sirt v3.9-4


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Supplementary Item Response Theory Models

Supplementary functions for item response models aiming to complement existing R packages. The functionality includes among others multidimensional compensatory and noncompensatory IRT models (Reckase, 2009, <doi:10.1007/978-0-387-89976-3>), MCMC for hierarchical IRT models and testlet models (Fox, 2010, <doi:10.1007/978-1-4419-0742-4>), NOHARM (McDonald, 1982, <doi:10.1177/014662168200600402>), Rasch copula model (Braeken, 2011, <doi:10.1007/s11336-010-9190-4>; Schroeders, Robitzsch & Schipolowski, 2014, <doi:10.1111/jedm.12054>), faceted and hierarchical rater models (DeCarlo, Kim & Johnson, 2011, <doi:10.1111/j.1745-3984.2011.00143.x>), ordinal IRT model (ISOP; Scheiblechner, 1995, <doi:10.1007/BF02301417>), DETECT statistic (Stout, Habing, Douglas & Kim, 1996, <doi:10.1177/014662169602000403>), local structural equation modeling (LSEM; Hildebrandt, Luedtke, Robitzsch, Sommer & Wilhelm, 2016, <doi:10.1080/00273171.2016.1142856>).



Supplementary Item Response Theory Models

If you use sirt and have suggestions for improvement or have found bugs, please email me at


The manual may be found here

CRAN version

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The official version of sirt is hosted on CRAN and may be found here. The CRAN version can be installed from within R using:


GitHub version

The version hosted here is the development version of sirt. The GitHub version can be installed using devtools as:


