Academic

Limited information goodness-of-fit (LIGOF) tests are increasingly recognized for their application in high-dimensional multivariate categorical data analysis. LIGOF tests address sparsity in contingency tables by leveraging summary statistics derived from univariate and bivariate residuals, effectively circumventing the reliability concerns associated with traditional goodness-of-fit tests. Previous studies on binary factor models have predominantly utilised maximum likelihood estimation, which itself can be computationally intensive when fitting large and complex models. This work examines the efficacy of LIGOF 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 the performance of LIGOF tests under this framework is of significant interest. The tests under consideration are based on quadratic forms of the residuals, including the classical Wald and Pearson tests. Modifications of these tests are also proposed with the aim of further reducing computational complexity. Moreover, the study is expanded to include scenarios that involve complex sampling procedures with known weights, thereby broadening the applicability of our findings.