The impact of a Hausman pretest on the coverage probability and expected length of confidence intervals

TL;DR

This paper examines how the use of a Hausman pretest in clustered and longitudinal data analysis affects the coverage probability and length of confidence intervals for slope parameters, revealing potential issues with coverage and efficiency.

Contribution

It provides an assessment of the impact of the Hausman pretest on confidence interval properties, highlighting problems at typical significance levels used in practice.

Findings

Minimum coverage probability can be significantly below nominal levels.

Expected length of the confidence interval can be larger than fixed effects intervals.

Pretest can lead to less reliable inference in practical applications.

Abstract

In the analysis of clustered and longitudinal data, which includes a covariate that varies both between and within clusters (e.g. time-varying covariate in longitudinal data), a Hausman pretest is commonly used to decide whether subsequent inference is made using the linear random intercept model or the fixed effects model. We assess the effect of this pretest on the coverage probability and expected length of a confidence interval for the slope parameter. Our results show that for the small levels of significance of the Hausman pretest commonly used in applications, the minimum coverage probability of this confidence interval can be far below nominal. Furthermore, the expected length of this confidence interval is, on average, larger than the expected length of a confidence interval for the slope parameter based on the fixed effects model with the same minimum coverage.