad        min        max
  ##   idstud   1 38243 1039653.91 19309.80 1037899.00 1039927.73 30240.59 1007168.00 1069949.00
  ##   group    2 38243       8.06     4.07       7.00       8.06     5.93       2.00      14.00
  ##   weight   3 38243      28.76    19.25      31.88      27.92    19.12       0.79     191.89
  ##   I1       4 37665       0.88     0.32       1.00       0.98     0.00       0.00       1.00
  ##   I2       5 37639       0.93     0.25       1.00       1.00     0.00       0.00       1.00
  ##   I3       6 37473       0.76     0.43       1.00       0.83     0.00       0.00       1.00
  ##   I4       7 37687       1.88     0.39       2.00       2.00     0.00       0.00       2.00
  ##   I5       8 37638       1.36     0.75       2.00       1.44     0.00       0.00       2.00
  ##   I6       9 37587       1.05     0.82       1.00       1.06     1.48       0.00       2.00
  ##   I7      10 37576       1.55     0.85       2.00       1.57     1.48       0.00       3.00
  ##   I8      11 37044       0.45     0.50       0.00       0.44     0.00       0.00       1.00
  ##   I9      12 37249       0.48     0.50       0.00       0.47     0.00       0.00       1.00
  ##   I10     13 37318       0.63     0.48       1.00       0.66     0.00       0.00       1.00
  ##   I11     14 37412       1.35     0.80       1.00       1.35     1.48       0.00       3.00

## End(Not run)

Description

Dataset for the estimation of the polytomous GDINA model.

Usage

data(data.pgdina)

Format

The dataset is a list with the item response data and the Q-matrix. The format is:

List of 2
$ dat : num [1:1000, 1:30] 1 1 1 1 1 0 1 1 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:30] "I1" "I2" "I3" "I4" ...
$ q.matrix: num [1:30, 1:5] 1 0 0 0 0 1 0 0 0 2 ...

Details

The dataset was simulated by the following R code:

set.seed(89)
# define Q-matrix
Qmatrix <- matrix(c(1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,
1,1,2,0,0,0,0,1,2,0,0,0,0,1,2,0,0,0,0,1,1,2,0,0,0,1,2,2,0,1,0,2,
1,0,0,1,1,0,2,2,0,0,2,1,0,1,0,0,2,2,1,2,0,0,0,0,0,2,0,0,0,0,0,2,
0,0,0,0,0,2,0,0,0,0,0,1,2,0,2,0,0,0,2,0,2,0,0,0,2,0,1,2,0,0,2,0,
0,2,0,0,1,1,0,0,1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1),
nrow=30, ncol=5, byrow=TRUE )
# define covariance matrix between attributes
Sigma <- matrix(c(1,.6,.6,.3,.3,.6,1,.6,.3,.3,.6,.6,1,
.3,.3,.3,.3,.3,1,.8,.3,.3,.3,.8,1), 5,5, byrow=TRUE )
# define thresholds for attributes
q1 <- c( -.5, .9 ) # attributes 1,...,4
q2 <- c(0) # attribute 5
# number of persons
N <- 1000
# simulate latent attributes
alpha1 <- mvrnorm(n=N, mu=rep(0,5), Sigma=Sigma)
alpha <- 0*alpha1
for (aa in 1:4){
alpha[ alpha1[,aa] > q1[1], aa ] <- 1
alpha[ alpha1[,aa] > q1[2], aa ] <- 2
}
aa <- 5 ; alpha[ alpha1[,aa] > q2[1], aa ] <- 1
# define item parameters
guess <- c(.07,.01,.34,.07,.11,.23,.27,.07,.08,.34,.19,.19,.25,.04,.34,
.03,.29,.05,.01,.17,.15,.35,.19,.16,.08,.18,.19,.07,.17,.34)
slip <- c(0,.11,.14,.09,.03,.09,.03,.1,.14,.07,.06,.19,.09,.19,.07,.08,
.16,.18,.16,.02,.11,.12,.16,.14,.18,.01,.18,.14,.05,.18)
# simulate item responses
I <- 30 # number of items
dat <- latresp <- matrix( 0, N, I, byrow=TRUE)
for (ii in 1:I){
# ii <- 2
# latent response matrix
latresp[,ii] <- 1*( rowMeans( alpha >=matrix( Qmatrix[ ii, ], nrow=N,
ncol=5, byrow=TRUE ) )==1 )
# response probability
prob <- ifelse( latresp[,ii]==1, 1-slip[ii], guess[ii] )
# simulate item responses
dat[,ii] <- 1 * ( runif(N ) < prob )
}
colnames(dat) <- paste0("I",1:I)

References

Chen, J., & de la Torre, J. (2013). A general cognitive diagnosis model for expert-defined polytomous attributes. Applied Psychological Measurement, 37, 419-437.

Description

This is a sub-dataset of the PISA 2000 of German students including 26 items of the reading test. The 26 items was analyzed in Chen and de la Torre (2014) and a subset of 20 items was analyzed in Chen and Chen (2016).

Usage

data(data.pisa00R.ct)
data(data.pisa00R.cc)

Format

• The format of the dataset data.pisa00R.ct (Chen & de la Torre, 2014) is:

  List of 3
$ data :'data.frame': 1095 obs. of 111 variables:
.. [list output truncated]
$ q.matrix: num [1:26, 1:8] 0 1 0 0 0 1 0 0 0 1 ...
..- attr(*, "dimnames")=List of 2
$ skills : chr [1:8] "Locating information" ...
  

• The format of the dataset data.pisa00R.cc (Q-matrix in Chen and Chen, 2016)

  List of 2
$ q.matrix:'data.frame': 20 obs. of 5 variables:
..$ A1: num [1:20] 1 1 0 0 1 1 1 0 0 0 ...
..$ A2: num [1:20] 0 0 0 1 0 1 1 1 1 1 ...
..$ A3: num [1:20] 1 1 0 1 1 0 1 0 1 0 ...
..$ A4: num [1:20] 0 1 1 1 0 0 0 0 0 0 ...
..$ A5: num [1:20] 0 0 1 0 0 0 0 1 0 1 ...
$ skills : Named chr [1:5] "Identifying Explicit Information" ...
..- attr(*, "names")=chr [1:5] "A1" "A2" "A3" "A4" ...
  

References

Chen, H., & Chen, J. (2016). Exploring reading comprehension skill relationships through the G-DINA model. Educational Psychology, 36(6), 1049-1064.

Chen, J., & de la Torre, J. (2014). A procedure for diagnostically modeling extant large-scale assessment data: the case of the programme for international student assessment in reading. Psychology, 5(18), 1967-1978.

Examples

#############################################################################
# EXAMPLE 1: PISA items from Chen and de la Torre (2014)
#            dichotomize item responses
#############################################################################

data(data.pisa00R.ct, package="CDM")
dat <- data.pisa00R.ct$data
Q <- data.pisa00R.ct$q.matrix
resp <- dat[, rownames(Q)]

#** extract item-wise maximum
maxK <- apply( resp, 2, max, na.rm=TRUE )
#** dichotomize response data
resp1 <- resp
for (ii in seq(1,ncol(resp)) ){
    resp1[,ii] <- 1 * ( resp[,ii]==maxK[ii] )
}

Description

This is a simulated dataset of the SDA6 study according to informations given in Jurich and Bradshaw (2014).

Usage

data(data.sda6)

Format

The datasets contains 17 items observed at 1710 students.