Functions in sirt

Name Description
Q3 Estimation of the \(Q_3\) Statistic (Yen, 1984)
automatic.recode Automatic Method of Finding Keys in a Dataset with Raw Item Responses
Q3.testlet \(Q_3\) Statistic of Yen (1984) for Testlets
R2noharm Estimation of a NOHARM Analysis from within R
IRT.mle Person Parameter Estimation
R2noharm.jackknife Jackknife Estimation of NOHARM Analysis
brm-Methods Functions for the Beta Item Response Model
R2noharm.EAP EAP Factor Score Estimation
R2conquest Running ConQuest From Within R
btm Extended Bradley-Terry Model
data.big5 Dataset Big 5 from qgraph Package
categorize Categorize and Decategorize Variables in a Data Frame
data.befki BEFKI Dataset (Schroeders, Schipolowski, & Wilhelm, 2015)
data.mixed1 Dataset with Mixed Dichotomous and Polytomous Item Responses
data.activity.itempars Item Parameters Cultural Activities
data.mcdonald Some Datasets from McDonald's Test Theory Book Dataset 'Liking For Science' Nonparametric Estimation of Conditional Covariances of Item Pairs
data.long Longitudinal Dataset
data.ess2005 Dataset European Social Survey 2005
data.eid Examples with Datasets from Eid and Schmidt (2014) Datasets from Borg and Staufenbiel (2007)
data.g308 C-Test Datasets
conf.detect Confirmatory DETECT and polyDETECT Analysis
data.reck Datasets from Reckase' Book Multidimensional Item Response Theory Dataset Reading Multilevel Datasets
class.accuracy.rasch Classification Accuracy in the Rasch Model
data.noharm Datasets for NOHARM Analysis
data.timss07.G8.RUS TIMSS 2007 Grade 8 Mathematics and Science Russia
data.ratings Rating Datasets
data.trees Dataset Used in Stoyan, Pommerening and Wuensche (2018) Datasets for Pairwise Comparisons
data.timss Dataset TIMSS Mathematics
data.pisaRead Dataset PISA Reading
data.sirt Some Example Datasets for the sirt Package
data.raw1 Dataset with Raw Item Responses
data.inv4gr Dataset for Invariance Testing with 4 Groups
dif.variance DIF Variance
data.lsem Datasets for Local Structural Equation Models / Moderated Factor Analysis
dirichlet.mle Maximum Likelihood Estimation of the Dirichlet Distribution
fuzdiscr Estimation of a Discrete Distribution for Fuzzy Data (Data in Belief Function Framework)
data.pars1.rasch Item Parameters for Three Studies Obtained by 1PL and 2PL Estimation
data.pirlsmissing Dataset from PIRLS Study with Missing Responses
dif.strata.variance Stratified DIF Variance
dif.logistic.regression Differential Item Functioning using Logistic Regression Analysis
eigenvalues.manymatrices Computation of Eigenvalues of Many Symmetric Matrices
dirichlet.simul Simulation of a Dirichlet Distributed Vectors
gom.em Discrete (Rasch) Grade of Membership Model
isop Fit Unidimensional ISOP and ADISOP Model to Dichotomous and Polytomous Item Responses
invariance.alignment Alignment Procedure for Linking under Approximate Invariance
data.math Dataset Mathematics
fit.isop Fitting the ISOP and ADISOP Model for Frequency Tables
data.pisaPars Item Parameters from Two PISA Studies
detect.index Calculation of the DETECT and polyDETECT Index
data.pisaMath Dataset PISA Mathematics
data.wide2long Converting a Data Frame from Wide Format in a Long Format
fuzcluster Clustering for Continuous Fuzzy Data
lc.2raters Latent Class Model for Two Exchangeable Raters and One Item
gom.jml Grade of Membership Model (Joint Maximum Likelihood Estimation)
greenyang.reliability Reliability for Dichotomous Item Response Data Using the Method of Green and Yang (2009)
likelihood.adjustment Adjustment and Approximation of Individual Likelihood Functions
equating.rasch Equating in the Generalized Logistic Rasch Model
linking.haberman Linking in the 2PL/Generalized Partial Credit Model
mirt.wrapper Some Functions for Wrapping with the mirt Package Random Item Response Model / Multilevel IRT Model Maximum Likelihood Estimation of Person or Group Parameters in the Generalized Partial Credit Model
mcmc.2pno MCMC Estimation of the Two-Parameter Normal Ogive Item Response Model
f1d.irt Functional Unidimensional Item Response Model
expl.detect Exploratory DETECT Analysis
linking.robust Robust Linking of Item Intercepts
latent.regression.em.raschtype Latent Regression Model for the Generalized Logistic Item Response Model and the Linear Model for Normal Responses
lavaan2mirt Converting a lavaan Model into a mirt Model
modelfit.sirt Assessing Model Fit and Local Dependence by Comparing Observed and Expected Item Pair Correlations
linking.haebara Haebara Linking of the 2PL Model for Multiple Studies
equating.rasch.jackknife Jackknife Equating Error in Generalized Logistic Rasch Model
isop.test Testing the ISOP Model
isop.scoring Scoring Persons and Items in the ISOP Model
matrixfunctions.sirt Some Matrix Functions
marginal.truescore.reliability True-Score Reliability for Dichotomous Data
monoreg.rowwise Monotone Regression for Rows or Columns in a Matrix
