Estimation of regression models with nested error structure and unequal error variances under two and three stage cluster sampling

A simple transformation method, proposed by Fuller and Battese (1973), for making inferences from one and two-fold nested error regression models with equal error variances under two and three-stage cluster sampling is extended here to the more realistic case of unequal error variances. The method permits the calculation of variance component estimates and making inferences on regression parameters, using only ordinary least squares on the transformed data. Normality of the random errors in the model is not assumed. The transformation method of estimating variance components may be regarded as an alternative technique for implementing the well-known Henderson's Method of Fitting Constants, but it remains numerically stable in situations where the Henderson method involves fitting a large number of parameters.