The format is:

List of 2
$ data : num [1:1710, 1:17] 0 1 0 1 0 0 0 0 1 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:17] "MCM01" "MCM03" "MCM13" "MCM17" ...
$ q.matrix:'data.frame':
..$ CM: int [1:17] 1 1 1 1 0 0 0 0 0 0 ...
..$ II: int [1:17] 0 0 0 0 1 1 1 1 0 0 ...
..$ PP: int [1:17] 0 0 0 0 0 0 0 0 1 1 ...
..$ DG: int [1:17] 0 0 0 0 0 0 0 0 0 0 ...

The meaning of the skills is

CM – Critique Methods

II – Identify Improvements

PP – Protect Participants

DG – Discern Generalizability

Source

Simulated data

References

Jurich, D. P., & Bradshaw, L. P. (2014). An illustration of diagnostic classification modeling in student learning outcomes assessment. International Journal of Testing, 14, 49-72.

Examples

## Not run: 
data(data.sda6, package="CDM")

data <- data.sda6$data
q.matrix <- data.sda6$q.matrix

#*** Model 1a: LCDM with gdina
mod1a <- CDM::gdina( data, q.matrix, rule="ACDM", linkfct="logit",
                  reduced.skillspace=FALSE )
summary(mod1a)

#*** Model 1b: estimate LCDM with gdm
mod1b <- CDM::gdm( data, q.matrix=q.matrix, theta.k=c(0,1) )
summary(mod1b)

#*** Model 2: LCDM with hierarchy II > CM
B <- "II > CM"
ss2 <- CDM::skillspace.hierarchy(B=B, skill.names=colnames(q.matrix ) )
mod2 <- CDM::gdina( data, q.matrix, rule="ACDM", linkfct="logit",
                skillclasses=ss2$skillspace.reduced,
                reduced.skillspace=FALSE )
summary(mod2)

#*** Model 3: LCDM with hierarchy II > CM and DG > CM
B <- "II > CM
      DG > CM"
ss2 <- CDM::skillspace.hierarchy(B=B, skill.names=colnames(q.matrix ) )
mod3 <- CDM::gdina( data, q.matrix, rule="ACDM", linkfct="logit",
               skillclasses=ss2$skillspace.reduced,
               reduced.skillspace=FALSE )
summary(mod3)

# model comparisons
anova(mod1a,mod2)
anova(mod1a,mod3)
# model fit
summary( CDM::modelfit.cor.din(mod1a))
summary( CDM::modelfit.cor.din(mod2) )
summary( CDM::modelfit.cor.din(mod3) )

## End(Not run)

Description

This dataset contains item responses of students at a scale of cultural activities (act), mathematics self concept (sc) and mathematics joyment (mj).

Usage

data(data.Students)

Format

A data frame with 2400 observations on the following 15 variables.

urban

Urbanization level: 1=town, 0=otherwise

female

A dummy variable for female student

act1

Visit a museum (0=never, 1=once or twice a year, 2=more than twice a year)

act2

Visit a theater or classical concert (0,1,2)

act3

Visit a rock or pop concert (0,1,2)

act4

Visit a cinema (0,1,2)

act5

Visit a public library (0,1,2)

sc1

Item 1 self concept "I am usually good at math." (0=do not agree at all, 1=rather do not agree, 2=rather agree, 3=completely agree)

sc2

Item 2 self concept: "Mathematics is harder for me than many of my classmates." (0,1,2,3) (reversed)

sc3

Item 3 self concept: "I am just not good at math." (0,1,2,3) (reversed)

sc4

Item 4 self concept: "I'm learning fast in math." (0,1,2,3)

mj1

Item 1 mathematics joyment: "I would like more math at school." (0,1,2,3)

mj2

Item 2 mathematics joyment: "I like to learn mathematics." (0,1,2,3)

mj3

Item 3 mathematics joyment: "Math is boring." (0,1,2,3) (reversed)

mj4

Item 4 mathematics joyment: "I like math." (0,1,2,3)

Source

Subsample of students from an Austrian survey of 8th grade students.

Examples

## Not run: 
library(psych)
data(data.Students, package="CDM")
psych::describe(data.Students)
  ##          var    n mean   sd median trimmed  mad min max range  skew kurtosis   se
  ##   urban    1 2400 0.31 0.46    0.0    0.27 0.00   0   1     1  0.81    -1.34 0.01
  ##   female   2 2400 0.51 0.50    1.0    0.51 0.00   0   1     1 -0.03    -2.00 0.01
  ##   act1     3 2248 0.65 0.73    0.5    0.56 0.74   0   2     2  0.64    -0.88 0.02
  ##   act2     4 2230 0.47 0.69    0.0    0.34 0.00   0   2     2  1.13    -0.06 0.01
  ##   act3     5 2218 0.33 0.60    0.0    0.21 0.00   0   2     2  1.62     1.48 0.01
  ##   act4     6 2342 1.35 0.76    2.0    1.44 0.00   0   2     2 -0.69    -0.96 0.02
  ##   act5     7 2223 0.52 0.74    0.0    0.40 0.00   0   2     2  1.05    -0.41 0.02
  ##   sc1      8 2352 0.96 0.80    1.0    0.91 1.48   0   3     3  0.45    -0.39 0.02
  ##   sc2      9 2347 0.90 0.88    1.0    0.81 1.48   0   3     3  0.66    -0.41 0.02
  ##   sc3     10 2335 0.86 0.96    1.0    0.73 1.48   0   3     3  0.84    -0.35 0.02
  ##   sc4     11 2337 1.29 0.90    1.0    1.24 1.48   0   3     3  0.24    -0.71 0.02
  ##   mj1     12 2351 2.26 0.82    2.0    2.37 1.48   0   3     3 -0.94     0.28 0.02
  ##   mj2     13 2345 1.89 0.91    2.0    1.95 1.48   0   3     3 -0.35    -0.80 0.02
  ##   mj3     14 2334 1.47 1.02    1.0    1.47 1.48   0   3     3  0.10    -1.11 0.02
  ##   mj4     15 2346 1.59 0.99    2.0    1.62 1.48   0   3     3 -0.03    -1.06 0.02

## End(Not run)

Description

This is a dataset with a subset of 23 Mathematics items from TIMSS 2003 items used in Su, Choi, Lee, Choi and McAninch (2013).

Usage

data(data.timss03.G8.su)

Format

The data contains scored item responses (data), the Q-matrix (q.matrix) and further item informations (iteminfo).

The format is

List of 3
$ data :'data.frame':
..$ idstud : num [1:757] 1e+07 1e+07 1e+07 1e+07 1e+07 ...
..$ idbook : num [1:757] 1 1 1 1 1 1 1 1 1 1 ...
..$ M012001 : num [1:757] 0 1 0 0 1 0 1 0 0 0 ...
..$ M012002 : num [1:757] 1 1 0 1 0 0 1 1 1 1 ...
..$ M012004 : num [1:757] 0 1 1 1 1 0 1 1 0 0 ...
[...]
..$ M022234B: num [1:757] 0 0 0 0 0 0 0 0 0 0 ...
..$ M022251 : num [1:757] 0 0 0 0 0 0 0 0 0 0 ...
..$ M032570 : num [1:757] 1 1 0 1 0 0 1 1 1 1 ...
..$ M032643 : num [1:757] 1 0 0 0 0 0 1 1 0 0 ...
$ q.matrix: int [1:23, 1:13] 1 0 0 0 0 0 1 0 0 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:23] "M012001" "M012002" "M012004" "M012016" ...
.. ..$ : chr [1:13] "S1" "S2" "S3" "S4" ...
$ iteminfo: chr [1:23, 1:9] "M012001" "M012002" "M012004" "M012016" ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:9] "item" "ItemType" "reporting_category" "content" ...

