Abstract
Limited information goodness of fit (GOF) tests have gained recognition in the literature for high-dimensional multivariate categorical data analysis. Sparsity issues in the ensuing contingency tables impair the dependability of GOF tests but can be circumvented by considering summary statistics involving univariate and bivariate residuals. Prior work in this area for factor models have focused mainly on maximum likelihood estimation, which itself can be computationally intensive when fitting large and complex models. This present work examines limited information GOF tests when composite likelihood estimation, specifically pairwise likelihood estimation, is used instead. Pairwise likelihood estimation offers a beneficial trade-off between computational efficiency and modelling accuracy in factor models, and hence we wanted to examine the performance of limited information GOF tests under this framework. The tests under consideration are based on the Pearson chi-squared test statistic and the Wald test statistic. We propose modifications to each of these tests with the aim of further reducing computational complexity. We then extend our findings beyond independent sampling to situations where complex sampling procedures (with known weights) are employed.
Haziq Jamil
Assistant Professor in Statistics
My research interests include statistical theory, methods and computation, with applications towards the social sciences.