(A) study of the test of each factor's effect in full model with missing cells

Abstract

In the analysis of linear models for designed experiments, SAS furnishes sums of squares corresponding to different four hypotheses defining a main effect. Elston (1964) suggests that it is still possible to test the main effect when some of the subclasses are empty. But this can be extended to any case in which missing cells exist. Even in case of full model that missing cells exists, we can obtain sum of squares (corresponding to Type IV) testing main effect. In general case we can find sum of squares that is reduced to main effect under $\Sigma$-restriction and $\gamma$ missing cell = 0