Modular Open-Source Software for Item Factor Analysis

This article introduces an item factor analysis (IFA) module for OpenMx, a free, open-source, and modular statistical modeling package that runs within the R programming environment on GNU/Linux, Mac OS X, and Microsoft Windows. The IFA module offers a novel model specification language that is well suited to programmatic generation and manipulation of models. Modular organization of the source code facilitates the easy addition of item models, item parameter estimation algorithms, optimizers, test scoring algorithms, and fit diagnostics all within an integrated framework. Three short example scripts are presented for fitting item parameters, latent distribution parameters, and a multiple group model. The availability of both IFA and structural equation modeling in the same software is a step toward the unification of these two methodologies.

[1]  R. D. Bock,et al.  Marginal maximum likelihood estimation of item parameters , 1982 .

[2]  David J. Bartholomew,et al.  The Goodness of Fit of Latent Trait Models in Attitude Measurement , 1999 .

[3]  Ke-Hai Yuan,et al.  Information Matrices and Standard Errors for MLEs of Item Parameters in IRT , 2014, Psychometrika.

[4]  Jan de Leeuw,et al.  On the relationship between item response theory and factor analysis of discretized variables , 1987 .

[5]  Raymond J. Adams,et al.  The Multidimensional Random Coefficients Multinomial Logit Model , 1997 .

[6]  Mike W.-L. Cheung,et al.  metaSEM: an R package for meta-analysis using structural equation modeling , 2015, Front. Psychol..

[7]  R. Jennrich,et al.  Standard errors for EM estimation , 2000 .

[8]  Taehoon Kang,et al.  An Investigation of the Performance of the Generalized S-X2 Item-Fit Index for Polytomous IRT Models , 2007 .

[9]  Rob Forsyth,et al.  Gross Motor Function Measure‐66 trajectories in children recovering after severe acquired brain injury , 2015, Developmental medicine and child neurology.

[10]  Halbert White,et al.  Estimation, inference, and specification analysis , 1996 .

[11]  D. Andrich.  Rating Scale Analysis , 1999 .

[12]  Li Cai,et al.  A Two-Tier Full-Information Item Factor Analysis Model with Applications , 2010 .

[13]  D. Thissen,et al.  Local Dependence Indexes for Item Pairs Using Item Response Theory , 1997 .

[14]  Mary Pommerich,et al.  Item Response Theory for Scores on Tests Including Polytomous Items with Ordered Responses , 1995 .

[15]  Lao Juan,et al.  Development and Validation of a Scale for Measuring Instructors' Attitudes toward Concept-Based or Reform-Oriented Teaching of Introductory Statistics in the Health and Behavioral Sciences , 2010, 1007.3219.

[16]  D. Oakes.  Direct calculation of the information matrix via the EM , 1999 .

[17]  E. Muraki,et al.  Full-Information Item Factor Analysis , 1988 .

[18]  Li Cai,et al.  HIGH-DIMENSIONAL EXPLORATORY ITEM FACTOR ANALYSIS BY A METROPOLIS–HASTINGS ROBBINS–MONRO ALGORITHM , 2010 .

[19]  D. Thissen,et al.  Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models , 2000 .

[20]  R. D. Bock,et al.  Adaptive EAP Estimation of Ability in a Microcomputer Environment , 1982 .

[21]  Li Cai,et al.  The Nominal Categories Item Response Model , 2010 .

[22]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[23]  Li Cai,et al.  Limited-information goodness-of-fit testing of hierarchical item factor models. , 2013, The British journal of mathematical and statistical psychology.

[24]  Eric Loken,et al.  Estimation of a four-parameter item response theory model. , 2010, The British journal of mathematical and statistical psychology.

[25]  Carol M. Woods.  Empirical Histograms in Item Response Theory With Ordinal Data , 2007 .

[26]  David Thissen,et al.  Trace Lines for Testlets: A Use of Multiple-Categorical-Response Models. , 1989 .

[27]  Li Cai.  High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm , 2010 .

[28]  R. Philip Chalmers,et al.  mirt: A Multidimensional Item Response Theory Package for the R Environment , 2012 .

[29]  Li Cai,et al.  Generalized full-information item bifactor analysis. , 2011, Psychological methods.

[30]  Kouichi Kishida,et al.  Evolution patterns of open-source software systems and communities , 2002, IWPSE '02.

[31]  Akihito Kamata,et al.  A Note on the Relation Between Factor Analytic and Item Response Theory Models , 2008 .

[32]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[33]  Mark Aberdour.  A people-focused , 2022 .

[34]  Xiao-Li Meng,et al.  Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm , 1991 .

[35]  G. Masters.  A rasch model for partial credit scoring , 1982 .

[36]  D. Watson,et al.  Development and validation of brief measures of positive and negative affect: the PANAS scales. , 1988, Journal of personality and social psychology.

[37]  Karl G. Jőreskog,et al.  LISREL: A General Computer Program for Estimating a Linear Structural Equation System Involving Multiple Indicators of Unmeasured Variables. , 1972 .

[38]  E. Muraki.  A GENERALIZED PARTIAL CREDIT MODEL: APPLICATION OF AN EM ALGORITHM , 1992 .

[39]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[40]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[41]  D. Thissen,et al.  Numerical Differentiation Methods for Computing Error Covariance Matrices in Item Response Theory Modeling , 2013 .

[42]  Margaret Wu,et al.  ACER conquest: generalised item response modelling software , 1998 .

[43]  F. Samejima.  Estimation of latent ability using a response pattern of graded scores , 1968 .

[44]  Carol M Woods,et al.  Ramsay-curve item response theory (RC-IRT) to detect and correct for nonnormal latent variables. , 2006, Psychological methods.

[45]  R. P. McDonald,et al.  Some algebraic properties of the Reticular Action Model for moment structures. , 1984, The British journal of mathematical and statistical psychology.

[46]  John Fox,et al.  OpenMx: An Open Source Extended Structural Equation Modeling Framework , 2011, Psychometrika.

[47]  R. D. Bock,et al.  Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm , 1981 .