lsem.permutationTest Permutation Test for a Local Structural Equation Model
lsem.estimate Local Structural Equation Models (LSEM)
lsdm Least Squares Distance Method of Cognitive Validation
prob.guttman Probabilistic Guttman Model
md.pattern.sirt Response Pattern in a Binary Matrix
mcmc.2pnoh MCMC Estimation of the Hierarchical IRT Model for Criterion-Referenced Measurement
pbivnorm2 Cumulative Function for the Bivariate Normal Distribution
mcmclist2coda Write Coda File from an Object of Class mcmc.list
mcmc_coef Some Methods for Objects of Class mcmc.list
pcm.conversion Conversion of the Parameterization of the Partial Credit Model Plot Method for Object of Class np.dich
mcmc.list.descriptives Computation of Descriptive Statistics for a mcmc.list Object
nedelsky-methods Functions for the Nedelsky Model
mcmc_Rhat Computation of the Rhat Statistic from a Single MCMC Chain
np.dich Nonparametric Estimation of Item Response Functions
mirt.specify.partable Specify or modify a Parameter Table in mirt
noharm.sirt NOHARM Model in R
parmsummary_extend Includes Confidence Interval in Parameter Summary Table
mcmc.3pno.testlet 3PNO Testlet Model
personfit.stat Person Fit Statistics for the Rasch Model Item and Person Fit Statistics for the Partial Credit Model
prior_model_parse Parsing a Prior Model
rasch.jml.biascorr Bias Correction of Item Parameters for Joint Maximum Likelihood Estimation in the Rasch model
rasch.jml Joint Maximum Likelihood (JML) Estimation of the Rasch Model
prmse.subscores.scales Proportional Reduction of Mean Squared Error (PRMSE) for Subscale Scores
rm.sdt Hierarchical Rater Model Based on Signal Detection Theory (HRM-SDT)
scale_group_means Scaling of Group Means and Standard Deviations
plot.mcmc.sirt Plot Function for Objects of Class mcmc.sirt
plausible.value.imputation.raschtype Plausible Value Imputation in Generalized Logistic Item Response Model
person.parameter.rasch.copula Person Parameter Estimation of the Rasch Copula Model (Braeken, 2011)
qmc.nodes Calculation of Quasi Monte Carlo Integration Points
rasch.copula2 Multidimensional IRT Copula Model
polychoric2 Polychoric Correlation
rasch.evm.pcm Estimation of the Partial Credit Model using the Eigenvector Method Estimation of the Rasch Model with Variational Approximation
stratified.cronbach.alpha Stratified Cronbach's Alpha
rasch.mirtlc Multidimensional Latent Class 1PL and 2PL Model
rasch.jml.jackknife1 Jackknifing the IRT Model Estimated by Joint Maximum Likelihood (JML)
smirt Multidimensional Noncompensatory, Compensatory and Partially Compensatory Item Response Model
rasch.prox PROX Estimation Method for the Rasch Model
sirt_eigenvalues First Eigenvalues of a Symmetric Matrix
sirt-utilities Utility Functions in sirt
rasch.pml3 Pairwise Marginal Likelihood Estimation for the Probit Rasch Model
rasch.pairwise.itemcluster Pairwise Estimation of the Rasch Model for Locally Dependent Items
rinvgamma2 Inverse Gamma Distribution in Prior Sample Size Parameterization
tetrachoric2 Tetrachoric Correlation Matrix
testlet.marginalized Marginal Item Parameters from a Testlet (Bifactor) Model
xxirt User Defined Item Response Model
xxirt_createParTable Create Item Response Functions and Item Parameter Table
tam2mirt Converting a fitted TAM Object into a mirt Object
summary.mcmc.sirt Summary Method for Objects of Class mcmc.sirt
rm.facets Rater Facets Models with Item/Rater Intercepts and Slopes
sia.sirt Statistical Implicative Analysis (SIA)
truescore.irt Conversion of Trait Scores \(\theta\) into True Scores \(\tau ( \theta )\)
sim.qm.ramsay Simulate from Ramsay's Quotient Model
sim.rasch.dep Simulation of the Rasch Model with Locally Dependent Responses
xxirt_createThetaDistribution Creates a User Defined Theta Distribution
sim.raschtype Simulate from Generalized Logistic Item Response Model
unidim.test.csn Test for Unidimensionality of CSN
reliability.nonlinearSEM Estimation of Reliability for Confirmatory Factor Analyses Based on Dichotomous Data
rasch.pairwise Pairwise Estimation Method of the Rasch Model
pgenlogis Calculation of Probabilities and Moments for the Generalized Logistic Item Response Model
rasch.mml2 Estimation of the Generalized Logistic Item Response Model, Ramsay's Quotient Model, Nonparametric Item Response Model, Pseudo-Likelihood Estimation and a Missing Data Item Response Model
resp_groupwise Creates Group-Wise Item Response Dataset
sirt-defunct Defunct sirt Functions
sirt-package sirt
wle.rasch Weighted Likelihood Estimation of Person Abilities
wle.rasch.jackknife Standard Error Estimation of WLE by Jackknifing
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Type Package
Date 2020-02-17 12:57:09
LinkingTo pbv, Rcpp, RcppArmadillo
License GPL (>= 2)
NeedsCompilation yes
Packaged 2020-02-17 12:05:12 UTC; sunpn563
Repository CRAN
Date/Publication 2020-02-17 19:00:03 UTC

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