GDM Software mdltm Including Parallel EM Algorithm

This chapter illustrates the use of the software mdltm (von Davier, A general diagnostic model applied to language testing data. ETS Research Report No. RR-05-16, Educational Testing Service, Princeton, 2005), for multidimensional discrete latent trait models. The software mdltm was designed to handle large data sets as well as complex test and sampling designs, providing high flexibility for operational analyses. It allows the estimation of many different latent variable models, includes different constraints for parameter estimation, and provides different model and item fit statistics as well as multiple methods for proficiency estimation. The software utilizes an computationally efficient parallel EM algorithm (von Davier, New results on an improved parallel EM algorithm for estimating generalized latent variable models. In van der Ark L, Wiberg M, Culpepper S, Douglas J, Wang WC (eds) Quantitative psychology. IMPS 2016. Springer Proceedings in Mathematics & Statistics, vol 196. Springer, New York, 2017) that allows estimation of high-dimensional diagnostic models for very large datasets. The software is illustrated by applying diagnostic models to data from the programme for international student assessment (PISA).

[1]  Matthias von Davier,et al.  LINKING FOR THE GENERAL DIAGNOSTIC MODEL , 2008 .

[2]  Li Cai,et al.  Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis , 2010 .

[3]  Shelby J. Haberman,et al.  Conditional Log-Linear Models for Analyzing Categorical Panel Data , 1994 .

[4]  Minjeong Jeon,et al.  A Third-Order Item Response Theory Model for Modeling the Effects of Domains and Subdomains in Large-Scale Educational Assessment Surveys , 2014 .

[5]  Donald Hedeker,et al.  Full-information item bi-factor analysis , 1992 .

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

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

[8]  E. Muraki.  A Generalized Partial Credit Model: Application of an EM Algorithm , 1992 .

[9]  A. Agresti.  Categorical data analysis , 1993 .

[10]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[11]  Matthias von Davier,et al.  International Large-Scale Assessment Data , 2010 .

[12]  Matthias von Davier,et al.  Linking Scales in International Large-Scale Assessments , 2013 .

[13]  H. Akaike.  A new look at the statistical model identification , 1974 .

[14]  M. Davier.  The Log‐Linear Cognitive Diagnostic Model (LCDM) as a Special Case of the General Diagnostic Model (GDM) , 2014 .

[15]  Matthias von Davier,et al.  Local Equating Using the Rasch Model, the OPLM, and the 2PL IRT Model—or—What Is It Anyway if the Model Captures Everything There Is to Know About the Test Takers? , 2013 .

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

[17]  Matthias von Davier,et al.  USING THE GENERAL DIAGNOSTIC MODEL TO MEASURE LEARNING AND CHANGE IN A LONGITUDINAL LARGE-SCALE ASSESSMENT , 2009 .

[18]  Matthias von Davier,et al.  A Unified Approach to IRT Scale Linking and Scale Transformations , 2004 .

[19]  Matthias von Davier,et al.  Logistic Mixture-Distribution Response Models , 2016 .

[20]  Matthias von Davier,et al.  A GENERAL DIAGNOSTIC MODEL APPLIED TO LANGUAGE TESTING DATA , 2005 .

[21]  M. Davier.  Hierarchical mixtures of diagnostic models , 2010 .

[22]  Matthias von Davier.  New Results on an Improved Parallel EM Algorithm for Estimating Generalized Latent Variable Models , 2016 .

[23]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[24]  Matthias von Davier,et al.  COMPARISON OF MULTIDIMENSIONAL ITEM RESPONSE MODELS: MULTIVARIATE NORMAL ABILITY DISTRIBUTIONS VERSUS MULTIVARIATE POLYTOMOUS ABILITY DISTRIBUTIONS , 2008 .

[25]  Minjeong Jeon,et al.  Fitting an item response theory model with random item effects across groups by a variational approximation method , 2013, Ann. Oper. Res..

[26]  Matthias von Davier,et al.  The DINA model as a constrained general diagnostic model: Two variants of a model equivalency. , 2014 .

[27]  Matthias von Davier,et al.  COMPARING MULTIPLE-GROUP MULTINOMIAL LOG-LINEAR MODELS FOR MULTIDIMENSIONAL SKILL DISTRIBUTIONS IN THE GENERAL DIAGNOSTIC MODEL , 2008 .

[28]  Minjeong Jeon,et al.  Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model , 2013 .

[29]  Minjeong Jeon,et al.  Recent developments in maximum likelihood estimation of MTMM models for categorical data , 2014, Front. Psychol..

[30]  Matthias von Davier,et al.  FITTING THE STRUCTURED GENERAL DIAGNOSTIC MODEL TO NAEP DATA , 2008 .

[31]  Matthias von Davier,et al.  High-Performance Psychometrics: The Parallel-E Parallel-M Algorithm for Generalized Latent Variable Models , 2016 .

[32]  Melvin R. Novick,et al.  Some latent train models and their use in inferring an examinee's ability , 1966 .

[33]  Matthias von Davier,et al.  Multivariate and Mixture Distribution Rasch Models: Extensions and Applications , 2006 .