Tuesday 16th July
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Generalized Latent Variable Modeling |
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| Convenor | Mr Dominik Becker (Technical University of Dortmund) |
Various frameworks have been proposed to overcome the shortcomings of so-called classical test theory and to address the issue of measurement error. Given certain similarities, these approaches still vary with respect to a couple of assumptions such as the metric of the latent variable (e.g. continuous in case of both Item Response Theory, IRT, and Confirmatory Factor Analysis, CFA; and categorical in case of Latent Class Analysis, LCA) or whether correlation of measurement error is allowed.
However, recently, several propositions have been published to address latent variable models in a common framework which is known as generalized latent variable modeling (Bartholomew/Knott 1999; Bollen 2002; Muthen 2002; Skrondal/Rabe-Hesketh 2007). An issue that has been addressed within that framework is the one of multilevel latent variable modeling considering measurement models at both the within and the between-level (Vermunt 2003; Raudenbush 2003, 2009; Asparouhov & Muthen 2008; Marsh et al. 2009). Moreover, also regarding the question of measurement equivalence - comparable parameter estimates of a given latent variable model in distinct groups -, respective tests of different latent variable frameworks such as multiple-group CFA and Differential Item Functioning were evaluated within a common model (e.g. Kankara et al. 2011).
Given the still limited amount of studies comparing results from different latent variable frameworks, this session cordially invites for both simulation-based and survey data-driven applications and evaluations of generalized latent variable modeling in general and their multilevel and/or measurement equivalence extensions in particular.
In latent variable modelling of cross-national survey data, substantive interest usually focuses on comparisons of the distributions of latent variables across countries. Measurement models of the observed variables are of lesser interest, but nevertheless need to be specified them appropriately before cross-national comparisons on the latent constructs can be made. A potentially serious problem is lack of measurement equivalence, where some survey items do not function similarly across all the countries. This talk examines issues in the analysis of measurement equivalence, focusing in particular on the sensitivity of conclusions to ignoring lack of equivalence. We consider latent variable models for categorical observed variables, i.e. latent class and latent trait models. Under a range of true models, we use numerical methods to examine which values parameter estimates converge to for different correctly and incorrectly specified models and thus how sensitive are estimates of latent distributions to different incorrect assumptions about measurement equivalence.
The present study addresses the question, how to model students' responses in the "PIRLS-Transfer" study for providing teachers with the most useful information about their students' performance. For that purpose, two empirical methods, the Rasch model (RM; Rasch, 1960) and the Deterministic Input Noisy-"And"-Gate (DINA; Haertel, 1989) model, are compared with respect to equivalence of results and accordance to the theoretical reading frameworks of parallel reading processes and hierarchical reading competences.
In a first step, five hierarchical reading competence levels are derived from a RM model (as in PIRLS). By assigning each level to exactly one skill, a Q-matrix for a hierarchically restricted DINA model (H-DINA) is established. Then we compared student classification into competence levels (RM) and skill classes (H-DINA). The results were promising: 90% of the students are classified in the same or at least an adjacent class.
Secondly, a non-hierarchical DINA model is considered. The Q-matrix for this model has been developed by experts, who assigned the items directly to the four reading processes. Results showed that the non-hierarchical DINA model can be considered slightly superior to the H-DINA. This is an important finding concerning the discussion of the linguistic acquisition and empirical modeling of reading competences.
Haertel, H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational measurement, 26, 333-352.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen. Danish Institute for Educational Research.
Idealiter, many concepts in empirical social research should not be measured by manifest but in terms of latent variables (Bollen 2002). If, in addition, the sample consists of several subgroups, and group-mean comparisons are intended, in a second step, measurement invariance of the latent variable model has to be tested for (Steenkamp & Baumgartner 1998).
Concerning variable-centered latent variable models (in contrast to observation-centered latent variable models such as latent class analysis), two group-specific invariance tests can be referred to: multiple group comparisons (MGC) in the framework of confirmatory factor analysis (CFA; cf. Millsap/Yun-Tein 2004), and tests for differential item functioning (DIF) in the framework of Item response theory (IRT; cf. Holland & Wainer, 1993).
This contribution aims to compare tests for measurement equivalence based on a sample of 31 upper-track secondary schools from the German federal state of North Rhine-Westphalia. Based on several indicators for parent involvement in school (e.g., helping out with school events; attending parent-teacher meetings) as measured in the parent survey of our sample (N=2729), we first analyze whether CFA and IRT arrive at the same conclusion regarding the dimensionality of our latent variable 'parent involvement'. In a second step, for both CFA and IRT we simultaneously estimate measurement models for parents both with and without migration background to validate if the same factor structure holds in different subgroups. And third, we elaborate on how to test for differences of parameter estimates between groups in both frameworks.