In this thesis we focus on balanced fully crossed mixed effects models, exploring their theoretical properties, practical challenges, and resampling techniques. First, we derive the best linear unbiased predictors (BLUPs) conditional on the variance components. We study how different model specifications affect the form. This also allows us to study the shrinkage factors of the BLUPs. Second, we investigate the impact of misspecifying the random effects structure. Using analytical derivations based on the Kullback-Leibler divergence, complemented by simulations, we show how omitting random effects affects the variance of fixed effect estimates, inflates Type I error rates, and compromises the validity of fixed effects inference. Finally, we introduce and evaluate four nonparametric bootstrap methods designed for balanced fully crossed designs, focusing on strategies to reinflate shrunken BLUPs when generating bootstrap samples. Simulation studies assess the comparative performance of these methods in realistic experimental scenarios. Overall, this work provides insights into estimation, inference, and bootstrap methodologies for fully crossed mixed effects models, with direct applications to psychological and other experimental research fields.