Alternative Specifications of Multivariate Multilevel Probit Ordinal Response Models
Leonardo Grilli () and
Carla Rampichini ()
Journal of Educational and Behavioral Statistics, 2003, vol. 28, issue 1, 31-44
Multivariate multilevel models for ordinal variables are quite complex with respect to both interpretation and estimation. The specification in terms of a multivariate latent distribution and a set of thresholds helps in the interpretation of the variance-covariance parameters. However, most existing estimation algorithms for multilevel models can be used only if the model is reparameterized as a univariate model with an additional dummy bottom level. Moreover, the univariate formulation allows the model to be cast in the framework of Generalized Linear Latent and Mixed Models ( Rabe-Hesketh, Pickles, & Skrondal, 2001a ), a rather general class that includes, as special cases, structural equations and factor models. This article outlines the multivariate latent distribution specification and the corresponding interpretation issues; it then shows the univariate formulation, along with some alternative parameterizations that are useful in the estimation phase. An application to student ratings data illustrates the interpretation of the parameters and the estimation procedures, with a discussion of some computational issues.
Keywords: latent variables; multilevel models; multivariate models; numerical integration; ordinal variables (search for similar items in EconPapers)
References: Add references at CitEc
Citations: View citations in EconPapers (8) Track citations by RSS feed
Downloads: (external link)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:28:y:2003:i:1:p:31-44
Access Statistics for this article
More articles in Journal of Educational and Behavioral Statistics
Bibliographic data for series maintained by SAGE Publications ().