Use of Sandwich Variance Estimation in Generalized Linear Mixed Models: for Binary Repeated Mesures Data

Abstract

Sandwich Variance Estimation (SVE) is a method of estimating variances of miss-specified models and has been popular for analyzing correlated/non-independent data to improve the variance estimation of models fitted for such data. This gained higher popularity when specialized models were not been developed for correlated data whereas with the development of statistical models for correlated data, the use of SVE in such models was at argument among the researches. Generalized Linear Mixed Models (GLMMs) are such models defined for correlated data. But, instances can be found in the literature where GLMMs have shown up model miss-specifications for correlated data. This brought forward the applicability of using SVE in GLMMs since SVE is a method of estimating variances of miss-specified models. Due to the dearth of literature on evaluating the impact of using SVE in GLMMS, this study was undertaken which used both simulated and actual data to evaluate the necessity of using SVE in GLMMs for analyzing Binary correlated data. Type I Error and power of the Type III F-test for fixed effects of the GLMMs fitted for both simulated and actual data showed up better results when GLMMs were fitted with SVE than fitted with the standard method of variance estimation. Further, simulation study demonstrated that at higher level of correlation present in the data, the necessity of using SVE in GLMMs becomes more desirable. Further, it was revealed that classical estimator of SVE perform poorly at small sample sizes (n<= 50) whereas small sample adjusted versions of the SVE showed up better performance at small sample sizes. Thus, this study highlighted that careful use of SVE in GLMMs can help on improving its functionality under model missspecifications.