For a detailed description of skills S1, S2, ..., S15 see Su et al. (2013, Table 2).

Source

Subset of US 8th graders (Booklet 1) in the TIMSS 2003 mathematics study

References

Skaggs, G., Wilkins, J. L. M., & Hein, S. F. (2016). Grain size and parameter recovery with TIMSS and the general diagnostic model. International Journal of Testing, 16(4), 310-330.

Su, Y.-L., Choi, K. M., Lee, W.-C., Choi, T., & McAninch, M. (2013). Hierarchical cognitive diagnostic analysis for TIMSS 2003 mathematics. CASMA Research Report 35. Center for Advanced Studies in Measurement and Assessment (CASMA), University of Iowa.

See Also

The TIMSS 2003 dataset for 8th graders (with a larger number of items) was also analyzed in Skaggs, Wilkins and Hein (2016).

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Data Su et al. (2013)
#############################################################################

data(data.timss03.G8.su, package="CDM")
data <- data.timss03.G8.su$data[,-c(1,2)]
q.matrix <- data.timss03.G8.su$q.matrix

#*** Model 1: DINA model with complete skill space of 2^13=8192 skill classes
mod1 <- CDM::din( data, q.matrix )

#*** Model 2: Skill space approximation with 3000 skill classes instead of
#    2^13=8192 classes as in Model 1
ss2 <- CDM::skillspace.approximation( L=3000, K=ncol(q.matrix) )
mod2 <- CDM::din( data, q.matrix, skillclasses=ss2 )

#*** Model 3: DINA model with a hierarchical skill space
#   see Su et al. (2013): Fig. 6
B <- "S1 > S2 > S7 > S8
      S15 > S9
      S3 > S9
      S13 > S4 > S9
      S14 > S5 > S6 > S11"
# Note that S10 and S12 are not included in the dataset contained in this package
skill.names <- colnames(q.matrix)
ss3 <- CDM::skillspace.hierarchy(B=B, skill.names=skill.names)
# The reduced skill space "only" contains 325 skill classes
mod3 <- CDM::din( data, q.matrix, skillclasses=ss3$skillspace.reduced )

## End(Not run)

Description

TIMSS 2007 (Grade 4) dataset with 25 mathematics (dichotomized) items used in Lee, Park and Taylan (2011), Park and Lee (2014) and Park, Xing and Lee (2018). The dataset includes a sample of 698 Austrian students.

Usage

data(data.timss07.G4.lee)
data(data.timss07.G4.py)
data(data.timss07.G4.Qdomains)

Format

• The dataset data.timss07.G4.lee is a list containing dichotomous item responses (data; information on booklet and gender included), the Q-matrix (q.matrix) and descriptions of the skills (skillinfo) used in Lee et al. (2011).

  The format is:

  List of 3
$ data :'data.frame':
..$ idstud : int [1:698] 10110 10111 20105 20106 30203 30204 40106 40107 60111 60112 ...
..$ idbook : int [1:698] 4 5 4 5 4 5 4 5 4 5 ...
..$ girl : int [1:698] 0 0 1 1 0 1 0 1 1 1 ...
..$ M041052 : num [1:698] 1 NA 1 NA 0 NA 1 NA 1 NA ...
..$ M041056 : num [1:698] 1 NA 0 NA 0 NA 0 NA 1 NA ...
..$ M041069 : num [1:698] 0 NA 0 NA 0 NA 0 NA 1 NA ...
..$ M041076 : num [1:698] 1 NA 0 NA 1 NA 1 NA 0 NA ...
..$ M041281 : num [1:698] 1 NA 0 NA 1 NA 1 NA 0 NA ...
..$ M041164 : num [1:698] 1 NA 1 NA 0 NA 1 NA 1 NA ...
..$ M041146 : num [1:698] 0 NA 0 NA 1 NA 1 NA 0 NA ...
..$ M041152 : num [1:698] 1 NA 1 NA 1 NA 0 NA 1 NA ...
..$ M041258A: num [1:698] 0 NA 1 NA 1 NA 0 NA 1 NA ...
..$ M041258B: num [1:698] 1 NA 0 NA 1 NA 0 NA 1 NA ...
..$ M041131 : num [1:698] 0 NA 0 NA 1 NA 1 NA 1 NA ...
..$ M041275 : num [1:698] 1 NA 0 NA 0 NA 1 NA 1 NA ...
..$ M041186 : num [1:698] 1 NA 0 NA 1 NA 1 NA 0 NA ...
..$ M041336 : num [1:698] 1 NA 1 NA 0 NA 1 NA 0 NA ...
..$ M031303 : num [1:698] 1 1 0 1 0 1 1 1 0 0 ...
..$ M031309 : num [1:698] 1 0 1 1 1 1 1 1 0 0 ...
..$ M031245 : num [1:698] 0 0 0 0 0 0 0 0 0 0 ...
..$ M031242A: num [1:698] 1 1 0 1 1 1 1 1 0 0 ...
..$ M031242B: num [1:698] 0 1 0 1 1 1 1 1 1 0 ...
..$ M031242C: num [1:698] 1 1 0 1 1 1 1 1 1 0 ...
..$ M031247 : num [1:698] 0 0 0 0 0 0 0 0 0 0 ...
..$ M031219 : num [1:698] 1 1 1 0 1 1 1 1 1 0 ...
..$ M031173 : num [1:698] 1 1 0 0 0 1 1 1 1 0 ...
..$ M031085 : num [1:698] 1 0 0 1 1 1 0 0 0 1 ...
..$ M031172 : num [1:698] 1 0 0 1 1 1 1 1 1 0 ...
$ q.matrix : int [1:25, 1:15] 1 0 0 0 0 0 0 1 0 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:25] "M041052" "M041056" "M041069" "M041076" ...
.. ..$ : chr [1:15] "NWN01" "NWN02" "NWN03" "NWN04" ...
$ skillinfo:'data.frame':
..$ skillindex : int [1:15] 1 2 3 4 5 6 7 8 9 10 ...
..$ skill : Factor w/ 15 levels "DOR15","DRI13",..: 12 13 14 15 8 9 10 11 4 6 ...
..$ content : Factor w/ 3 levels "D","G","N": 3 3 3 3 3 3 3 3 2 2 ...
..$ content_label : Factor w/ 3 levels "Data Display",..: 3 3 3 3 3 3 3 3 2 2 ...
..$ subcontent : Factor w/ 9 levels "FD","LA","LM",..: 9 9 9 9 1 1 4 6 2 8 ...
..$ subcontent_label: Factor w/ 9 levels "Fractions and Decimals",..: 9 9 9 9 1 1 4 6 2 8 ...
  

• The dataset data.timss07.G4.py uses the same items as data.timss07.G4.lee but employs a simplified Q-matrix with 7 skills. This Q-matrix was used in Park and Lee (2014) and Park et al. (2018).

  List of 3
$ q.matrix:'data.frame': 25 obs. of 7 variables:
..$ N1: num [1:25] 1 0 1 1 1 0 0 1 0 0 ...
..$ N2: num [1:25] 0 1 1 1 0 0 0 0 0 0 ...
..$ N3: num [1:25] 0 0 0 0 1 0 0 0 0 0 ...
..$ G4: num [1:25] 0 0 0 0 0 0 1 0 0 1 ...
..$ G5: num [1:25] 0 0 0 0 0 1 1 1 1 1 ...
..$ G6: num [1:25] 0 0 0 0 0 1 1 0 0 0 ...
..$ D7: num [1:25] 0 0 0 0 0 0 0 0 0 0 ...
$ domains : Named chr [1:3] "Number" "Geometric Shapes and Measures" "Data Display"
..- attr(*, "names")=chr [1:3] "N" "G" "D"
$ skills : Named chr [1:7] "Whole Numbers" ...
..- attr(*, "names")=chr [1:7] "N1" "N2" "N3" "G4" ...
  

