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  "Title": "Supplementary Item Response Theory Models",
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  "Date": "2026-04-16 10:43:29",
  "Authors@R": "c( person(given = \"Alexander\",\nfamily = \"Robitzsch\",\nrole = c(\"aut\", \"cre\"),\nemail = \"robitzsch@ipn.uni-kiel.de\",\ncomment = c(ORCID = \"0000-0002-8226-3132\")) )",
  "Maintainer": "Alexander Robitzsch <robitzsch@ipn.uni-kiel.de>",
  "Description": "Supplementary functions for item response models aiming to\ncomplement existing R packages. The functionality includes\namong others multidimensional compensatory and noncompensatory\nIRT models (Reckase, 2009, <doi:10.1007/978-0-387-89976-3>),\nMCMC for hierarchical IRT models and testlet models (Fox, 2010,\n<doi:10.1007/978-1-4419-0742-4>), NOHARM (McDonald, 1982,\n<doi:10.1177/014662168200600402>), Rasch copula model (Braeken,\n2011, <doi:10.1007/s11336-010-9190-4>; Schroeders, Robitzsch &\nSchipolowski, 2014, <doi:10.1111/jedm.12054>), faceted and\nhierarchical rater models (DeCarlo, Kim & Johnson, 2011,\n<doi:10.1111/j.1745-3984.2011.00143.x>), ordinal IRT model\n(ISOP; Scheiblechner, 1995, <doi:10.1007/BF02301417>), DETECT\nstatistic (Stout, Habing, Douglas & Kim, 1996,\n<doi:10.1177/014662169602000403>), local structural equation\nmodeling (LSEM; Hildebrandt, Luedtke, Robitzsch, Sommer &\nWilhelm, 2016, <doi:10.1080/00273171.2016.1142856>).",
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  "License": "GPL (>= 2)",
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  "Date/Publication": "2026-04-16 09:01:10 UTC",
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      "object": "data.timss",
      "file": "data.timss.rda",
      "class": [
        "list"
      ],
      "fields": [],
      "table": false,
      "tojson": true
    },
    {
      "name": "data.timss07.G8.RUS",
      "title": "TIMSS 2007 Grade 8 Mathematics and Science Russia",
      "object": "data.timss07.G8.RUS",
      "file": "data.timss07.G8.RUS.rda",
      "class": [
        "list"
      ],
      "fields": [],
      "table": false,
      "tojson": true
    },
    {
      "name": "data.trees",
      "title": "Dataset Used in Stoyan, Pommerening and Wuensche (2018)",
      "object": "data.trees",
      "file": "data.trees.rda",
      "class": [
        "data.frame"
      ],
      "fields": [
        "Number",
        "FM1",
        "FM2",
        "FM3",
        "FM4",
        "FM5",
        "FM6",
        "FM7",
        "FM8",
        "FM9",
        "FM10",
        "FM11",
        "FM12",
        "FM13",
        "FM14",
        "FM15"
      ],
      "rows": 387,
      "table": true,
      "tojson": true
    }
  ],
  "_help": [
    {
      "page": "sirt-package",
      "title": "Supplementary Item Response Theory Models",
      "topics": [
        "sirt-package",
        "sirt"
      ]
    },
    {
      "page": "automatic.recode",
      "title": "Automatic Method of Finding Keys in a Dataset with Raw Item Responses",
      "topics": [
        "automatic.recode"
      ]
    },
    {
      "page": "brm.sim",
      "title": "Functions for the Beta Item Response Model",
      "topics": [
        "brm.irf",
        "brm.sim"
      ]
    },
    {
      "page": "btm",
      "title": "Extended Bradley-Terry Model",
      "topics": [
        "btm",
        "btm_sim",
        "predict.btm",
        "summary.btm"
      ]
    },
    {
      "page": "categorize",
      "title": "Categorize and Decategorize Variables in a Data Frame",
      "topics": [
        "categorize",
        "decategorize"
      ]
    },
    {
      "page": "ccov.np",
      "title": "Nonparametric Estimation of Conditional Covariances of Item Pairs",
      "topics": [
        "ccov.np"
      ]
    },
    {
