Evaluating Ordinal Multivariate Models under Multicollinearity via Pairwise Likelihood: A Simulation Perspective

This study examines the effect of multicollinearity on ordinal regression through a two-stage Monte Carlo simulation. A synthetic population of 2,000,000 observations was generated with predictors drawn from a normal distribution, and responses simulated using an ordinal probit model. A Monte Carlo procedure was employed with 10 repetitions, each consisting of 100 random samples of 1,000 observations. Parameter estimation employed Maximum Likelihood Estimation (MLE) for univariate models and Pairwise Likelihood (PL) for multivariate models, with performance assessed using mean squared error (MSE), bias, and computation time. Results show that multicollinearity had negligible impact on estimator bias and MSE, confirming the robustness of both MLE and PL to correlated predictors. However, severe multicollinearity substantially increased computation time, indicating a trade-off between estimator stability and efficiency. These findings highlight PL as a viable approach for analyzing complex ordinal data, particularly in applications such as socio-economic surveys and health metrics where predictor correlation is unavoidable.