Open AccessCOMPARISON OF MULTIDIMENSIONAL ITEM RESPONSE MODELS: MULTIVARIATE NORMAL ABILITY DISTRIBUTIONS VERSUS MULTIVARIATE POLYTOMOUS ABILITY DISTRIBUTIONS
Author(s) -
Haberman Shelby J.,
Davier Matthias,
Lee YiHsuan
Publication year - 2008
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2333-8504.2008.tb02131.x
Subject(s) - polytomous rasch model , multivariate statistics , mathematics , multivariate normal distribution , comparability , multivariate analysis , statistics , item response theory , psychometrics , combinatorics
Multidimensional item response models can be based on multivariate normal ability distributions or on multivariate polytomous ability distributions. For the case of simple structure in which each item corresponds to a unique dimension of the ability vector, some applications of the two‐parameter logistic model to empirical data are employed to illustrate how, at least for the example under study, comparable results can be achieved with either approach. Comparability involves quality of model fit as well as similarity in terms of parameter estimates and computational time required. In both cases, numerical work can be performed quite efficiently. In the case of the multivariate normal ability distribution, multivariate adaptive Gauss‐Hermite quadrature can be employed to greatly reduce computational labor. In the case of a polytomous ability distribution, use of log‐linear models permits efficient computations.