      "page": "cfa_meas_inv",
      "title": "Estimation of a Unidimensional Factor Model under Full and Partial Measurement Invariance",
      "topics": [
        "cfa_meas_inv"
      ]
    },
    {
      "page": "class.accuracy.rasch",
      "title": "Classification Accuracy in the Rasch Model",
      "topics": [
        "class.accuracy.rasch"
      ]
    },
    {
      "page": "conf.detect",
      "title": "Confirmatory DETECT and polyDETECT Analysis",
      "topics": [
        "conf.detect",
        "summary.conf.detect"
      ]
    },
    {
      "page": "data.activity.itempars",
      "title": "Item Parameters Cultural Activities",
      "topics": [
        "data.activity.itempars"
      ]
    },
    {
      "page": "data.befki",
      "title": "BEFKI Dataset (Schroeders, Schipolowski, & Wilhelm, 2015)",
      "topics": [
        "data.befki",
        "data.befki_resp"
      ]
    },
    {
      "page": "data.big5",
      "title": "Dataset Big 5 from 'qgraph' Package",
      "topics": [
        "data.big5",
        "data.big5.qgraph"
      ]
    },
    {
      "page": "data.bs",
      "title": "Datasets from Borg and Staufenbiel (2007)",
      "topics": [
        "data.bs",
        "data.bs07a"
      ]
    },
    {
      "page": "data.eid",
      "title": "Examples with Datasets from Eid and Schmidt (2014)",
      "topics": [
        "data.eid",
        "data.eid.kap4",
        "data.eid.kap5",
        "data.eid.kap6",
        "data.eid.kap7"
      ]
    },
    {
      "page": "data.elfe",
      "title": "ELFE Dataset",
      "topics": [
        "data.elfe"
      ]
    },
    {
      "page": "data.ess2005",
      "title": "Dataset European Social Survey 2005",
      "topics": [
        "data.ess2005"
      ]
    },
    {
      "page": "data.g308",
      "title": "C-Test Datasets",
      "topics": [
        "data.g308"
      ]
    },
    {
      "page": "data.inv4gr",
      "title": "Dataset for Invariance Testing with 4 Groups",
      "topics": [
        "data.inv4gr"
      ]
    },
    {
      "page": "data.kess",
      "title": "Datasets for Longitudinal KESS Study",
      "topics": [
        "data.kess",
        "data.kess.figIntell",
        "data.kess.math",
        "data.kess.read",
        "data.kess.sci"
      ]
    },
    {
      "page": "data.liking.science",
      "title": "Dataset 'Liking For Science'",
      "topics": [
        "data.liking.science"
      ]
    },
    {
      "page": "data.long",
      "title": "Longitudinal Dataset",
      "topics": [
        "data.long"
      ]
    },
    {
      "page": "data.lsem",
      "title": "Datasets for Local Structural Equation Models / Moderated Factor Analysis",
      "topics": [
        "data.lsem01",
        "data.lsem02",
        "data.lsem03"
      ]
    },
    {
      "page": "data.math",
      "title": "Dataset Mathematics",
      "topics": [
        "data.math"
      ]
    },
    {
      "page": "data.mcdonald",
      "title": "Some Datasets from McDonald's _Test Theory_ Book",
      "topics": [
        "data.mcdonald.act15",
        "data.mcdonald.LSAT6",
        "data.mcdonald.rape"
      ]
    },
    {
      "page": "data.mixed1",
      "title": "Dataset with Mixed Dichotomous and Polytomous Item Responses",
      "topics": [
        "data.mixed1"
      ]
    },
    {
      "page": "data.ml",
      "title": "Multilevel Datasets",
      "topics": [
        "data.ml",
        "data.ml1",
        "data.ml2"
      ]
    },
    {
      "page": "data.noharm",
      "title": "Datasets for NOHARM Analysis",
      "topics": [
        "data.noharm18",
        "data.noharmExC"
      ]
    },
    {
      "page": "data.pars1.rasch",
      "title": "Item Parameters for Three Studies Obtained by 1PL and 2PL Estimation",
      "topics": [
        "data.pars1.2pl",
