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

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.