Oftentimes in many fields of the social and natural sciences, data are obtained within a nested structure (e.g., students within schools). To effectively analyze data with such a structure, multilevel models are frequently employed. The present study utilizes a Monte Carlo simulation to compare several novel multilevel classification algorithms across several varied data conditions for the purpose of prediction. Among these models, the panel neural network and Bayesian generalized mixed effects model (multilevel Bayes) consistently yielded the highest prediction accuracy in test data across nearly all data conditions.