        "data.pars1.rasch"
      ]
    },
    {
      "page": "data.pirlsmissing",
      "title": "Dataset from PIRLS Study with Missing Responses",
      "topics": [
        "data.pirlsmissing"
      ]
    },
    {
      "page": "data.pisa2006Read",
      "title": "Dataset PISA 2006 Reading",
      "topics": [
        "data.pisa2006Read"
      ]
    },
    {
      "page": "data.pisaMath",
      "title": "Dataset PISA Mathematics",
      "topics": [
        "data.pisaMath"
      ]
    },
    {
      "page": "data.pisaPars",
      "title": "Item Parameters from Two PISA Studies",
      "topics": [
        "data.pisaPars"
      ]
    },
    {
      "page": "data.pisaRead",
      "title": "Dataset PISA Reading",
      "topics": [
        "data.pisaRead"
      ]
    },
    {
      "page": "data.pw01",
      "title": "Datasets for Pairwise Comparisons",
      "topics": [
        "data.pw01"
      ]
    },
    {
      "page": "data.ratings1",
      "title": "Rating Datasets",
      "topics": [
        "data.ratings",
        "data.ratings1",
        "data.ratings2",
        "data.ratings3"
      ]
    },
    {
      "page": "data.raw1",
      "title": "Dataset with Raw Item Responses",
      "topics": [
        "data.raw1"
      ]
    },
    {
      "page": "data.read",
      "title": "Dataset Reading",
      "topics": [
        "data.read"
      ]
    },
    {
      "page": "data.reck",
      "title": "Datasets from Reckase' Book _Multidimensional Item Response Theory_",
      "topics": [
        "data.reck",
        "data.reck21",
        "data.reck61DAT1",
        "data.reck61DAT2",
        "data.reck73C1a",
        "data.reck73C1b",
        "data.reck75C2",
        "data.reck78ExA",
        "data.reck79ExB"
      ]
    },
    {
      "page": "data.si",
      "title": "Some Example Datasets for the 'sirt' Package",
      "topics": [
        "data.si01",
        "data.si02",
        "data.si03",
        "data.si04",
        "data.si05",
        "data.si06",
        "data.si07",
        "data.si08",
        "data.si09",
        "data.si10",
        "data.sirt"
      ]
    },
    {
      "page": "data.timss",
      "title": "Dataset TIMSS Mathematics",
      "topics": [
        "data.timss"
      ]
    },
    {
      "page": "data.timss07.G8.RUS",
      "title": "TIMSS 2007 Grade 8 Mathematics and Science Russia",
      "topics": [
        "data.timss07.G8.RUS"
      ]
    },
    {
      "page": "data.trees",
      "title": "Dataset Used in Stoyan, Pommerening and Wuensche (2018)",
      "topics": [
        "data.trees"
      ]
    },
    {
      "page": "data.wide2long",
      "title": "Converting a Data Frame from Wide Format in a Long Format",
      "topics": [
        "data.wide2long"
      ]
    },
    {
      "page": "detect.index",
      "title": "Calculation of the DETECT and polyDETECT Index",
      "topics": [
        "detect.index"
      ]
    },
    {
      "page": "dif.logistic.regression",
      "title": "Differential Item Functioning using Logistic Regression Analysis",
      "topics": [
        "dif.logistic.regression"
      ]
    },
    {
      "page": "dif.strata.variance",
      "title": "Stratified DIF Variance",
      "topics": [
        "dif.strata.variance"
      ]
    },
    {
      "page": "dif.variance",
      "title": "DIF Variance",
      "topics": [
        "dif.variance"
      ]
    },
    {
      "page": "dirichlet.mle",
      "title": "Maximum Likelihood Estimation of the Dirichlet Distribution",
      "topics": [
        "dirichlet.mle"
      ]
    },
    {
      "page": "dirichlet.simul",
      "title": "Simulation of a Dirichlet Distributed Vectors",
      "topics": [
        "dirichlet.simul"
      ]
    },
    {
      "page": "dmlavaan",
