[IRT] Item Response Theory - Stata

1 Stata ITEM Response THEORYREFERENCE MANUALRELEASE 18 A Stata Press PublicationStataCorp LLCC ollege Station, Texas Copyrightc 1985 2023 StataCorp LLCAll rights reservedVersion 18 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in TEXISBN-10: 1-59718-386-5 ISBN-13: 978-1-59718-386-4 This manual is protected by copyright. All rights are reserved. No part of this manual may be reproduced, storedin a retrieval system, or transcribed, in any form or by any means electronic, mechanical, photocopy, recording, orotherwise without the prior written permission of StataCorp LLC unless permitted subject to the terms and conditionsof a license granted to you by StataCorp LLC to use the software and documentation.

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4 : Release 18. Statistical Software. College Station, TX: StataCorp .. introduction to IRT models1 Control Panel .. IRT Control Panel20irt 1pl .. One-parameter logistic model29irt 1pl postestimation .. Postestimation tools for irt 1pl40irt 2pl .. Two-parameter logistic model45irt 2pl postestimation .. Postestimation tools for irt 2pl56irt 3pl .. Three-parameter logistic model61irt 3pl postestimation .. Postestimation tools for irt 3pl73irt grm .. Graded Response model78irt grm postestimation .. Postestimation tools for irt grm89irt nrm .. Nominal Response model94irt nrm postestimation .. Postestimation tools for irt nrm 104irt pcm.

5 Partial credit model 109irt pcm postestimation .. Postestimation tools for irt pcm 119irt rsm .. Rating scale model 124irt rsm postestimation .. Postestimation tools for irt rsm 134irt hybrid .. Hybrid IRT models 139irt hybrid postestimation .. Postestimation tools for irt hybrid 154irt, group( ) .. IRT models for multiple groups 160irt, group( ) postestimation .. Postestimation tools for group IRT 173irt constraints .. Specifying constraints 177estat report .. Report estimated IRT parameters 188estat greport .. Report estimated group IRT parameters 195irtgraph icc .. Item characteristic curve plot 202irtgraph tcc.

6 Test characteristic curve plot 218irtgraph iif .. Item information function plot 223irtgraph tif .. Test information function plot 229 DIF .. introduction to differential item functioning 235diflogistic .. Logistic regression DIF 238difmh .. Mantel Haenszel DIF 243 Glossary ..249 Subject and author index ..253iCross-referencing the documentationWhen reading this manual, you will find references to other Stata manuals, for example,[U] 27 Overview of Stata estimation commands; [R]regress; and [D]reshape. The first ex-ample is a reference to chapter 27,Overview of Stata estimation commands, in theUser s Guide;the second is a reference to theregressentry in theBase Reference Manual.

7 And the third is areference to thereshapeentry in theData Management Reference the manuals in the Stata Documentation have a shorthand notation:[GSM]Getting Started with Stata for Mac[GSU]Getting Started with Stata for Unix[GSW]Getting Started with Stata for Windows[U] Stata User s Guide[R] Stata Base Reference Manual[ADAPT] Stata Adaptive Designs: Group Sequential Trials Reference Manual[BAYES] Stata Bayesian analysis Reference Manual[BMA] Stata Bayesian Model Averaging Reference Manual[CAUSAL] Stata Causal Inference and Treatment-Effects Estimation Reference Manual[CM] Stata Choice Models Reference Manual[D] Stata Data Management Reference Manual[DSGE] Stata Dynamic Stochastic General Equilibrium Models Reference Manual[ERM] Stata Extended Regression Models Reference Manual[FMM] Stata Finite Mixture Models Reference Manual[FN] Stata Functions Reference Manual[G] Stata Graphics Reference Manual[IRT] Stata Item Response Theory Reference Manual[LASSO]

8 Stata Lasso Reference Manual[XT] Stata Longitudinal-Data/Panel-Data Reference Manual[META] Stata Meta- analysis Reference Manual[ME] Stata Multilevel Mixed-Effects Reference Manual[MI] Stata Multiple-Imputation Reference Manual[MV] Stata Multivariate Statistics Reference Manual[PSS] Stata Power, Precision, and Sample-Size Reference Manual[P] Stata Programming Reference Manual[RPT] Stata Reporting Reference Manual[SP] Stata Spatial Autoregressive Models Reference Manual[SEM] Stata Structural Equation Modeling Reference Manual[SVY] Stata Survey Data Reference Manual[ST] Stata Survival analysis Reference Manual[TABLES] Stata Customizable Tables and Collected Results Reference Manual[TS] Stata time -Series Reference Manual[ I ] Stata Index[M]Mata Reference ManualiiTitleirt introduction to IRT modelsDescriptionRemarks and examplesReferencesAlso seeDescriptionItem Response Theory (IRT) is used in the design, analysis , scoring, and comparison of tests andsimilar instruments whose purpose is to measure unobservable characteristics of the respondents.

9 Thisentry discusses some fundamental and theoretical aspects ofIRTand illustrates these with entries that follow describe how you can use theirtsuite of commands to fit a variety ofIRTmodels and to evaluate the results. The commands for fitting models can be grouped by the typeof responses you are Response modelsirt 1plOne-parameter logistic modelirt 2plTwo-parameter logistic modelirt 3plThree-parameter logistic modelCategorical Response modelsirt grmGraded Response modelirt nrmNominal Response modelirt pcmPartial credit modelirt rsmRating scale modelMultiple IRT models combinedirt hybridHybrid IRT modelsThese models can allow for differences across groups in the IRT modelsirt, group( )

10 IRT models for multiple groupsConstraints can be applied when fitting anyIRTmodel, and they are particularly useful forconstraining parameters across groups in multiple-group constraintsSpecifying constraints12 irt introduction to IRT modelsAfter fitting anyIRTmodel, results can be reported, interpreted, and evaluated using graphsirtgraph iccItem characteristic curve plotirtgraph tccTest characteristic curve plotirtgraph iifItem information function plotirtgraph tifTest information function plotIRT reportsestat reportReport estimated IRT parametersestat greportReport estimated group IRT parametersModel-specific postestimation overviewirt 1pl postestimationPostestimation tools for irt 1plirt 2pl postestimationPostestimation tools for irt 2plirt 3pl postestimationPostestimation tools for irt 3plirt grm postestimationPostestimation tools for irt grmirt nrm postestimationPostestimation tools for irt nrmirt pcm postestimationPostestimation tools for irt pcmirt rsm