Second-order item response theory models have been used for assessments consisting of several domains, such as content areas. We extend the second-order model to a third-order model for assessments that include subdomains nested in domains. Using a graphical model framework, it is shown how the model does not suffer from the curse of…

The authors present a generalization of the multiple-group bifactor model that extends the classical bifactor model for categorical outcomes by relaxing the typical assumption of independence of the specific dimensions. In addition to the means and variances of all dimensions, the correlations among the specific dimensions are allowed to differ…

Testlet effects can be taken into account by incorporating specific dimensions in addition to the general dimension into the item response theory model. Three such multidimensional models are described: the bi-factor model, the testlet model, and a second-order model. It is shown how the second-order model is formally equivalent to the testlet…

As is the case for any statistical model, a multidimensional latent growth model comes with certain requirements with respect to the data collection design. In order to measure growth, repeated measurements of the same set of individuals are required. Furthermore, the data collection design should be specified such that no individual is given the…

Maximum marginal likelihood estimation of multidimensional item response theory (IRT) models has been hampered by the calculation of the multidimensional integral over the ability distribution. However, the researcher often has a specific hypothesis about the conditional (in)dependence relations among the latent variables. Exploiting these…

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations…