Adaptive inference for multi-stage unbalanced exponential survey data

Two-stage sampling usually leads to higher variances for estimators of means and regression coefficients, because of intra-cluster homogeneity. One way of allowing for clustering in fitting a linear regression model is to use a linear mixed model with two levels. If the estimated intra-cluster correlation is close to zero, it may be acceptable to ignore clustering and use a single level model. In this paper, an adaptive strategy is evaluated 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.