Modeling residual dependencies in item response models

Johan Braeken PhD

Project at: Department of Psychology, K.U.Leuven, Belgium

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

Project running from: 1 October 2004 – 1 October 2008

Summary:
In this project we will introduce the concept of copula functions in item response models to take into account residual dependencies. In mathematics a copula is a function that connects a multidimensional function with its margins. These copula functions have some nice properties with regard to the modeling of dependence. Applications of copula functions are common for modeling dependence between continuous variables in the domains of insurances and finances, but can also allow for new modeling possibilities for the modeling of conditional dependencies (violations of the assumption of local independence) in item response theory. However, applications with discrete variables as in item response theory are rather rare. The focus lies upon exploring the possibilities, advantages and limitations of these copula functions within the modeling framework of item response theory.

Date of defence: 18 December 2008

Title of thesis: Modeling residual dependencies in latent variable models with copulas