• The Q-matrix data.timss07.G4.Qdomains is a simplification of data.timss07.G4.py$q.matrix to 3 domains and involves a simple structure of skills.

  num [1:25, 1:3] 1 1 1 1 1 0 0 1 0 0 ...
- attr(*, "dimnames")=List of 2
..$ : chr [1:25] "M041052" "M041056" "M041069" "M041076" ...
..$ : chr [1:3] "N" "G" "D"
  

Source

TIMSS 2007 study, 4th Grade, Austrian sample on booklets 4 and 5

References

Lee, Y. S., Park, Y. S., & Taylan, D. (2011). A cognitive diagnostic modeling of attribute mastery in Massachusetts, Minnesota, and the US national sample using the TIMSS 2007. International Journal of Testing, 11, 144-177.

Park, Y. S., & Lee, Y. S. (2014). An extension of the DINA model using covariates: Examining factors affecting response probability and latent classification. Applied Psychological Measurement, 38(5), 376-390.

Park, Y. S., Xing, K., & Lee, Y. S. (2018). Explanatory cognitive diagnostic models: Incorporating latent and observed predictors. Applied Psychological Measurement, 42(5), 376-392.

Yamaguchi, K., & Okada, K. (2018). Comparison among cognitive diagnostic models for the TIMSS 2007 fourth grade mathematics assessment. PloS ONE, 13(2), e0188691.

See Also

A comparison of several countries based on the 25 items is conducted in Yamaguchi and Okada (2018).

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: DINA model Lee et al. (2011) - 15 skills
#############################################################################

data(data.timss07.G4.lee, package="CDM")
dat <- data.timss07.G4.lee$data
q.matrix <- data.timss07.G4.lee$q.matrix
# extract items
items <- grep( "M0", colnames(dat), value=TRUE )

#*** Model 1: estimate DINA model
mod1 <- CDM::din( dat[,items], q.matrix )
summary(mod1)

#############################################################################
# EXAMPLE 2: DINA models Park and Lee (2014) - 7 skills and 3 skills
#############################################################################

data(data.timss07.G4.lee, package="CDM")
data(data.timss07.G4.py, package="CDM")
data(data.timss07.G4.Qdomains, package="CDM")

dat <- data.timss07.G4.lee$data
q.matrix <- data.timss07.G4.py$q.matrix
items <- rownames(q.matrix)

#*** Model 1: estimate DINA model
mod1 <- CDM::din( dat[,items], q.matrix )
summary(mod1)

#*** Model 2: estimate DINA model with Q-matrix defined by domains
Q <- data.timss07.G4.Qdomains
mod2 <- CDM::din( dat[,items], q.matrix=Q )
summary(mod2)

## End(Not run)

Description

This is the TIMSS 2011 dataset of 4668 Austrian fourth-graders. See George and Robitzsch (2014, 2015, 2018) for publications using the TIMSS 2011 dataset for cognitive diagnosis modeling. The dataset has also been analyzed by Sedat and Arican (2015).

Usage

data(data.timss11.G4.AUT)
data(data.timss11.G4.AUT.part)
data(data.timss11.G4.sa)

Format

• The format of the dataset data.timss11.G4.AUT is:

  List of 4
$ data :'data.frame':
..$ uidschool: int [1:4668] 10040001 10040001 10040001 10040001 10040001 10040001 10040001 10040001 10040001 10040001 ...
..$ uidstud : num [1:4668] 1e+13 1e+13 1e+13 1e+13 1e+13 ...
..$ IDCNTRY : int [1:4668] 40 40 40 40 40 40 40 40 40 40 ...
..$ IDBOOK : int [1:4668] 10 12 13 14 1 2 3 4 5 6 ...
..$ IDSCHOOL : int [1:4668] 1 1 1 1 1 1 1 1 1 1 ...
..$ IDCLASS : int [1:4668] 102 102 102 102 102 102 102 102 102 102 ...
..$ IDSTUD : int [1:4668] 10201 10203 10204 10205 10206 10207 10208 10209 10210 10211 ...
..$ TOTWGT : num [1:4668] 17.5 17.5 17.5 17.5 17.5 ...
..$ HOUWGT : num [1:4668] 1.04 1.04 1.04 1.04 1.04 ...
..$ SENWGT : num [1:4668] 0.111 0.111 0.111 0.111 0.111 ...
..$ SCHWGT : num [1:4668] 11.6 11.6 11.6 11.6 11.6 ...
..$ STOTWGTU : num [1:4668] 524 524 524 524 524 ...
..$ WGTADJ1 : int [1:4668] 1 1 1 1 1 1 1 1 1 1 ...
..$ WGTFAC1 : num [1:4668] 11.6 11.6 11.6 11.6 11.6 ...
..$ JKCREP : int [1:4668] 1 1 1 1 1 1 1 1 1 1 ...
..$ JKCZONE : int [1:4668] 1 1 1 1 1 1 1 1 1 1 ...
..$ female : int [1:4668] 1 0 1 1 1 1 1 1 0 0 ...
..$ M031346A : int [1:4668] NA NA NA 1 1 NA NA NA NA NA ...
..$ M031346B : int [1:4668] NA NA NA 0 0 NA NA NA NA NA ...
..$ M031346C : int [1:4668] NA NA NA 1 1 NA NA NA NA NA ...
..$ M031379 : int [1:4668] NA NA NA 0 0 NA NA NA NA NA ...
..$ M031380 : int [1:4668] NA NA NA 0 0 NA NA NA NA NA ...
..$ M031313 : int [1:4668] NA NA NA 1 1 NA NA NA NA NA ...
.. [list output truncated]
$ q.matrix1:'data.frame':
..$ item : Factor w/ 174 levels "M031004","M031009",..: 29 30 31 32 33 25 8 5 17 163 ...
..$ Co_DA: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_DK: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_DR: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_GA: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_GK: int [1:174] 0 0 0 0 0 0 1 1 0 0 ...
..$ Co_GR: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_NA: int [1:174] 1 0 0 0 0 1 0 0 0 1 ...
..$ Co_NK: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_NR: int [1:174] 0 1 1 1 1 0 0 0 1 0 ...
$ q.matrix2:'data.frame':
..$ item : Factor w/ 174 levels "M031004","M031009",..: 29 30 31 32 33 25 8 5 17 163 ...
..$ CONT_D: int [1:174] 0 0 0 0 0 0 0 0 0 0 ...
..$ CONT_G: int [1:174] 0 0 0 0 0 0 1 1 0 0 ...
..$ CONT_N: int [1:174] 1 1 1 1 1 1 0 0 1 1 ...
$ q.matrix3:'data.frame': 174 obs. of 4 variables:
..$ item : Factor w/ 174 levels "M031004","M031009",..: 29 30 31 32 33 25 8 5 17 163 ...
..$ COGN_A: int [1:174] 1 0 0 0 0 1 0 0 0 1 ...
..$ COGN_K: int [1:174] 0 0 0 0 0 0 1 1 0 0 ...
..$ COGN_R: int [1:174] 0 1 1 1 1 0 0 0 1 0 ...
  

