# Bootstrapping F test for testing Random Effects in Linear Mixed Models

## TL;DR

This paper evaluates the F test for random effects in linear mixed models, exploring its power under non-normal errors and proposing bootstrap methods to improve performance with small clusters or non-normality.

## Contribution

It extends previous work by analyzing the F test's power under non-normal errors and introduces bootstrap alternatives for better accuracy in small or non-normal cases.

## Key findings

- F test maintains good power under non-normal errors
- Bootstrap methods improve test accuracy for small cluster sizes
- Enhanced testing procedures for linear mixed models

## Abstract

Recently Hui et al. (2018) use F tests for testing a subset of random effect, demonstrating its computational simplicity and exactness when the first two moment of the random effects are specified. We extended the investigation of the F test in the following two aspects: firstly, we examined the power of the F test under non-normality of the errors. Secondly, we consider bootstrap counterparts to the F test, which offer improvement for the cases with small cluster size or for the cases with non-normal errors.