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sirt

Supplementary Item Response Theory Models

If you use sirt and have suggestions for improvement or have found bugs, please email me at robitzsch@leibniz-ipn.de. Please always provide a minimal dataset, necessary to demonstrate the problem, a minimal runnable code necessary to reproduce the issue, which can be run on the given dataset, and all necessary information on the used librarys, the R version, and the OS it is run on, perhaps a sessionInfo().

CRAN version

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

utils::install.packages("sirt")

GitHub version

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

devtools::install_github("alexanderrobitzsch/sirt")

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Version

Install

install.packages('sirt')

Monthly Downloads

11,682

Version

4.2-133

License

GPL (>= 2)

Issues

Pull Requests

Stars

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Repository

https://github.com/alexanderrobitzsch/sirt

Homepage

https://sites.google.com/view/alexander-robitzsch/software

Maintainer

Alexander Robitzsch

Last Published

September 27th, 2025

Functions in sirt (4.2-133)

Functions for the Beta Item Response Model

Estimation of the \(Q_3\) Statistic (Yen, 1984)

Person Parameter Estimation

Extended Bradley-Terry Model

R2noharm.jackknife

Jackknife Estimation of NOHARM Analysis

Running ConQuest From Within R

\(Q_3\) Statistic of Yen (1984) for Testlets

automatic.recode

Automatic Method of Finding Keys in a Dataset with Raw Item Responses

EAP Factor Score Estimation

Estimation of a NOHARM Analysis from within R

Confirmatory DETECT and polyDETECT Analysis

data.activity.itempars

Item Parameters Cultural Activities

Categorize and Decategorize Variables in a Data Frame

Estimation of a Unidimensional Factor Model under Full and Partial Measurement Invariance

Examples with Datasets from Eid and Schmidt (2014)

Datasets from Borg and Staufenbiel (2007)

class.accuracy.rasch

Classification Accuracy in the Rasch Model

Nonparametric Estimation of Conditional Covariances of Item Pairs

BEFKI Dataset (Schroeders, Schipolowski, & Wilhelm, 2015)

Dataset Big 5 from qgraph Package

Dataset with Mixed Dichotomous and Polytomous Item Responses

Dataset for Invariance Testing with 4 Groups

Multilevel Datasets

Datasets for Local Structural Equation Models / Moderated Factor Analysis

Longitudinal Dataset

data.pirlsmissing

Dataset from PIRLS Study with Missing Responses

data.liking.science

Dataset 'Liking For Science'

Dataset with Raw Item Responses

Rating Datasets

data.pisa2006Read

Dataset PISA 2006 Reading

C-Test Datasets

Dataset European Social Survey 2005

Datasets for Pairwise Comparisons

Dataset PISA Reading

Dataset Mathematics

Datasets for NOHARM Analysis

data.pars1.rasch

Item Parameters for Three Studies Obtained by 1PL and 2PL Estimation

Some Datasets from McDonald's Test Theory Book

Dataset PISA Mathematics

Item Parameters from Two PISA Studies

dif.logistic.regression

Differential Item Functioning using Logistic Regression Analysis

Dataset Reading

Datasets from Reckase' Book Multidimensional Item Response Theory

dif.strata.variance

Stratified DIF Variance

Dataset TIMSS Mathematics

Converting a Data Frame from Wide Format in a Long Format

Some Example Datasets for the sirt Package

data.timss07.G8.RUS

TIMSS 2007 Grade 8 Mathematics and Science Russia

Dataset Used in Stoyan, Pommerening and Wuensche (2018)

Calculation of the DETECT and polyDETECT Index

equating.rasch.jackknife

Jackknife Equating Error in Generalized Logistic Rasch Model

eigenvalues.manymatrices

Computation of Eigenvalues of Many Symmetric Matrices

dirichlet.simul

Simulation of a Dirichlet Distributed Vectors

Functional Unidimensional Item Response Model

Exploratory DETECT Analysis

Comparing Regression Parameters of Different lavaan Models Fitted to the Same Dataset

Maximum Likelihood Estimation of the Dirichlet Distribution

Fitting the ISOP and ADISOP Model for Frequency Tables

Equating in the Generalized Logistic Rasch Model

Estimation of a Discrete Distribution for Fuzzy Data (Data in Belief Function Framework)

Clustering for Continuous Fuzzy Data

Fit Unidimensional ISOP and ADISOP Model to Dichotomous and Polytomous Item Responses

Testing the ISOP Model

invariance.alignment

Alignment Procedure for Linking under Approximate Invariance

Grade of Membership Model (Joint Maximum Likelihood Estimation)

Discrete (Rasch) Grade of Membership Model

latent.regression.em.raschtype

Latent Regression Model for the Generalized Logistic Item Response Model and the Linear Model for Normal Responses

greenyang.reliability

Reliability for Dichotomous Item Response Data Using the Method of Green and Yang (2009)

