Mixed-effects models are powerful tools for analyzing experimental design data involving subjects and items as random effects. 

Researchers commonly use crossed-random effect models to analyze data from experiments or customer ratings in fields such as psychology, linguistics, neuroscience, and digital markets.
In this context, we present a nonparametric score test based on random orthogonal transformations, which resamples only the component of the score lying in the null space of the random-effects design.  
The proposed method does not rely on distributional assumptions for the error components and remains valid even in small samples and unbalanced data.