• The dataset data.timss11.G4.AUT.part is a part of data.timss11.G4.AUT and contains only the first three booklets (with N=1010 students). The format is

  List of 4
$ data :'data.frame': 1010 obs. of 109 variables:
..$ uidschool: int [1:1010] 10040001 10040001 10040001 10040001 ...
..$ uidstud : num [1:1010] 1e+13 1e+13 1e+13 1e+13 1e+13 ...
..$ IDCNTRY : int [1:1010] 40 40 40 40 40 40 40 40 40 40 ...
..$ IDBOOK : int [1:1010] 1 2 3 1 2 1 2 3 1 2 ...
..$ IDSCHOOL : int [1:1010] 1 1 1 1 1 2 2 2 3 3 ...
..$ IDCLASS : int [1:1010] 102 102 102 102 102 ...
..$ IDSTUD : int [1:1010] 10206 10207 10208 10220 ...
..$ TOTWGT : num [1:1010] 17.5 17.5 17.5 17.5 17.5 ...
..$ HOUWGT : num [1:1010] 1.04 1.04 1.04 1.04 1.04 ...
..$ SENWGT : num [1:1010] 0.111 0.111 0.111 0.111 0.111 ...
..$ SCHWGT : num [1:1010] 11.6 11.6 11.6 11.6 11.6 ...
..$ STOTWGTU : num [1:1010] 524 524 524 524 524 ...
..$ WGTADJ1 : int [1:1010] 1 1 1 1 1 1 1 1 1 1 ...
..$ WGTFAC1 : num [1:1010] 11.6 11.6 11.6 11.6 11.6 ...
..$ JKCREP : int [1:1010] 1 1 1 1 1 0 0 0 0 0 ...
..$ JKCZONE : int [1:1010] 1 1 1 1 1 1 1 1 2 2 ...
..$ female : int [1:1010] 1 1 1 1 0 1 1 1 1 1 ...
..$ M031346A : int [1:1010] 1 NA NA 1 NA 1 NA NA 1 NA ...
..$ M031346B : int [1:1010] 0 NA NA 1 NA 0 NA NA 0 NA ...
..$ M031346C : int [1:1010] 1 NA NA 0 NA 0 NA NA 0 NA ...
..$ M031379 : int [1:1010] 0 NA NA 0 NA 0 NA NA 1 NA ...
..$ M031380 : int [1:1010] 0 NA NA 0 NA 0 NA NA 0 NA ...
..$ M031313 : int [1:1010] 1 NA NA 0 NA 1 NA NA 0 NA ...
..$ M031083 : int [1:1010] 1 NA NA 1 NA 1 NA NA 1 NA ...
..$ M031071 : int [1:1010] 0 NA NA 0 NA 1 NA NA 0 NA ...
..$ M031185 : int [1:1010] 0 NA NA 1 NA 0 NA NA 0 NA ...
..$ M051305 : int [1:1010] 1 1 NA 1 0 0 0 NA 0 1 ...
..$ M051091 : int [1:1010] 1 1 NA 1 1 1 1 NA 1 0 ...
.. [list output truncated]
$ q.matrix1:'data.frame': 47 obs. of 10 variables:
..$ item : Factor w/ 174 levels "M031004","M031009",..: 29 30 31 32 33 25 8 5 17 163 ...
..$ Co_DA: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_DK: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_DR: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_GA: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_GK: int [1:47] 0 0 0 0 0 0 1 1 0 0 ...
..$ Co_GR: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_NA: int [1:47] 1 0 0 0 0 1 0 0 0 1 ...
..$ Co_NK: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ Co_NR: int [1:47] 0 1 1 1 1 0 0 0 1 0 ...
$ q.matrix2:'data.frame': 47 obs. of 4 variables:
..$ item : Factor w/ 174 levels "M031004","M031009",..: 29 30 31 32 33 25 8 5 17 163 ...
..$ CONT_D: int [1:47] 0 0 0 0 0 0 0 0 0 0 ...
..$ CONT_G: int [1:47] 0 0 0 0 0 0 1 1 0 0 ...
..$ CONT_N: int [1:47] 1 1 1 1 1 1 0 0 1 1 ...
$ q.matrix3:'data.frame': 47 obs. of 4 variables:
..$ item : Factor w/ 174 levels "M031004","M031009",..: 29 30 31 32 33 25 8 5 17 163 ...
..$ COGN_A: int [1:47] 1 0 0 0 0 1 0 0 0 1 ...
..$ COGN_K: int [1:47] 0 0 0 0 0 0 1 1 0 0 ...
..$ COGN_R: int [1:47] 0 1 1 1 1 0 0 0 1 0 ...
  

• The dataset data.timss11.G4.sa contains the Q-matrix used in Sedat and Arican (2015).

  List of 2
$ q.matrix:'data.frame': 31 obs. of 13 variables:
..$ N1 : num [1:31] 1 0 0 1 1 0 0 0 0 0 ...
..$ N2 : num [1:31] 1 1 0 0 1 0 0 0 0 0 ...
..$ N3 : num [1:31] 0 0 0 0 1 0 0 0 0 0 ...
..$ A4 : num [1:31] 0 0 1 0 0 1 1 1 0 0 ...
..$ A5 : num [1:31] 0 0 0 0 0 1 0 1 0 0 ...
..$ A6 : num [1:31] 0 0 0 0 0 0 0 0 0 0 ...
..$ A7 : num [1:31] 0 0 1 0 0 0 0 0 0 0 ...
..$ G8 : num [1:31] 0 0 0 0 0 0 0 0 1 1 ...
..$ G9 : num [1:31] 0 0 0 0 0 0 0 0 1 1 ...
..$ G10: num [1:31] 0 0 0 0 0 0 0 0 1 1 ...
..$ G11: num [1:31] 0 0 0 0 0 1 0 0 0 0 ...
..$ D12: num [1:31] 0 0 0 0 0 0 0 0 0 0 ...
..$ D13: num [1:31] 0 0 0 0 0 0 0 0 0 0 ...
$ skills : Named chr [1:13] "Possesses understanding of" __truncated__ ...
..- attr(*, "names")=chr [1:13] "N1" "N2" "N3" "A4" ...
  

References

George, A. C., & Robitzsch, A. (2014). Multiple group cognitive diagnosis models, with an emphasis on differential item functioning. Psychological Test and Assessment Modeling, 56(4), 405-432.

George, A. C., & Robitzsch, A. (2015) Cognitive diagnosis models in R: A didactic. The Quantitative Methods for Psychology, 11, 189-205.

George, A. C., & Robitzsch, A. (2018). Focusing on interactions between content and cognition: A new perspective on gender differences in mathematical sub-competencies. Applied Measurement in Education, 31(1), 79-97.

Sedat, S. E. N., & Arican, M. (2015). A diagnostic comparison of Turkish and Korean students' Mathematics performances on the TIMSS 2011 assessment. Journal of Measurement and Evaluation in Education and Psychology, 6(2), 238-253.

Description

Computes the variance of a nonlinear parameter using the delta method.

Usage

deltaMethod(derived.pars, est, Sigma, h=1e-05)

Arguments

Value

See Also

See car::deltaMethod or msm::deltamethod.

