Estimation of a Multilevel Item Response Theory Model with a Latent Interaction Effect using an EM Algorithm

Abstract

The size and therefore the complexity of collected datasets has been growing over time as computational capacities increase. Therefore, estimation methods that can take this complexity into account are needed. One such complex dataset is the Programme for International Student Assessment (PISA) by the Organisation for Economic Co-operation and Development (OECD), which is carried out to measure reading, mathematics, and science knowledge of 15-year-old students. PISA is conducted in different countries with different educational systems. Countries are ranked according to their students’ performance, which can have direct political consequences for the educational system, especially in countries with lower ranks than their self-image would dictate.

Latent abilities are estimated in the PISA test using a 2PL model from the Item Response Theory (IRT) family. Before 2015, however, the Rasch model was used to describe the data until studies could show that the rankings change if more complex (and more plausible) models are used to analyze the PISA datasets. Kreiner (2014), for example, demonstrated the usefulness of the inclusion of differential item functioning.

In this thesis, a multilevel IRT model with nonlinear latent variable effects model (MINoLEM) is presented. An estimation procedure based on the Expectation-Maximization algorithm is deduced. The accuracy of this estimation approach will be proven in several simulation studies and its usefulness will be shown through comparisons to other IRT software with the potential to include multilevel structures or nonlinear latent variable effects. The applicability of the MINoLEM estimation technique to real data is demonstrated by re-examining a PISA dataset and showing that latent interaction effects can be found.