The multidimensional extension we consider is called multidimensional 2 parameter logistic (M2PL) model, and has the following expression: P(X ij= xj i;a j;d j) = ex(a0 j i+d) 1+ea0j i+d j (2) where both a jand iare m dimensional vectors, so that the sum in the exponent of e can be rewritten as a0 j i+ d j = P m t=1 a jt it+ d j. This model. 1 more latent traits are simultaneously considered (multidimensionality) 2 these latent traits are represented by a random vector with a discrete distribution common to all subjects (each support point of such a distribution identiﬁes a different latent class of individuals) 3 either a Rasch or a two-parameter logistic (Birnbaum, ). The current study proposes an alternative feasible Bayesian algorithm for the three-parameter logistic model (3PLM) from a mixture-modeling perspective, namely, the Bayesian Expectation-Maximization-Maximization (Bayesian EMM, or BEMM). As a new maximum likelihood estimation (MLE) alternative to the marginal MLE EM (MMLE/EM) for the 3PLM, the EMM can explore the likelihood function much . Instead of estimating a between-item multidimensional Rasch model, a between-item multidimensional model that allows for varying item discrimination parameters should be used (see, for example, Adams & Wu, ; Muraki, ). Such a model is identified by fixing the variance of both latent dimensions to 1.

Multilevel and multidimensional item response models are two commonly used examples as extensions of the conventional item response models. In this dissertation, I investigate extensions and applications of multilevel and multidimensional item response models, with a primary focus on longitudinal item response data that include students' school switching, classification of examinees . The Rasch model, named after Georg Rasch, is a psychometric model for analyzing categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. For example, they may be used to estimate a student's reading ability or the. We also consider the three-parameter model that further includes a guessing probability c j, that is, P(y j = 1j ;a j;b j;c j) = c j+ (1 c j)F(Ta j+ b j): (3) By setting c j = 0, the above model recovers (1). In addition, the latent trait vector follows the multivariate normal prior . Extensions of unidimensional linking procedures to multidimensional latent trait models are explored. Adams, Wilson, and Wang discuss the multidimensional random coefficients multinomial logit model. This model generalizes a wide range of Rasch models to the multidimensional case, including the simple APPLIED PSYCHOLOGICAL MEASUREMENT.

The Joe E. Covington Award for Research on Testing for Licensure is intended to provide support for graduate students in any discipline doing research germane to testing and measurement, particularly in a high-stakes licensure setting. View past award recipients and access the Call for Proposals. This paper introduces multilevel extensions for the general diagnostic model (GDM) following recent developments on extensions of latent class analysis (LCA) to hierarchical models. The GDM is based on LCA as well as discrete latent trait models and may be viewed as a general modeling framework for con rmatory multidimensional item response models. where α c3 and α c4 are latent variables for Attributes 3 and 4, respectively. The logit of the correct response includes the intercept (λ 2,0), a main effect for Attribute 3 (λ 2,1,(3)), a main effect for Attribute 4 (λ 2,1,(4)), and a two-way interaction term between Attributes 3 and 4 (λ 2,2,(3,4)).The second subscript on the item parameters denotes the level of the effect, where 0. The difficulty parameter is called b. the two important assumptions are local independence and unidimensionality. The Item Response Theory has three models. They are one parameter logistic model, two parameter logistic model and three parameter logistic model. In addition, Polychromous IRT Model are also useful (Hambleton & Swaminathan, ).