The random effects model may be used to model the heterogeneity across the study sites with the assumption of treating the site effects as random. In this case, we are interested in testing whether the variance of random effects is equal to zero (a test for heterogeneity). However, the site effects may be larger than those which can be attributed to random variation. Perhaps, this extra variation can be modeled through the variable defined for each site. In this talk, I propose a method of model expansion to consider this extra variation, and derive a diagnostic test for heterogeneity based on score statistic