Estimating the Context Effect in a Multilevel Latent Model with Small Sample Sizes: A Monte Carlo Simulation Study

In multilevel modeling, the relationships between the criterion and predictors are investigated at different levels. Often, the cluster-level predictors are measured by aggregating the individual-level measures. However, the aggregated clusterlevel predictors do not always reliably measure the cluster-level regression coefficient, and therefore the context coefficient. This study investigates an alternative approach: estimating cluster-level predictor on the latent cluster mean by using multilevel latent. A comparison is made of the accuracy of the context coefficient and standard error under a wide range of conditions. Results reveal that bias for context effect is small in multilevel latent model. Maximum likelihood (ML) estimator yields more accurate standard error estimation than robust maximum likelihood (MLR) when cluster number is small (less than 50). Very small cluster sample sizes (less than 10) should be avoided because they lack power and empirical sampling variance.