Package 'mnlfa'

Title: Moderated Nonlinear Factor Analysis
Description: Conducts moderated nonlinear factor analysis (e.g., Curran et al., 2014, <doi:10.1080/00273171.2014.889594>). Regularization methods are implemented for assessing non-invariant items. Currently, the package includes dichotomous items and unidimensional item response models. Extensions will be included in future package versions.
Authors: Alexander Robitzsch [aut,cre]
Maintainer: Alexander Robitzsch <[email protected]>
License: GPL (>= 2)
Version: 0.4-2
Built: 2024-03-12 08:56:33 UTC
Source: https://github.com/alexanderrobitzsch/mnlfa

Help Index


Moderated Nonlinear Factor Analysis

Description

Conducts moderated nonlinear factor analysis (e.g., Curran et al., 2014, <doi:10.1080/00273171.2014.889594>). Regularization methods are implemented for assessing non-invariant items. Currently, the package includes dichotomous items and unidimensional item response models. Extensions will be included in future package versions.

Author(s)

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Maintainer: Alexander Robitzsch <[email protected]>

References

Curran, P. J., McGinley, J. S., Bauer, D. J., Hussong, A. M., Burns, A., Chassin, L., Sher, K., & Zucker, R. (2014). A moderated nonlinear factor model for the development of commensurate measures in integrative data analysis. Multivariate Behavioral Research, 49(3), 214-231. http://dx.doi.org/10.1080/00273171.2014.889594


Example Datasets for mnlfa Package

Description

Example datasets for mnlfa package.

Usage

data(data.mnlfa01)

Format


Moderated Nonlinear Factor Analysis

Description

General function for conducting moderated nonlinear factor analysis (Curran et al., 2014). Item slopes and item intercepts can be modeled as functions of person covariates.

Parameter regularization is allowed. For categorical covariates, group lasso can be used for regularization.

Usage

mnlfa(dat, items, item_type="2PL", formula_int=~1, formula_slo=~1, formula_mean=~0,
   formula_sd=~0, theta=NULL, parm_list_init=NULL, parm_trait_init=NULL, prior_init=NULL,
   regular_lam=c(0, 0), regular_type=c("none", "none"), maxit=1000, msteps=4, conv=1e-05,
   conv_mstep=1e-04, h=1e-04, parms_regular_types=NULL, parms_regular_lam=NULL,
   parms_iterations=NULL, center_parms=NULL, center_max_iter=6, L_max=.07,
   verbose=TRUE)

## S3 method for class 'mnlfa'
summary(object, file=NULL, ...)

Arguments

dat

Data frame with item responses

items

Vector containing item names

item_type

String or vector of item types. Currently, only item types "1PL" or "2PL" can be chosen.

formula_int

String or list with formula for item intercepts

formula_slo

String or list with formula for item slopes

formula_mean

Formula for mean of the trait distribution

formula_sd

Formula for standard deviation of the trait distribution

theta

Grid of θ\theta values used for approximation of normally distributed trait

parm_list_init

Optional list of initial item parameters

parm_trait_init

Optional list of initial parameters for trait distribution

prior_init

Optional matrix of prior distribution for persons

regular_lam

Vector of length two containing two general regularization parameters for item intercepts and item slopes

regular_type

Type of regularization method. Can be "none", "lasso", "scad" or "mcp".

maxit

Maximum number of iterations

msteps

Maximum number of M-steps

conv

Convergence criterion with respect to parameters

conv_mstep

Convergence criterion in M-step

h

Numerical differentiation parameter

parms_regular_types

Optional list containing parameter specific regularization types

parms_regular_lam

Optional list containing parameter specific regularization parameters

parms_iterations

Optional list containing sequence of parameter indices used for updating

center_parms

Optional list indicating which parameters should be centered during initial iterations.

center_max_iter

Maximum number of iterations in which parameters should be centered.

L_max

Majorization parameter used in regularization

verbose

Logical indicating whether output should be printed

object

Object of class mnlfa

file

Optional file name

...

