Self-normalized score-based tests to detect parameter heterogeneity for mixed models

TL;DR

This paper introduces a self-normalized score-based testing method for mixed models that effectively detects parameter heterogeneity even when scores are dependent, overcoming limitations of traditional tests.

Contribution

The paper proposes a novel self-normalized score-based test for mixed models, addressing dependence issues in scores and expanding applicability.

Findings

Self-normalized tests outperform traditional tests with dependent scores.

Simulation studies confirm the robustness of the new method.

Real data examples demonstrate practical utility.

Abstract

Score-based tests have been used to study parameter heterogeneity across many types of statistical models. This chapter describes a new self-normalization approach for score-based tests of mixed models, which addresses situations where there is dependence between scores. This differs from the traditional score-based tests, which require independence of scores. We first review traditional score-based tests and then propose a new, self-normalized statistic that is related to previous work by Shao and Zhang (2010) and Zhang, Shao, Hayhoe, and Wuebbles (2011). We then provide simulation studies that demonstrate how traditional score-based tests can fail when scores are dependent, and that also demonstrate the good performance of the self-normalized tests. Next, we illustrate how the statistics can be used with real data. Finally, we discuss the potential broad application of self-normalized, score-based tests in mixed models and other models with dependent observations.