Random effect approaches of individual differences in complex models for categorical data

Jorge González PhD
Department of Psychology, K.U.Leuven, Belgium

Supervisors: Prof. dr Jan Beirlant, prof. dr Paul De Boeck, prof. dr Francis Tuerlinckx

Project running from: 1 January 2004 – 1 January 2008

Summary:
The statistical project is inspired by a substantive theory about feeling responses as studied in psychology. Feeling responses are assumed to follow from situational features which can be observed, and from appraisal responses which cannot be observed.  Further, it is assumed that  individual differences play in the process of feeling responses. The data which are collected are commonly of the ordered-category type, and data are observed in a set of representative situations. The hypothesized relationship between feeling responses and situational features and unobserved appraisal responses is implemented in the model by a feeling response parameter that is a linear function of (1) the situational features and (2) situational appraisal parameters.
Two kinds of individual differences will are considered:

1. Differences in the propensity for a given feeling response, or for the corresponding ap–praisal responses.
2. Differences in the association between feeling responses and the situational features and appraisals.

These individual differences will be modeled as random effects. The kind of model we are using is of the nonlinear mixed type. It is of the nonlinear type because products of parameters are used, and it is of the mixed type because of the random effects. The specific model, MIRID, is published in its basic form in Psychometrika, 1998.
An important extension we plan is to handle situational differences with a random effects approach, so that a double MIRID is obtained (in fact a double-structure structural equation model), with latent variables for persons and for situations.
The challenge of the project stems from the fact that the model is of a high dimensionality, especially because the random effects of persons and situations are crossed. We plan the following:

1. An exploration of quasi-MonteCarlo methods for a more efficient numerical integration required in the estimation procedure for the MIRID and the double MIRID, because the Gaussian quadrature method is too heavy. The method will be compared with Gaussian quadrature and Monte Carlo on feasible problems.
2. The development and investigation (with simulations) of a MCMC estimation and testing procedure for the double MIRID.
3. The development and investigation of model selection and model comparison methods.

Date of defence: 17 December 2007

Title of thesis: Random effects approaches of individual differences in complex models for categorical data. ISBN: 978-90-8649-152-0.