Nonparametric Functional Analysis of Generalized Linear Models Under Nonlinear Constraints

TL;DR

This paper presents a new nonparametric approach for generalized linear models that improves prediction, inference, and classification, especially for asymmetric data, and offers broad model diagnostic capabilities.

Contribution

It introduces a nonparametric methodology that extends parametric models, providing better performance and diagnostics for categorical data analysis under nonlinear constraints.

Findings

Outperforms parametric models in asymmetric data scenarios

Provides statistically significant improvements in model fit and classification

Can be used for broad model diagnostics across sciences

Abstract

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages. Requiring minimal assumptions, it extends recently published parametric versions of the methodology and generalizes it. If the underlying data generating process is asymmetric, it gives uniformly better prediction and inference performance over the parametric formulation. Furthermore, it introduces a new classification statistic utilizing which I show that overall, it has better model fit, inference and classification performance than the parametric version, and the difference in performance is statistically significant especially if the data generating process is asymmetric. In addition, the methodology can be used to perform model diagnostics for any model specification. This is a highly useful result, and it extends existing work for categorical model diagnostics broadly across the sciences. The mathematical results also highlight important new findings regarding the interplay of statistical significance and scientific significance. Finally, the methodology is applied to various real-world datasets to show that it may outperform widely used existing models, including Random Forests and Deep Neural Networks with very few iterations.