Examples

#############################################################################
# EXAMPLE 1: Nonlinear parameter
#############################################################################

#-- parameter estimate
est <- c( 510.67, 102.57)
names(est) <- c("mu", "sigma")
#-- covariance matrix
Sigma <- matrix( c(5.83, 0.45, 0.45, 3.21 ), nrow=2, ncol=2 )
colnames(Sigma) <- rownames(Sigma) <- names(est)
#-- define derived nonlinear parameters
derived.pars <- list( "d"=~ I( ( mu - 508 ) / sigma ),
                      "dsig"=~ I( sigma / 100 - 1) )

#*** apply delta method
res <- CDM::deltaMethod( derived.pars, est, Sigma )
res

Description

din provides parameter estimation for cognitive diagnosis models of the types “DINA”, “DINO” and “mixed DINA and DINO”.

Usage

din(data, q.matrix, skillclasses=NULL,
      conv.crit=0.001, dev.crit=10^(-5), maxit=500,
      constraint.guess=NULL, constraint.slip=NULL,
      guess.init=rep(0.2, ncol(data)), slip.init=guess.init,
      guess.equal=FALSE, slip.equal=FALSE, zeroprob.skillclasses=NULL,
      weights=rep(1, nrow(data)), rule="DINA",
      wgt.overrelax=0, wgtest.overrelax=FALSE, param.history=FALSE,
      seed=0, progress=TRUE, guess.min=0, slip.min=0, guess.max=1, slip.max=1)

## S3 method for class 'din'
print(x, ...)

Arguments

Details

In the CDM DINA (deterministic-input, noisy-and-gate; de la Torre & Douglas, 2004) and DINO (deterministic-input, noisy-or-gate; Templin & Henson, 2006) models endorsement probabilities are modeled based on guessing and slipping parameters, given the different skill classes. The probability of respondent $n$ (or corresponding respondents class $n$) for solving item $j$ is calculated as a function of the respondent's latent response $\eta_{nj}$ and the guessing and slipping rates $g_j$ and $s_j$ for item $j$ conditional on the respondent's skill class $\alpha_n$:

$P(X_{nj}=1 | \alpha_n)=g_j^{(1- \eta_{nj})}(1 - s_j) ^{\eta_{nj}}.$

The respondent's latent response (class) $\eta_{nj}$ is a binary number, 0 or 1, where 1 indicates presence of all (rule="DINO") or at least one (rule="DINO") required skill(s) for item $j$, respectively.

DINA and DINO parameter estimation is performed by maximization of the marginal likelihood of the data. The a priori distribution of the skill vectors is a uniform distribution. The implementation follows the EM algorithm by de la Torre (2009).

The function din returns an object of the class din (see ‘Value’), for which plot, print, and summary methods are provided; plot.din, print.din, and summary.din, respectively.

Value

Note

The calculation of standard errors using sampling weights which represent multistage sampling schemes is not correct. Please use replication methods (like Jackknife) instead.

References

de la Torre, J. (2009). DINA model parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34, 115–130.

de la Torre, J., & Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333–353.

Lee, Y.-S., de la Torre, J., & Park, Y. S. (2012). Relationships between cognitive diagnosis, CTT, and IRT indices: An empirical investigation. Asia Pacific Educational Research, 13, 333-345.

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Templin, J., & Henson, R. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287–305.

See Also

plot.din, the S3 method for plotting objects of the class din; print.din, the S3 method for printing objects of the class din; summary.din, the S3 method for summarizing objects of the class din, which creates objects of the class summary.din; din, the main function for DINA and DINO parameter estimation, which creates objects of the class din.

See the gdina function for the estimation of the generalized DINA (GDINA) model.

For assessment of model fit see modelfit.cor.din and anova.din.

See itemfit.sx2 for item fit statistics.

See discrim.index for computing discrimination indices.

See also CDM-package for general information about this package.

See the NPCD::JMLE function in the NPCD package for joint maximum likelihood estimation of the DINA, DINO and NIDA model.

See the dina::DINA_Gibbs function in the dina package for MCMC based estimation of the DINA model.

Examples

#############################################################################
# EXAMPLE 1: Examples based on dataset fractions.subtraction.data
#############################################################################

## dataset fractions.subtraction.data and corresponding Q-Matrix
head(fraction.subtraction.data)
fraction.subtraction.qmatrix

## Misspecification in parameter specification for method CDM::din()
## leads to warnings and terminates estimation procedure. E.g.,

# See Q-Matrix specification
fractions.dina.warning1 <- CDM::din(data=fraction.subtraction.data,
  q.matrix=t(fraction.subtraction.qmatrix))

# See guess.init specification
fractions.dina.warning2 <- CDM::din(data=fraction.subtraction.data,
  q.matrix=fraction.subtraction.qmatrix, guess.init=rep(1.2,
  ncol(fraction.subtraction.data)))

# See rule specification
fractions.dina.warning3 <- CDM::din(data=fraction.subtraction.data,
  q.matrix=fraction.subtraction.qmatrix, rule=c(rep("DINA",
  10), rep("DINO", 9)))

## Parameter estimation of DINA model
# rule="DINA" is default
fractions.dina <- CDM::din(data=fraction.subtraction.data,
  q.matrix=fraction.subtraction.qmatrix, rule="DINA")
attributes(fractions.dina)
str(fractions.dina)

## For instance assessing the guessing parameters through
## assignment
fractions.dina$guess

## corresponding summaries, including IDI,
## most frequent skill classes and information
## criteria AIC and BIC
summary(fractions.dina)

## In particular, assessing detailed summary through assignment
detailed.summary.fs <- summary(fractions.dina)
str(detailed.summary.fs)

## Item discrimination index of item 8 is too low. This is also
## visualized in the first plot
plot(fractions.dina)

## The reason therefore is a high guessing parameter
round(fractions.dina$guess[,1], 2)

## Estimate DINA model with different random initial parameters using seed=1345
fractions.dina1 <- CDM::din(data=fraction.subtraction.data,
  q.matrix=fraction.subtraction.qmatrix, rule="DINA", seed=1345)

## Fix the guessing parameters of items 5, 8 and 9 equal to .20
# define a constraint.guess matrix
constraint.guess <-  matrix(c(5,8,9, rep(0.2, 3)), ncol=2)
fractions.dina.fixed <- CDM::din(data=fraction.subtraction.data,
  q.matrix=fraction.subtraction.qmatrix,
  constraint.guess=constraint.guess)

## The second plot shows the expected (MAP) and observed skill
## probabilities. The third plot visualizes the skill class
## occurrence probabilities; Only the 'top.n.skill.classes' most frequent
## skill classes are labeled; it is obvious that the skill class '11111111'
## (all skills are mastered) is the most probable in this population.
## The fourth plot shows the skill probabilities conditional on response
## patterns; in this population the skills 3 and 6 seem to be
## mastered easier than the others. The fourth plot shows the
## skill probabilities conditional on a specified response
## pattern; it is shown whether a skill is mastered (above
## .5+'uncertainty') unclassifiable (within the boundaries) or
## not mastered (below .5-'uncertainty'). In this case, the
## 527th respondent was chosen; if no response pattern is
## specified, the plot will not be shown (of course)
pattern <- paste(fraction.subtraction.data[527, ], collapse="")
plot(fractions.dina, pattern=pattern, display.nr=4)

#uncertainty=0.1, top.n.skill.classes=6 are default
plot(fractions.dina.fixed, uncertainty=0.1, top.n.skill.classes=6,
  pattern=pattern)

## Not run: 
#############################################################################
# EXAMPLE 2: Examples based on dataset sim.dina
#############################################################################

# DINA Model
d1 <- CDM::din(sim.dina, q.matr=sim.qmatrix, rule="DINA",
  conv.crit=0.01, maxit=500, progress=TRUE)
summary(d1)

