Data-driven transformations and survey-weighting for linear mixed models

Many variables that social and economic researchers seek to analyze through regression analysis violate normality assumptions. A standard remedy in that case is the logarithmic transformation. However, taking logarithms is not always sufficient to reestablish model assumptions. A more general approach is to determine a family of transformations and to estimate the adequate parameter of such a transformation. This can also be done in mixed effects models, which can account for unobserved heterogeneity in grouped data. When the analyzed data is gathered from a complex survey whose design is informative for the model - which is difficult to exclude a priori - a bias on the transformed linear mixed models can occur. As the bias affects the transformation parameter, too, the distortion to the parameters in the population is even more problematic than in standard regression. In standard regression, survey weights are used to account for the design. To the best of our knowledge, none of the existing algorithms allows to include survey weights in these transformed linear mixed models. This paper adapts a recently suggested algorithm to include survey weights to Box-Cox or dual transformed mixed models. A simulation study demonstrates the need to account for informative survey design.