A locally most powerful test for homogeneity with many strata

A locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting. The test is based on the difference between the square of the score and the observed information about the nuisance parameters, all evaluated at the null hypothesis. Several examples including constant normal mean with possibly different variances and matched case-control studies are presented in detail. The relative efficiencies of the unstratified estimator of parameter of interest versus the stratified one are calculated. Two data sets on matched case-control studies are used for illustration.