# DINA model with hierarchical skill classes (Hierarchical DINA model)
# 1st step:  estimate an initial full model to look at the indexing
#    of skill classes
d0 <- CDM::din(sim.dina, q.matr=sim.qmatrix, maxit=1)
d0$attribute.patt.splitted
#      [,1] [,2] [,3]
# [1,]    0    0    0
# [2,]    1    0    0
# [3,]    0    1    0
# [4,]    0    0    1
# [5,]    1    1    0
# [6,]    1    0    1
# [7,]    0    1    1
# [8,]    1    1    1
#
# In this example, following hierarchical skill classes are only allowed:
# 000, 001, 011, 111
# We define therefore a vector of indices for skill classes with
# zero probabilities (see entries in the rows of the matrix
# d0$attribute.patt.splitted above)
zeroprob.skillclasses <- c(2,3,5,6)     # classes 100, 010, 110, 101
# estimate the hierarchical DINA model
d1a <- CDM::din(sim.dina, q.matr=sim.qmatrix,
          zeroprob.skillclasses=zeroprob.skillclasses )
summary(d1a)

# Mixed DINA and DINO Model
d1b <- CDM::din(sim.dina, q.matr=sim.qmatrix, rule=
          c(rep("DINA", 7), rep("DINO", 2)), conv.crit=0.01,
          maxit=500, progress=FALSE)
summary(d1b)

# DINO Model
d2 <- CDM::din(sim.dina, q.matr=sim.qmatrix, rule="DINO",
  conv.crit=0.01, maxit=500, progress=FALSE)
summary(d2)

# Comparison of DINA and DINO estimates
lapply(list("guessing"=rbind("DINA"=d1$guess[,1],
  "DINO"=d2$guess[,1]), "slipping"=rbind("DINA"=
  d1$slip[,1], "DINO"=d2$slip[,1])), round, 2)

# Comparison of the information criteria
c("DINA"=d1$AIC, "MIXED"=d1b$AIC, "DINO"=d2$AIC)

# following estimates:
d1$coef            # guessing and slipping parameter
d1$guess           # guessing parameter
d1$slip            # slipping parameter
d1$skill.patt      # probabilities for skills
d1$attribute.patt  # skill classes with probabilities
d1$subj.pattern    # pattern per subject

# posterior probabilities for every response pattern
d1$posterior

# Equal guessing parameters
d2a <- CDM::din( data=sim.dina, q.matrix=sim.qmatrix,
            guess.equal=TRUE, slip.equal=FALSE )
d2a$coef

# Equal guessing and slipping parameters
d2b <- CDM::din( data=sim.dina, q.matrix=sim.qmatrix,
            guess.equal=TRUE, slip.equal=TRUE )
d2b$coef

#############################################################################
# EXAMPLE 3: Examples based on dataset sim.dino
#############################################################################

# DINO Estimation
d3 <- CDM::din(sim.dino, q.matr=sim.qmatrix, rule="DINO",
        conv.crit=0.005, progress=FALSE)

# Mixed DINA and DINO Model
d3b <- CDM::din(sim.dino, q.matr=sim.qmatrix,
          rule=c(rep("DINA", 4), rep("DINO", 5)), conv.crit=0.001,
          progress=FALSE)

# DINA Estimation
d4 <- CDM::din(sim.dino, q.matr=sim.qmatrix, rule="DINA",
  conv.crit=0.005, progress=FALSE)

# Comparison of DINA and DINO estimates
lapply(list("guessing"=rbind("DINO"=d3$guess[,1],  "DINA"=d4$guess[,1]),
       "slipping"=rbind("DINO"=d3$slip[,1], "DINA"=d4$slip[,1])), round, 2)

# Comparison of the information criteria
c("DINO"=d3$AIC, "MIXED"=d3b$AIC, "DINA"=d4$AIC)

#############################################################################
# EXAMPLE 4: Example estimation with weights based on dataset sim.dina
#############################################################################

# Here, a weighted maximum likelihood estimation is used
# This could be useful for survey data.

# i.e. first 200 persons have weight 2, the other have weight 1
(weights <- c(rep(2, 200), rep(1, 200)))

d5 <- CDM::din(sim.dina, sim.qmatrix, rule="DINA", conv.crit=
  0.005, weights=weights, progress=FALSE)

# Comparison of the information criteria
c("DINA"=d1$AIC, "WEIGHTS"=d5$AIC)

#############################################################################
# EXAMPLE 5: Example estimation within a balanced incomplete
##           block (BIB) design generated on dataset sim.dina
#############################################################################

# generate BIB data

# The next example shows that the din function works for
# (relatively arbitrary) missing value pattern

# Here, a missing by design is generated in the dataset dinadat.bib
sim.dina.bib <- sim.dina
sim.dina.bib[1:100, 1:3] <- NA
sim.dina.bib[101:300, 4:8] <- NA
sim.dina.bib[301:400, c(1,2,9)] <- NA

d6 <- CDM::din(sim.dina.bib, sim.qmatrix, rule="DINA",
         conv.crit=0.0005, weights=weights, maxit=200)

d7 <- CDM::din(sim.dina.bib, sim.qmatrix, rule="DINO",
         conv.crit=0.005, weights=weights)

# Comparison of DINA and DINO estimates
lapply(list("guessing"=rbind("DINA"=d6$guess[,1],
  "DINO"=d7$guess[,1]), "slipping"=rbind("DINA"=
  d6$slip[,1], "DINO"=d7$slip[,1])), round, 2)

#############################################################################
# EXAMPLE 6: DINA model with attribute hierarchy
#############################################################################

set.seed(987)
# assumed skill distribution: P(000)=P(100)=P(110)=P(111)=.245 and
#     "deviant pattern": P(010)=.02
K <- 3 # number of skills

# define alpha
alpha <- scan()
    0 0 0
    1 0 0
    1 1 0
    1 1 1
    0 1 0

alpha <- matrix( alpha, length(alpha)/K, K, byrow=TRUE )
alpha <- alpha[ c( rep(1:4,each=245), rep(5,20) ),  ]

# define Q-matrix
q.matrix <- scan()
    1 0 0   1 0 0   1 0 0
    0 1 0   0 1 0   0 1 0
    0 0 1   0 1 0   0 0 1
    1 1 0   1 0 1   0 1 1

q.matrix <- matrix( q.matrix, nrow=length(q.matrix)/K, ncol=K, byrow=TRUE )

# simulate DINA data
dat <- CDM::sim.din( alpha=alpha, q.matrix=q.matrix )$dat

#*** Model 1: estimate DINA model | no skill space restriction
mod1 <- CDM::din( dat, q.matrix )

#*** Model 2: DINA model | hierarchy A2 > A3
B <- "A2 > A3"
skill.names <- paste0("A",1:3)
skillspace <- CDM::skillspace.hierarchy( B, skill.names )$skillspace.reduced
mod2 <- CDM::din( dat, q.matrix, skillclasses=skillspace )

#*** Model 3: DINA model | linear hierarchy A1 > A2 > A3
#   This is a misspecied model because due to P(010)=.02 the relation A1>A2
#   does not hold.
B <- "A1 > A2
      A2 > A3"
skill.names <- paste0("A",1:3)
skillspace <- CDM::skillspace.hierarchy( B, skill.names )$skillspace.reduced
mod3 <- CDM::din( dat, q.matrix, skillclasses=skillspace )

