A comparison of some lack of fit tests based on near replicates

Several tests for regression lack of fit proposed by Christensen (1989), Shillington (1979) and Neill and Johnson (1985) are compared. The tests considered are applicable for the case of nonreplication and reduce to the classical lack of fit test when independent replications are available. A simulation study is used to compare the size and power of the test procedures for small sample sizes and various configurations of nonreplication. In addition, each test is shown to be consistent as well as invariant with respect to location and scale changes made on the regressor variables.