Robustness of Adaptive Methods for Non-Normal Data: Skewed Normal Data as an Example

Estimation of variances of the estimated regression coefficients and their estimators is based on fitting a linear regression model. One method for allowing for clustering in fitting a linear regression model is to use a linear mixed model with two levels. It is probably suitable to ignore clustering and use a single level model if the intra-class correlation estimate is close to zero. In this paper, a two-stage survey is used to evaluate an adaptive strategy for estimating the variances of estimated regression coefficients. The strategy is based on testing the null hypothesis that random effect variance component is zero. If this hypothesis is accepted the estimated variances of estimated regression coefficients are extracted from the one-level linear model. Otherwise, the estimated variance is based on the linear mixed model, or, alternatively the Huber-White robust variance estimator is used. A simulation study is used to show that the adaptive approach provides reasonably correct inference in a simple case.