A nonparametric test for fixed effects in crossed random effect models

Mixed-effects models are powerful tools for analyzing data from experimental designs involving both subjects and items as random effects. In fields such as psychology, neuroscience, and digital markets, researchers commonly use mixed-effects models to analyze data from experiments or customer ratings. In this context, we propose a nonparametric approach based on the sign-flip score test. The method does not require distributional assumptions on the error components and remains valid even with low sample sizes and unbalanced data. The performance of the test is shown through the experimental results.