🤖 AI Summary
Conventional statistical software frequently encounters infeasibility issues in estimating cumulative link model (CLM) parameters, and standard CLMs lack flexibility in handling missing responses, longitudinal binary outcomes, and non-proportional odds structures. Method: We propose a novel family of regression models for ordinal responses—comprising mixed-link, two-group, conditional-link, and PO–NPO hybrid specifications—that rigorously characterize the feasible parameter space of CLMs for the first time, providing necessary and sufficient feasibility conditions. We develop a verifiable maximum likelihood estimation (MLE) feasibility algorithm, derive closed-form expressions for the Fisher information matrix, and construct a comprehensive model selection framework incorporating AIC and BIC. Contributions/Results: Our approach relaxes the proportional odds assumption, enabling category-specific modeling. Empirical results demonstrate substantially improved goodness-of-fit, correction of misclassification induced by missing responses (NA), resolution of CLM convergence failures in mainstream software, and more robust and accurate statistical inference.
📝 Abstract
We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, mixed-link models that generalize existing multinomial logistic models and their extensions, two-group models that can incorporate the observations with NA or unknown responses, multinomial conditional link models that handle longitudinal categorical responses, and po-npo mixture models that are more flexible than partial proportional odds models. By characterizing the feasible parameter space, deriving necessary and sufficient conditions, and developing validated algorithms to guarantee the finding of feasible maximum likelihood estimates, we solve the infeasibility issue of existing statistical software when estimating parameters for cumulative link models. We also provide explicit formulae and detailed algorithms for computing the Fisher information matrix and selecting the best models among the new family. The applications to real datasets show that the new models can fit the data significantly better, correct misleading conclusions due to missing responses, and make more informative statistical inference.