Inequality constrained Bayesian models for the multivariate normal covariance matrix

Carel Peeters
Department of Methodology and Statistics, Faculty of Social Sciences, Utrecht University

Project: Part of the NWO Vici project Learning more from empirical data using prior knowledge, granted to professor Herbert Hoijtink at Utrecht University.

Project running from: 1 February 2007 – 1 September 2011

Promotor: Prof. dr. P.G.M. van der Heijden

Summary of project
Researchers often have competing theories that can be translated into inequality constrained models. Such theoretical models cannot be addressed with standard null-hypothesis testing. In this project inequality constrained Bayesian statistical models for the multivariate normal covariance matrix will be developed. Models for the multivariate normal covariance matrix encompass such techniques as: factor analysis, growth curve models, multilevel models, path-models and errors in variables models. The formulation of these models under inequality constraints should make possible the evaluation of substantive inequality constrained theory. Issues such as formal Bayesian prior formulation, parameter estimation using sampling techniques, model selection and multiple group testing will be addressed. Next to articles, the project will also result in a statistical package which, in addition to the other procedures developed in the VICI project ‘Learning more from Empirical Data using Prior Knowledge’, will also encapsulate inequality constrained Bayesian statistics for models based on the multivariate normal covariance matrix.

Date of defence:   4 June 2012

Title of thesis:   Bayesian exploratory and confirmatory factor analysis.

ISBN:   978-90-393-5787-3