      "title": "Comparing Regression Parameters of Different lavaan Models Fitted to the Same Dataset",
      "topics": [
        "dmlavaan"
      ]
    },
    {
      "page": "eigenvalues.manymatrices",
      "title": "Computation of Eigenvalues of Many Symmetric Matrices",
      "topics": [
        "eigenvalues.manymatrices"
      ]
    },
    {
      "page": "equating.rasch",
      "title": "Equating in the Generalized Logistic Rasch Model",
      "topics": [
        "equating.rasch"
      ]
    },
    {
      "page": "equating.rasch.jackknife",
      "title": "Jackknife Equating Error in Generalized Logistic Rasch Model",
      "topics": [
        "equating.rasch.jackknife"
      ]
    },
    {
      "page": "expl.detect",
      "title": "Exploratory DETECT Analysis",
      "topics": [
        "expl.detect"
      ]
    },
    {
      "page": "f1d.irt",
      "title": "Functional Unidimensional Item Response Model",
      "topics": [
        "f1d.irt"
      ]
    },
    {
      "page": "fit.isop",
      "title": "Fitting the ISOP and ADISOP Model for Frequency Tables",
      "topics": [
        "fit.adisop",
        "fit.isop"
      ]
    },
    {
      "page": "fuzcluster",
      "title": "Clustering for Continuous Fuzzy Data",
      "topics": [
        "fuzcluster",
        "summary.fuzcluster"
      ]
    },
    {
      "page": "fuzdiscr",
      "title": "Estimation of a Discrete Distribution for Fuzzy Data (Data in Belief Function Framework)",
      "topics": [
        "fuzdiscr"
      ]
    },
    {
      "page": "gom.em",
      "title": "Discrete (Rasch) Grade of Membership Model",
      "topics": [
        "anova.gom",
        "gom.em",
        "IRT.irfprob.gom",
        "IRT.likelihood.gom",
        "IRT.modelfit.gom",
        "IRT.posterior.gom",
        "logLik.gom",
        "summary.gom",
        "summary.IRT.modelfit.gom"
      ]
    },
    {
      "page": "gom.jml",
      "title": "Grade of Membership Model (Joint Maximum Likelihood Estimation)",
      "topics": [
        "gom.jml"
      ]
    },
    {
      "page": "greenyang.reliability",
      "title": "Reliability for Dichotomous Item Response Data Using the Method of Green and Yang (2009)",
      "topics": [
        "greenyang.reliability"
      ]
    },
    {
      "page": "invariance.alignment",
      "title": "Alignment Procedure for Linking under Approximate Invariance",
      "topics": [
        "invariance.alignment",
        "invariance_alignment_cfa_config",
        "invariance_alignment_constraints",
        "invariance_alignment_simulate",
        "summary.invariance.alignment",
        "summary.invariance_alignment_constraints"
      ]
    },
    {
      "page": "IRT.mle",
      "title": "Person Parameter Estimation",
      "topics": [
        "IRT.mle"
      ]
    },
    {
      "page": "isop",
      "title": "Fit Unidimensional ISOP and ADISOP Model to Dichotomous and Polytomous Item Responses",
      "topics": [
        "isop.dich",
        "isop.poly",
        "plot.isop",
        "summary.isop"
      ]
    },
    {
      "page": "isop.scoring",
      "title": "Scoring Persons and Items in the ISOP Model",
      "topics": [
        "isop.scoring"
      ]
    },
    {
      "page": "isop.test",
      "title": "Testing the ISOP Model",
      "topics": [
        "isop.test",
        "summary.isop.test"
      ]
    },
    {
      "page": "latent.regression.em.raschtype",
      "title": "Latent Regression Model for the Generalized Logistic Item Response Model and the Linear Model for Normal Responses",
      "topics": [
        "latent.regression.em.normal",
        "latent.regression.em.raschtype",
        "summary.latent.regression"
      ]
    },
    {
      "page": "lavaan2mirt",
      "title": "Converting a 'lavaan' Model into a 'mirt' Model",
      "topics": [
