Cluster randomized trials (CRTs) are types of randomized controlled trials in which groups of subjects, rather than individuals, are randomly assigned to the different interventions. Defining strata in CRTs should be based on baseline cluster-level data that will be used in the analysis stage, or surrogate indicators for other factors that may be correlated with the outcome of the study. Regression adjustments with CRTs require more complicated models because they may include both individual- and cluster-level baseline covariates, as well as an adjustment for the correlation of individuals within groups. Two main types of models have been proposed as possible analysis methods for data in CRTs: multilevel generalized linear models and generalized estimating equations (GEE). However, there is limited literature on the exact specification and comparison of these models and methods. We describe multiple possible specifications of multilevel models and GEEs that have been suggested to analyze CRTs. Using simulation analysis for both continuous and binary outcomes, we aim to determine how adjustment for stratification variables in cluster randomized trials affects model performance.