Linear Mixed Effect Models (LMEM) have become a popular method for analyzing nested experimental data, which are often encountered in psycholinguistics and other fields. This approach allows experimental results to be generalized to the greater population of both subjects and experimental stimuli. In an influential paper Bar and his colleagues (2013; https://doi.org/10.1016/j.jml.2012.11.001) recommend specifying the maximal random effect structure allowed by the experimental design, which includes random intercepts and random slopes for all within-subjects and within-items experimental factors, as well as correlations between the random effects components. The goal of this paper is to formally investigate whether their recommendations can be generalized to wider variety of experimental conditions. The simulation results revealed that complex models (i.e., with more parameters) lead to a dramatic increase in the non-convergence rate. Furthermore, AIC and BIC were found to select the true model in the majority of cases, although selection accuracy varied by LMEM random effect structure.