        "lavaan2mirt"
      ]
    },
    {
      "page": "lc.2raters",
      "title": "Latent Class Model for Two Exchangeable Raters and One Item",
      "topics": [
        "lc.2raters",
        "summary.lc.2raters"
      ]
    },
    {
      "page": "likelihood.adjustment",
      "title": "Adjustment and Approximation of Individual Likelihood Functions",
      "topics": [
        "likelihood.adjustment"
      ]
    },
    {
      "page": "linking_2groups",
      "title": "Linking Two Groups",
      "topics": [
        "linking_2groups"
      ]
    },
    {
      "page": "linking.haberman",
      "title": "Linking in the 2PL/Generalized Partial Credit Model",
      "topics": [
        "L0_polish",
        "linking.haberman",
        "linking.haberman.lq",
        "linking_haberman_itempars_convert",
        "linking_haberman_itempars_prepare",
        "summary.linking.haberman",
        "summary.linking.haberman.lq"
      ]
    },
    {
      "page": "linking.haebara",
      "title": "Haebara and Stocking-Lord Linking of the 2PL Model for Multiple Studies",
      "topics": [
        "linking.haebara",
        "summary.linking.haebara"
      ]
    },
    {
      "page": "linking.robust",
      "title": "Robust Linking of Item Intercepts",
      "topics": [
        "linking.robust",
        "plot.linking.robust",
        "summary.linking.robust"
      ]
    },
    {
      "page": "locpolycor",
      "title": "Local Modeling of Thresholds and Polychoric Correlations",
      "topics": [
        "locpolycor"
      ]
    },
    {
      "page": "lq_fit",
      "title": "Fit a L_q Regression Model",
      "topics": [
        "dexppow",
        "lq_fit",
        "lq_fit_estimate_power",
        "rexppow"
      ]
    },
    {
      "page": "lsdm",
      "title": "Least Squares Distance Method of Cognitive Validation",
      "topics": [
        "lsdm",
        "plot.lsdm",
        "summary.lsdm"
      ]
    },
    {
      "page": "lsem.estimate",
      "title": "Local Structural Equation Models (LSEM)",
      "topics": [
        "lsem.bootstrap",
        "lsem.estimate",
        "lsem.MGM.stepfunctions",
        "lsem_local_weights",
        "plot.lsem",
        "summary.lsem"
      ]
    },
    {
      "page": "lsem.permutationTest",
      "title": "Permutation Test for a Local Structural Equation Model",
      "topics": [
        "lsem.permutationTest",
        "plot.lsem.permutationTest",
        "summary.lsem.permutationTest"
      ]
    },
    {
      "page": "lsem.test",
      "title": "Test a Local Structural Equation Model Based on Bootstrap",
      "topics": [
        "lsem.test"
      ]
    },
    {
      "page": "marginal.truescore.reliability",
      "title": "True-Score Reliability for Dichotomous Data",
      "topics": [
        "marginal.truescore.reliability"
      ]
    },
    {
      "page": "matrixfunctions.sirt",
      "title": "Some Matrix Functions",
      "topics": [
        "colCumsums.sirt",
        "rowCumsums.sirt",
        "rowIntervalIndex.sirt",
        "rowKSmallest.sirt",
        "rowKSmallest2.sirt",
        "rowMaxs.sirt",
        "rowMins.sirt"
      ]
    },
    {
      "page": "mcmc_coef",
      "title": "Some Methods for Objects of Class 'mcmc.list'",
      "topics": [
        "mcmc_coef",
        "mcmc_confint",
        "mcmc_derivedPars",
        "mcmc_plot",
        "mcmc_summary",
        "mcmc_vcov",
        "mcmc_WaldTest",
        "summary.mcmc_WaldTest"
      ]
    },
    {
      "page": "mcmc_Rhat",
      "title": "Computation of the Rhat Statistic from a Single MCMC Chain",
      "topics": [
        "mcmc_Rhat"
      ]
    },
    {
      "page": "mcmc.2pno",
      "title": "MCMC Estimation of the Two-Parameter Normal Ogive Item Response Model",
      "topics": [
        "mcmc.2pno"
