Laudy, Olav

Translation of theories into statistical models using inequality constrained loglinear/ latent class models


Olav Laudy

Project: Project at Utrecht University

Project running from: 1 September 2001 – 1 September 2006

Supervisor: Prof. dr H.J.A. Hoijtink

The project will focus in the analysis and selection of the best of a number of competing models that can be formulated for a contingency table consisting of observed and latent ordinal and categorical data. Depending on the actual data, each model will be based on a loglinear and/or a latent class model. An example of the type of data that will be considered is given in Boom, Hoijtink, & Kunen (2001). They use 25 balance items (that can be answered right or wrong) to distinguish different classes of children (each class corresponds to a strategy to solve the items) and have different theories about the relation between class membership, gender and age groups. Although it is possible to determine if class membership can be predicted using gender and age (see, for example, Van der Heijden, Dessens, & Bockenholt (1996) and Vermunt (1996, pp. 63-65), this is not the approach that will be taken in this project. Here inequality constraints among the parameters of the latent class model (Hoijtink and Molenaar, 1997; Hoijtink, 1999) and the parameters of the loglinear model/ the probabilities of the cells in the contingency table (Agresti and Coull, to appear; Vermunt, 1999) will be used to translate a number of theories into competing models. Subsequently, each model will be analysed and the best theory will be selected. In the context of the complex kind of models considered in this project, it may be difficult or even impossible to select the best model using classical approaches based on the testing of hypotheses. Bayesian model selection procedures constitute a novel, viable and interesting alternative (Marden, 2000; Hoijtink, 2001)

Date of defence: 27 October 2006

Title of thesis: Bayesian inequality constrained models for categorical data