ABSTRACT
Once an adequate covariance model has been selected to describe the relationship between the dependent variable and the covariates, it often is of interest to see if the models differ from one treatment to the next or from treatment combination to treatment combination. If one is concerned about the experiment-wise error rate in an analysis involving many tests of hypotheses, this procedure can provide that protection if it is used as a first step in comparing the treatments’ models. Suppose the selected analysis of covariance model is
(8.1)
for i = 1, 2, …, t and j = 1, 2, …, n
. The equal model hypothesis is
This type of hypothesis can be tested by constructing a set of contrast statements in either PROC GLM or PROC MIXED or the model comparison method can be used to compute the value of the test statistic. The methodology described in this chapter is an application of the model comparison method that can easily be used to test the equality of models in many different settings. Schaff et al. (1988) and Hinds and Milliken (1987) used the method to compare nonlinear models. Section 8.2 describes the methodology to develop the statistics to test the equal model hypothesis for a one-way treatment structure, and methodology for the two-way treatment structure is discussed in Section 8.3. For two-way and higher order treatment structures, this process generates Type II sums of squares (Milliken and Johnson, 1992). Three examples are used to demonstrate the methods.
