GLM Introductory Overview - Doubly Multivariate Designs
If the product of the number of levels for each within-subject factor is equal to the number of original dependent variables, the within-subject design is called a univariate repeated measures design. The within design is univariate because there is one dependent variable representing each combination of levels of the within-subject factors. Note that this use of the term univariate design is not to be confused with the univariate and multivariate approach to the analysis of repeated measures designs, both of which can be used to analyze such univariate (single-dependent-variable-only) designs. When there are two or more dependent variables for each combination of levels of the within-subject factors, the within-subject design is called a multivariate repeated measures design, or more commonly, a doubly multivariate within-subject design. This term is used because the analysis for each dependent measure can be done via the multivariate approach; so when there is more than one dependent measure, the design can be considered doubly-multivariate.
Doubly multivariate design are analyzed using a combination of univariate repeated measures and multivariate analysis techniques. To illustrate, suppose in an algebra skills study, tests are administered three times (repeated measures factor Time with 3 levels). Two test scores are recorded at each level of Time: a Number Problem score and a Word Problem score. Thus, scores on the two types of tests could be treated as multiple measures on which improvement (or deterioration) across Time could be assessed. M transformed variables could be computed for each set of test measures, and multivariate tests of significance could be performed on the multiple transformed measures, as well as on the each individual test measure.
Between-subject designs
Within-subject (repeated measures) designs
Multivariate designs