Testing homogeneity in a random intercept model using asymptotic, posterior predictive and plug-in p-values

In this paper three statistics and three discrepancy measures with which homogeneity in the random intercept model can be investigated will be evaluated. The first two can be used to test the homogeneity of level one residual variances across level two units and the third can be used to test whether effects should be fixed or random. Each statistic and discrepancy measure will be evaluated using asymptotic (if available), posterior predictive and plug in p -values. A simulation study will be used to investigate the frequency properties of these p -values. In the discussion it will be indicated how the results obtained for the random intercept model with one explanatory variable can be useful during the construction of general two level models.