Hierarchical General Diagnostic Models

Abstract

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.The multilevel extensions presented in this paper enable one to check the impact of clustered data, such as data for students within schools in large scale educational surveys, on the structural parameter estimates of the GDM. Moreover, the multilevel version of the GDM allows study of di erences in skill distributions across these clusters. ii

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

“…In the case of simple-structure models such as those found in large-scale surveys, multidimensional GDMs can be used to simultaneously estimate the different IRT scales and the multidimensional ability distribution. (b) The GDM also allowed the use of multiple-group (Xu & von Davier, 2006) and mixturedistribution versions of IRT and MIRT models (von Davier & Rost, 2006) and mixture distribution diagnostic models (von Davier, 2007a(von Davier, , 2007b(von Davier, , 2010. Multiple-group extensions of IRT (Bock & Zimowski, 1997) should be used whenever a sample is drawn from a population that comprises multiple subpopulations.…”

Different Approaches to Covariate Inclusion in the Mixture Rasch Model

“…In addition, η ix is a real valued difficulty parameter and γ ikx is a K-dimensional slope parameter for each non-zero response category (von Davier, 2005a(von Davier, , 2008a(von Davier, , 2010. Thus, when there are m i +1 categories in the response data, m i × k slope parameters are specified for item i.…”

“…The η ixg , and γ ikxg are class-specific item difficulty and slope parameter respectively (von Davier, 2010). g ∈ {1,…,G} is the group index which could be manifest, latent or partially observed.…”

“…Such modeling approaches include multilevel LCA (e.g., Vermunt, 2003), multilevel IRT models (e.g., Kamata, 2001), all of which are special cases of the hierarchical GDM (HGDM; von Davier, 2007Davier, , 2010.…”

Modelos de diagnóstico cognitivo: Fundamentos, didáctica y aplicaciones en ciencias del comportamiento.

“…Respecto a la parametrización de los modelos, la investigación se ha centrado alternativas al modelo saturado en el componente estructural de los CDM, esto ha resultado en modelos que asumen independencia entre los atributos latentes αk (Maris, 1999), modelo con variables latentes de orden superior que flexibilizan la independencia condicional de los atributos (de la Torre & Douglas, 2004;DeCarlo, 2012), modelos con distribuciones alternativas para los atributos latentes (Hartz, 2002;Templin & Henson, 2006), y modelos con jerarquías entre los atributos (von Davier, 2010). Además, Xu y Zhang (2016) recientemente demostraron los requisitos mínimos que debe cumplir la matriz Q para poder identificar los modelos de diagnóstico cognitivo.…”