Modelling partially cross-classified multilevel data

This article proposes an approach to modelling partially cross-classified multilevel data where some of the level-1 observations are nested in one random factor and some are cross-classified by two random factors. Comparisons between a proposed approach to two other commonly used approaches which treat the partially cross-classified data as either fully nested or fully cross-classified are completed with a simulation study. Results show that the proposed approach demonstrates desirable performance in terms of parameter estimates and statistical inferences. Both the fully nested model and the fully cross-classified model suffer from biased estimates of some variance components and statistical inferences of some fixed effects. Results also indicate that the proposed model is robust against cluster size imbalance.