Further arguments to be passed

Details

The moderated factor analysis model for dichotomous responses defined as

P(Xpi=1θp)=invlogit(apiθpbpi)P(X_{pi}=1 | \theta_p )=invlogit( a_{pi} \theta_p - b_{pi} )

The trait distribution θpN(μp,σp2)\theta_p \sim N( \mu_p, \sigma_p^2) allows a latent regression of person covariates on the mean with μp=Xpγ\mu_p=\bold{X}_p \bold{\gamma} (to be specified in formula_mean) and the logarithm of the standard deviation logσp=Zpδ\log \sigma_p=\bold{Z}_p \bold{\delta} (to be specified in formula_sd). Item intercepts and item slopes can be moderated by person covariates, i.e. api=Wpiαia_{pi}=\bold{W}_{pi} \bold{\alpha}_i and bpi=Vpiβib_{pi}=\bold{V}_{pi} \bold{\beta}_i. Regularization on (some of) the αi\bold{\alpha}_i or βi\bold{\beta}_i parameters is allowed.

The model is estimated using an EM algorithm with the coordinate descent method during the M-step (Sun et al., 2016).

Value

List with model results including

item

Summary table for item parameters

trait

Summary table for trait parameters

References

Curran, P. J., McGinley, J. S., Bauer, D. J., Hussong, A. M., Burns, A., Chassin, L., Sher, K., & Zucker, R. (2014). A moderated nonlinear factor model for the development of commensurate measures in integrative data analysis. Multivariate Behavioral Research, 49(3), 214-231. http://dx.doi.org/10.1080/00273171.2014.889594

Sun, J., Chen, Y., Liu, J., Ying, Z., & Xin, T. (2016). Latent variable selection for multidimensional item response theory models via L1 regularization. Psychometrika, 81(4), 921-939. https://doi.org/10.1007/s11336-016-9529-6

See Also

See also the aMNLFA package for automatized moderated nonlinear factor analysis which provides convenient wrapper functions for automized analysis in the Mplus software.

See the GPCMlasso package for the regularized generalized partial credit model.

Examples

#############################################################################
# EXAMPLE 1: Dichotomous data, 1PL model
#############################################################################

data(data.mnlfa01, package="mnlfa")

dat <- data.mnlfa01
# extract items from dataset
items <- grep("I[0-9]", colnames(dat), value=TRUE)
I <- length(items)

# maximum number of iterations (use only few iterations for the only purpose of
# providing CRAN checks)
maxit <- 10

#***** Model 1: 1PL model without moderating parameters and without covariates for traits

# no covariates for trait
formula_mean <- ~0
formula_sd <- ~1
# no item covariates
formula_int <- ~1
formula_slo <- ~1

mod1 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int,
             formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd,
             maxit=maxit )
summary(mod1)


#***** Model 2: 1PL model without moderating parameters and with covariates for traits

# covariates for trait
formula_mean <- ~female + age
formula_sd <- ~1

mod2 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int,
             formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd)
summary(mod2)

#***** Model 3: 1PL model with moderating parameters and with covariates for traits
#***   Regularization method 'mcp'

# covariates for trait
formula_mean <- ~female + age
formula_sd <- ~1
# moderation effects for items
formula_int <- ~1+female+age
formula_slo <- ~1

# center parameters for female and age in initial iterations for improving convergence
center_parms <- list( rep(2,I), rep(3,I) )

# regularization parameters for item intercept and item slope, respectively
regular_lam <- c(.06, .25)
regular_type <- c("mcp","none")

mod3 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int,
            formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd,
            center_parms=center_parms, regular_lam=regular_lam, regular_type=regular_type )
summary(mod3)


#***** Model 4: 1PL model with selected moderated item parameters

#* trait distribution
formula_mean <- ~0+female+age
formula_sd <- ~1

#* formulas for item intercepts
formula_int <- ~1
formula_int <- mnlfa::mnlfa_expand_to_list(x=formula_int, names_list=items)
mod_items <- c(4,5,6,7)
for (ii in mod_items){
    formula_int[[ii]] <- ~1+female+age
}
formula_slo <- ~1

mod4 <- mnlfa::mnlfa( dat=dat, items, item_type="1PL", formula_int=formula_int,
              formula_slo=formula_slo, formula_mean=formula_mean, formula_sd=formula_sd)
mod4$item
mod4$trait
summary(mod4)

Expands Input Into a List

Description

Expands an input into a list.

Usage

mnlfa_expand_to_list(x, names_list)

Arguments

x

An R object

names_list

Names of the list

Value

A list

Examples

#############################################################################
# EXAMPLE 1: Test example
#############################################################################

formula_int <- ~1+female+age
items <- paste0("I",1:12)
formula_int <- mnlfa::mnlfa_expand_to_list(x=formula_int, names_list=items)
formula_int[[1]] <- ~0