      ]
    },
    {
      "page": "mcmc.2pno.ml",
      "title": "Random Item Response Model / Multilevel IRT Model",
      "topics": [
        "mcmc.2pno.ml"
      ]
    },
    {
      "page": "mcmc.2pnoh",
      "title": "MCMC Estimation of the Hierarchical IRT Model for Criterion-Referenced Measurement",
      "topics": [
        "mcmc.2pnoh"
      ]
    },
    {
      "page": "mcmc.3pno.testlet",
      "title": "3PNO Testlet Model",
      "topics": [
        "mcmc.3pno.testlet"
      ]
    },
    {
      "page": "mcmc.list.descriptives",
      "title": "Computation of Descriptive Statistics for a 'mcmc.list' Object",
      "topics": [
        "mcmc.list.descriptives"
      ]
    },
    {
      "page": "mcmclist2coda",
      "title": "Write Coda File from an Object of Class 'mcmc.list'",
      "topics": [
        "mcmclist2coda"
      ]
    },
    {
      "page": "md.pattern.sirt",
      "title": "Response Pattern in a Binary Matrix",
      "topics": [
        "md.pattern.sirt"
      ]
    },
    {
      "page": "mgsem",
      "title": "Estimation of Multiple-Group Structural Equation Models",
      "topics": [
        "mgsem"
      ]
    },
    {
      "page": "mirt.specify.partable",
      "title": "Specify or modify a Parameter Table in 'mirt'",
      "topics": [
        "mirt.specify.partable"
      ]
    },
    {
      "page": "mirt.wrapper",
      "title": "Some Functions for Wrapping with the 'mirt' Package",
      "topics": [
        "IRT.expectedCounts.MultipleGroupClass",
        "IRT.expectedCounts.SingleGroupClass",
        "IRT.irfprob.MultipleGroupClass",
        "IRT.irfprob.SingleGroupClass",
        "IRT.likelihood.MultipleGroupClass",
        "IRT.likelihood.SingleGroupClass",
        "IRT.posterior.MultipleGroupClass",
        "IRT.posterior.SingleGroupClass",
        "mirt.wrapper",
        "mirt.wrapper.coef",
        "mirt.wrapper.fscores",
        "mirt.wrapper.itemplot",
        "mirt.wrapper.posterior",
        "mirt_summary"
      ]
    },
    {
      "page": "mle.pcm.group",
      "title": "Maximum Likelihood Estimation of Person or Group Parameters in the Generalized Partial Credit Model",
      "topics": [
        "mle.pcm.group"
      ]
    },
    {
      "page": "modelfit.sirt",
      "title": "Assessing Model Fit and Local Dependence by Comparing Observed and Expected Item Pair Correlations",
      "topics": [
        "IRT.modelfit.sirt",
        "modelfit.cor.poly",
        "modelfit.sirt"
      ]
    },
    {
      "page": "monoreg.rowwise",
      "title": "Monotone Regression for Rows or Columns in a Matrix",
      "topics": [
        "monoreg.colwise",
        "monoreg.rowwise"
      ]
    },
    {
      "page": "nedelsky.sim",
      "title": "Functions for the Nedelsky Model",
      "topics": [
        "nedelsky.irf",
        "nedelsky.latresp",
        "nedelsky.sim"
      ]
    },
    {
      "page": "noharm.sirt",
      "title": "NOHARM Model in R",
      "topics": [
        "noharm.sirt",
        "summary.noharm.sirt"
      ]
    },
    {
      "page": "np.dich",
      "title": "Nonparametric Estimation of Item Response Functions",
      "topics": [
        "np.dich"
      ]
    },
    {
      "page": "parmsummary_extend",
      "title": "Includes Confidence Interval in Parameter Summary Table",
      "topics": [
        "parmsummary_extend"
      ]
    },
    {
      "page": "pbivnorm2",
      "title": "Cumulative Function for the Bivariate Normal Distribution",
      "topics": [
        "pbivnorm2"
      ]
    },
    {
      "page": "pcm.conversion",
      "title": "Conversion of the Parameterization of the Partial Credit Model",
      "topics": [
        "pcm.conversion"
      ]
    },
    {
      "page": "pcm.fit",
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