#*** Model 4: 2PL model in gdm
mod4 <- CDM::gdm( dat, theta.k=seq(-5,5,len=21),
           decrease.increments=TRUE, skillspace="normal" )
summary(mod4)

anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC  Chisq df       p
  ##   2 Model 2 -7052.460 14104.92    29 14162.92 14305.24 0.9174  2 0.63211
  ##   1 Model 1 -7052.001 14104.00    31 14166.00 14318.14     NA NA      NA

anova(mod2,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
  ##   2 Model 2 -7059.058 14118.12    27 14172.12 14304.63 13.19618  2 0.00136
  ##   1 Model 1 -7052.460 14104.92    29 14162.92 14305.24       NA NA      NA

anova(mod2,mod4)
  ##       Model  loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -7220.05 14440.10    24 14488.10 14605.89 335.1805  5  0
  ##   1 Model 1 -7052.46 14104.92    29 14162.92 14305.24       NA NA NA

# compare fit statistics
summary( CDM::modelfit.cor.din( mod2 ) )
summary( CDM::modelfit.cor.din( mod4 ) )

#############################################################################
# EXAMPLE 7: Fitting the basic local independence model (BLIM) with din
#############################################################################

library(pks)
data(DoignonFalmagne7, package="pks")
  ##  str(DoignonFalmagne7)
  ##    $ K  : int [1:9, 1:5] 0 1 0 1 1 1 1 1 1 0 ...
  ##     ..- attr(*, "dimnames")=List of 2
  ##     .. ..$ : chr [1:9] "00000" "10000" "01000" "11000" ...
  ##     .. ..$ : chr [1:5] "a" "b" "c" "d" ...
  ##    $ N.R: Named int [1:32] 80 92 89 3 2 1 89 16 18 10 ...
  ##     ..- attr(*, "names")=chr [1:32] "00000" "10000" "01000" "00100" ...

# The idea is to fit the local independence model with the din function.
# This can be accomplished by specifying a DINO model with
# prespecified skill classes.

# extract dataset
dat <- as.numeric( unlist( sapply( names(DoignonFalmagne7$N.R),
    FUN=function( ll){ strsplit( ll, split="") } ) ) )
dat <- matrix( dat, ncol=5, byrow=TRUE )
colnames(dat) <- colnames(DoignonFalmagne7$K)
rownames(dat) <- names(DoignonFalmagne7$N.R)

# sample weights
weights <- DoignonFalmagne7$N.R

# define Q-matrix
q.matrix <- t(DoignonFalmagne7$K)
v1 <- colnames(q.matrix) <- paste0("S", colnames(q.matrix))
q.matrix <- q.matrix[, - 1] # remove S00000

# define skill classes
SC <- ncol(q.matrix)
skillclasses <- matrix( 0, nrow=SC+1, ncol=SC)
colnames(skillclasses) <- colnames(q.matrix)
rownames(skillclasses) <- v1
skillclasses[ cbind( 2:(SC+1), 1:SC ) ] <- 1

# estimate BLIM with din function
mod1 <- CDM::din(data=dat, q.matrix=q.matrix, skillclasses=skillclasses,
            rule="DINO", weights=weights   )
summary(mod1)
  ##   Item parameters
  ##     item guess  slip   IDI rmsea
  ##   a    a 0.158 0.162 0.680 0.011
  ##   b    b 0.145 0.159 0.696 0.009
  ##   c    c 0.008 0.181 0.811 0.001
  ##   d    d 0.012 0.129 0.859 0.001
  ##   e    e 0.025 0.146 0.828 0.007

# estimate basic local independence model with pks package
mod2 <- pks::blim(K, N.R, method="ML") # maximum likelihood estimation by EM algorithm
mod2
  ##   Error and guessing parameters
  ##         beta      eta
  ##   a 0.164871 0.103065
  ##   b 0.163113 0.095074
  ##   c 0.188839 0.000004
  ##   d 0.079835 0.000003
  ##   e 0.088648 0.019910

## End(Not run)

Description

Check necessary and sufficient identifiability conditions of the DINA model according Gu and Xu (xxxx) for a given Q-matrix.

Usage

din_identifiability(q.matrix)

## S3 method for class 'din_identifiability'
summary(object, ...)

Arguments

Value

List with values

References

Gu, Y., & Xu, G. (2018). The sufficient and necessary condition for the identifiability and estimability of the DINA model. Psychometrika, xx(xx), xxx-xxx. https://doi.org/10.1007/s11336-018-9619-8

See Also

See din.equivalent.class for equivalent (i.e., non-distinguishable) skill classes in the DINA model.

Examples

#############################################################################
# EXAMPLE 1: Some examples of Gu and Xu (2019)
#############################################################################

#* Matrix 1 in Equation (5) of Gu & Xu (2019)
Q1 <- diag(3)
Q2 <- matrix( scan(text="1 1 0 1 0 1 1 1 1 1 1 1"), ncol=3, byrow=TRUE)
Q <- rbind(Q1, Q2)

res <- CDM::din_identifiability(q.matrix=Q)
summary(res)

# remove two items
res <- CDM::din_identifiability(q.matrix=Q[-c(2,5),])
summary(res)

#* Matrix 1 in Equation (6) of Gu & Xu (2019)
Q1 <- diag(3)
Q2 <- matrix( c(1,1,1), nrow=4, ncol=3, byrow=TRUE)
Q <- rbind(Q1, Q2)

res <- CDM::din_identifiability(q.matrix=Q)
summary(res)

Description

This function allows the estimation of the mixed DINA/DINO model by joint maximum likelihood and a deterministic classification based on ideal latent responses.

Usage

din.deterministic(dat, q.matrix, rule="DINA", method="JML", conv=0.001,
    maxiter=300, increment.factor=1.05, progress=TRUE)

Arguments

Value

A list with following entries

References

Chiu, C. Y., & Douglas, J. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification, 30, 225-250.

See Also

For estimating the mixed DINA/DINO model using marginal maximum likelihood estimation see din.

See also the NPCD::JMLE function in the NPCD package for joint maximum likelihood estimation of the DINA or the DINO model.

Examples

#############################################################################
# EXAMPLE 1: 13 items and 3 attributes
#############################################################################

set.seed(679)
N <- 3000
# specify true Q-matrix
q.matrix <- matrix( 0, 13, 3 )
q.matrix[1:3,1] <- 1
q.matrix[4:6,2] <- 1
q.matrix[7:9,3] <- 1
q.matrix[10,] <- c(1,1,0)
q.matrix[11,] <- c(1,0,1)
q.matrix[12,] <- c(0,1,1)
q.matrix[13,] <- c(1,1,1)
q.matrix <- rbind( q.matrix, q.matrix )
colnames(q.matrix) <- paste0("Attr",1:ncol(q.matrix))

# simulate data according to the DINA model
dat <- CDM::sim.din( N=N, q.matrix)$dat

# Joint maximum likelihood estimation (the default: method="JML")
res1 <- CDM::din.deterministic( dat, q.matrix )

# Adaptive estimation of guessing and slipping parameters
res <- CDM::din.deterministic( dat, q.matrix, method="adaptive" )

# Classification using Hamming distance
res <- CDM::din.deterministic( dat, q.matrix, method="hamming" )

# Classification using weighted Hamming distance
res <- CDM::din.deterministic( dat, q.matrix, method="weighted.hamming" )

## Not run: 
#********* load NPCD library for JML estimation
library(NPCD)

# DINA model
res <- NPCD::JMLE( Y=dat[1:100,], Q=q.matrix, model="DINA" )
as.data.frame(res$par.est )   # item parameters
res$alpha.est                 # skill classifications

# RRUM model
res <- NPCD::JMLE( Y=dat[1:100,], Q=q.matrix, model="RRUM" )
as.data.frame(res$par.est )

## End(Not run)