IRTPRO

IRT Models in IRTPRO

As in conventional IRT programs, IRTPRO provides popular unidimensional models that are suitable for a test measuring a single construct. The item response function (IRF) in IRTPRO, which describes the relation between latent trait scores and an expected item score, has the cumulative logistic function form rather than the normal ogive function that has been popular in the past.

For unidimensional dichotomously scored item responses, the Rasch, the two-parameter logistic (2PL), and the three-parameter logistic (3PL) models are included in IRTPRO. For unidimensional polytomously scored categorical item responses, the graded response (for ordinal responses), the generalized partial credit (for ordinal), and the nominal (for nominal responses) models are available in addition to the Rasch family polytomous ordinal item response models, such as the rating scale and the partial credit models.

When a test measures more than a single construct, multidimensional IRT models can be used. Commonly observed multidimensionality includes a simple structure (or between-item multidimensionality), in which there are multiple sets of items and each item set measures a single construct such that an item loads only onto a single factor (e.g., a test battery that consists of item sets measuring correlated multiple constructs), and a bifactor structure in which an item loads always on both one primary (or general) factor and one specific [Page 883]factor (e.g., a reading test in which there are reading passages and a set of items are associated with each reading passage). Multidimensional versions of the aforementioned unidimensional models are available in IRTPRO. Also, a multidimensional model with a complex dimensionality (e.g., within-item multidimensionality in which some items load onto a single dimension and other items load onto a few dimensions) that does not follow the previously mentioned dimensional structures or a user-specified unidimensional and multidimensional models can be estimated through imposing model parameter constraints (equality and fixing as an arbitrary value).

Estimation of IRT Models in IRTPRO

A traditional estimation method for popular IRT models has been the marginalized maximum likelihood estimation with the expectation-maximization algorithm (MMLE-EM). IRTPRO is equipped with MMLE-EM. In addition, IRTPRO has a fully Bayesian Markov chain Monte Carlo and two other non-Bayesian model estimation methods, which are Metropolis-Hastings Robbins-Monro (MH-RM) and an adaptive quadrature with MMLE-EM. The latter two are non-Bayesian high-dimensional model estimation methods. MH-RM can handle high-dimensional models more efficiently than the adaptive quadrature method as the number of dimension increases. The fully Bayesian Markov chain Monte Carlo method can be used for unidimensional and multidimensional model estimations. To take full advantage of MH-RM or the MCME method, especially for high-dimensional models, it is recommended to fine-tune their option values (rather than simply using the program’s default values) that are best suited to the data under analysis.

...