Scoring Persons and Items in the ISOP Model

Fit of a \(L_q\) Regression Model

linking.haebara

Haebara Linking of the 2PL Model for Multiple Studies

Local Modeling of Thresholds and Polychoric Correlations

linking_2groups

Linking Two Groups

Converting a lavaan Model into a mirt Model

Latent Class Model for Two Exchangeable Raters and One Item

Robust Linking of Item Intercepts

likelihood.adjustment

Adjustment and Approximation of Individual Likelihood Functions

linking.haberman

Linking in the 2PL/Generalized Partial Credit Model

Least Squares Distance Method of Cognitive Validation

matrixfunctions.sirt

Some Matrix Functions

Random Item Response Model / Multilevel IRT Model

mcmc.3pno.testlet

3PNO Testlet Model

Test a Local Structural Equation Model Based on Bootstrap

MCMC Estimation of the Hierarchical IRT Model for Criterion-Referenced Measurement

marginal.truescore.reliability

True-Score Reliability for Dichotomous Data

mcmc.list.descriptives

Computation of Descriptive Statistics for a mcmc.list Object

MCMC Estimation of the Two-Parameter Normal Ogive Item Response Model

Local Structural Equation Models (LSEM)

lsem.permutationTest

Permutation Test for a Local Structural Equation Model

md.pattern.sirt

Response Pattern in a Binary Matrix

monoreg.rowwise

Monotone Regression for Rows or Columns in a Matrix

Some Functions for Wrapping with the mirt Package

Write Coda File from an Object of Class mcmc.list

Assessing Model Fit and Local Dependence by Comparing Observed and Expected Item Pair Correlations

Maximum Likelihood Estimation of Person or Group Parameters in the Generalized Partial Credit Model

Estimation of Multiple-Group Structural Equation Models

Computation of the Rhat Statistic from a Single MCMC Chain

mirt.specify.partable

Specify or modify a Parameter Table in mirt

Some Methods for Objects of Class mcmc.list

Nonparametric Estimation of Item Response Functions

Item and Person Fit Statistics for the Partial Credit Model

person.parameter.rasch.copula

Person Parameter Estimation of the Rasch Copula Model (Braeken, 2011)

Person Fit Statistics for the Rasch Model

Calculation of Probabilities and Moments for the Generalized Logistic Item Response Model

parmsummary_extend

Includes Confidence Interval in Parameter Summary Table

Cumulative Function for the Bivariate Normal Distribution

Conversion of the Parameterization of the Partial Credit Model

NOHARM Model in R

nedelsky-methods

Functions for the Nedelsky Model

plausible.value.imputation.raschtype

Plausible Value Imputation in Generalized Logistic Item Response Model

Polychoric Correlation

Probabilistic Guttman Model

Plot Method for Object of Class np.dich

Multidimensional IRT Copula Model

Plot Function for Objects of Class mcmc.sirt

Estimation of the Partial Credit Model using the Eigenvector Method

prmse.subscores.scales

Proportional Reduction of Mean Squared Error (PRMSE) for Subscale Scores

Calculation of Quasi Monte Carlo Integration Points

prior_model_parse

Parsing a Prior Model

rasch.jml.jackknife1

Jackknifing the IRT Model Estimated by Joint Maximum Likelihood (JML)

Multidimensional Latent Class 1PL and 2PL Model

Joint Maximum Likelihood (JML) Estimation of the Rasch Model

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

rasch.pairwise.itemcluster

Pairwise Estimation of the Rasch Model for Locally Dependent Items

rasch.jml.biascorr

Bias Correction of Item Parameters for Joint Maximum Likelihood Estimation in the Rasch model

Estimation of the Rasch Model with Variational Approximation

PROX Estimation Method for the Rasch Model

Pairwise Marginal Likelihood Estimation for the Probit Rasch Model

Pairwise Estimation Method of the Rasch Model

Inverse Gamma Distribution in Prior Sample Size Parameterization

Hierarchical Rater Model Based on Signal Detection Theory (HRM-SDT)

reliability.nonlinearSEM

Estimation of Reliability for Confirmatory Factor Analyses Based on Dichotomous Data

scale_group_means

Scaling of Group Means and Standard Deviations

Simulate from Ramsay's Quotient Model

Simulation of the Rasch Model with Locally Dependent Responses

Statistical Implicative Analysis (SIA)

Simulation of a Multivariate Normal Distribution with Exact Moments

Creates Group-Wise Item Response Dataset

Rater Facets Models with Item/Rater Intercepts and Slopes

stratified.cronbach.alpha

Stratified Cronbach's Alpha

tools:::Rd_package_title("sirt")

Simulate from Generalized Logistic Item Response Model

Converting a fitted TAM Object into a mirt Object

summary.mcmc.sirt

Summary Method for Objects of Class mcmc.sirt

sirt_eigenvalues

First Eigenvalues of a Symmetric Matrix

testlet.marginalized

Marginal Item Parameters from a Testlet (Bifactor) Model

Defunct sirt Functions

Multidimensional Noncompensatory, Compensatory and Partially Compensatory Item Response Model

Utility Functions in sirt

Weighted Likelihood Estimation of Person Abilities

unidim.test.csn

Test for Unidimensionality of CSN

Tetrachoric Correlation Matrix

Conversion of Trait Scores \(\theta\) into True Scores \(\tau ( \theta )\)

wle.rasch.jackknife

Standard Error Estimation of WLE by Jackknifing

xxirt_createParTable

Create Item Response Functions and Item Parameter Table

User Defined Item Response Model

xxirt_createThetaDistribution

Creates a User Defined Theta Distribution