Comparing Multiple‐group Multinomial Log‐linear Models for Multidimensional Skill Distributions in the General Diagnostic Model

Abstract

ETS, the ETS logo, and LISTENING. LEARNING. LEADING. are registered trademarks of Educational Testing Service (ETS).As part of its educational and social mission and in fulfilling the organization's nonprofit charter and bylaws, ETS has and continues to learn from and also to lead research that furthers educational and measurement research to advance quality and equity in education and assessment for all users of the organization's products and services.ETS Research Reports provide preliminary and limited dissemination of ETS research prior to publication. To obtain a PDF or a print copy of a report, please visit:http://www.ets.org/research/contact.html AbstractThe general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume separate sets of parameters to fit the distribution of latent variables in each group of a multiple-group model. Estimation of these constrained log-linear models using iterative weighted least squares (IWLS) methods is outlined and an application to NAEP data exemplifies the differences between constrained and unconstrained models in the presence of larger numbers of group-specific proficiency distributions.The use of log-linear models for the latent skill space distributions using constraints across populations allows for efficient computations in models that include many proficiency distributions.

Measuring Growth in a Longitudinal Large-Scale Assessment with a General Latent Variable Model

“…In Equation (15), the model is defined for binary responses only. Note that this is a simplification of the original GDM, which is defined both for dichotomous and polytomous response variables (von Davier and Yamamoto, 2004;von Davier, 2005von Davier, , 2008.…”

“…One two-dimensional distribution is fitted in the case of the single-group models, four bivariate distributions are fitted for the 4-population school-type models, and two bivariate distributions in the case of the 2-population hierarchical-mixture models. We fitted two moments for each ability dimension in each population and one parameter for the covariance between the two dimensions, which results in 5 parameters fitted for each of the bivariate ability distributions in the estimated models-higher-order moments (see Xu & von Davier, 2008) were not estimated. The hierarchical discrete mixture required two additional parameters for estimation of the Dirichlet distribution of the class sizes (see von Davier, 2007bvon Davier, , 2010.…”

The R Package CDM for Cognitive Diagnosis Models

“…Xu and von Davier 2008b) or the reduction of the skill space (cf. Xu and von Davier 2008a). In addition, the user may specify hierarchies on skills (skillspace.hierarchy; cf.…”

“…Note that the process of parameter estimation is carried out in the same way if different items follow different condensation rules. Note also that for reasons of simplicity we present the parameter estimation process by the example of the DINA model (i.e., the DINO model, depending on the definition of the dichotomous latent response η ij ), but it may be extended to more complex CDMs in a straightforward manner (Xu and von Davier 2008a). …”

Review of Diagnostic Measurement: Theories, Methods, and Applications

“…Specifically, when DCMs are applied to large survey data, measurement is not diagnostic in the sense of an individual (pedagogical or clinical) diagnosis with a test battery, where one student takes several tests to determine what his or her specific strengths and weaknesses are. Instead, diagnostic in large-scale survey educational testing programs is more about estimating distributions of skills in student populations, typically with shorter instruments per skill and mixed items (Xu & von Davier, 2006, 2008a, 2008b, 2008c.…”