Comparative Analysis of Frequentist and Bayesian Approaches in Fitting Stereotype Models for Ordinal Outcomes

Abstract

Introduction: Stereotype regression models provide a parsimonious solution for analyzing ordinal response variables. When the proportional odds assumption is violated, these models offer a viable alternative to more commonly used cumulative logit models. However, their adoption in research remains limited due to a lack of standardization. Our study compares frequentist and Bayesian approaches for fitting stereotype models for ordinal outcomes, elucidating the benefits of each method to encourage broader utilization. Methods: We simulated ordinal data to contrast a Bayesian approach for an ordered stereotype model with two frequentist methods in R: Reduced-Rank Vector Generalized Linear Models (RRVGLM) for unordered scores and Ordered Stereotype Model (OSM) for ordered scores. Metrics included mean squared error (MSE) and bias across multiple simulation scenarios with various sample sizes and the introduction of multicollinear predictors. Lastly, a real dataset was utilized to demonstrate the application of these approaches. Results: Both frequentist methods exhibited errors in simulations and real data when the sample size was small and when multicollinearity was present. In simulation scenarios with small sample size (N=50, 70), frequentist methods often failed to converge or produced large standard errors, while the Bayesian approach always converged and yielded lower MSEs. In scenarios with large sample sizes (N=300, 500), all methods produced comparable MSEs. However, frequentist methods produced slightly less biased estimates. Conclusion: RRVGLM offers fast, accurate results but may encounter errors or produce unordered scores complicating interpretation. In these cases, OSM may provide better results. Bayesian models excel with small sample sizes and complex data with issues such as multicollinearity but require more computation time.