Although the generalized deterministic inputs, noisy "and" gate model (G-DINA; de la Torre, 2011) is a general cognitive diagnosis model (CDM), it does not account for the heterogeneity that is rooted from the existing latent groups in the population of examinees. To address this, this study proposes the mixture G-DINA model, a CDM that…

Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

Presents two binary programming models with a special network structure that can be explored computationally for simultaneous test construction. Uses an efficient special purpose network algorithm to solve these models. An empirical study illustrates the approach. (SLD)

Describes the maximum likelihood (ML) estimation of mean and covariance structure models when data are missing. Describes expectation maximization (EM), generalized expectation maximization, Fletcher-Powell, and Fisher-scoring algorithms for parameter estimation and shows how software can be used to implement each algorithm. (Author/SLD)

Examines the ways in which level-1 outliers can impact the estimation of fixed effects and random effects in hierarchical models (HMs). Also outlines and illustrates the use of Markov Chain Monte Carlo algorithms for conducting sensitivity analyses under "t" level-1 assumptions, including algorithms for settings in which the degrees of…

Proposes an algorithm that minimizes the asymptotic variance of the maximum-likelihood (ML) estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy to evaluate. Also shows how the algorithm can be modified if the interest is in a test with a "simple ability structure."…