GLM Unique Features - Analysis of Incomplete Designs
The analysis of incomplete designs, such as a 3 * 2 factorial design with one cell missing (unobserved), leaving only 5 cells for the analysis, poses numerous special problems. In particular, it is difficult and sometimes impossible to construct meaningful tests of the standard main effect and interaction hypotheses. Numerous solutions have been proposed, and one that is most widely implemented in other GLM programs is the so-called Type IV sums of squares solution. Interestingly, however, many statisticians who have closely examined the "performance" of this solution have concluded that it can lead to arbitrary, and sometimes grossly misleading results (e.g., Milliken & Johnson, 1992; Searle, 1987; see also Hocking, 1985); these issues are also discussed in some detail in the Type IV sums of squares topic.
STATISTICA GLM offers two additional solutions (see Six types of sums of squares): A solution we have called Type V sums of squares, which produces results consistent with the manner in which highly fractionalized designs are often analyzed in applied industrial experimentation (see Introductory Overview to Experimental Design), and a solution we propose to call Type VI sums of squares, which is identical to the effective hypothesis approach described by Hocking (1985; note that this approach applies to the Sigma-restricted solution; see also Sigma-restricted and overparameterized model).
Some authors (e.g., Milliken & Johnson, 1992) have also suggested that in factorial designs with "randomly" occurring missing cells, one should carefully construct planned comparisons for the means in the observed cells, to test the most meaningful hypotheses for the research questions at hand; Planned comparisons of least squares means describes the unique features available in GLM to pursue this strategy.