A simulation comparison of cluster based lack of fit tests

Abstract

Cluster based lack of fit tests for linear regression models are generally effective in detecting model inadequacy due to between- or within-cluster lack of fit. Typically, lack of fit exists as a combination of these two pure types, and can be extremely difficult to detect depending on the nature of the mixture. Su and Yang (2006) and Miller and Neill (2007) have proposed lack of fit tests which address this problem. Based on a simulation comparison of the two testing procedures, it is concluded that the Su and Yang test can be expected to be effective when the true model is locally well approximated within each specified cluster and the lack of fit is not due to an unspecified predictor variable. The Miller and Neill test accommodates a broader alternative, which can thus result in comparatively lower but effective power. However, the latter test demonstrated the ability to detect model inadequacy when the lack of fit was a function of an unspecified predictor variable and does not require a specified clustering for implementation.