Multivariate GLM, MANOVA, and MANCOVA

Multivariate GLM is the extended form of GLM, and it deals with more than one dependent variable and one or more independent variables. It involves MANOVA and MANCOVA, which are the extended forms of ANOVA and ANCOVA, for multiple parameters.

MANOVA in multivariate GLM is used to observe the main and the interaction effects of categorical variables on which multiple interval natured dependent variables depend, it is used to test the null hypothesis.  In other words, it is used to test that the vectors of means on multiple dependent variables are equal across the groups.  In SPSS, it is done by selecting “General Linear Model” from the analyze menu, and then selecting the “Multivariate” option from the General Linear Model.  MANOVA is appropriate when there are two or more dependent variables that are correlated.

MANCOVA in multivariate GLM is an extension of ANCOVA.  MANCOVA involves examining the influence of uncontrolled independent variables, while examining the differences in the mean values of more than one dependent variable related to the effect of controlled independent variables.  MANCOVA is similar to MANOVA in multivariate GLM, except that the interval independents are added with covariates.  These covariates in MANCOVA serve as control variables for the independent factors.  In SPSS, MANCOVA is done by selecting “General Linear Model” from the analyze menu, and then selecting the “Multivariate” option from the General Linear Model.

MANCOVA is a kind of ‘what if analysis’ in which the researcher analyzes what the results would be if all the cases scored equally on the covariates, such that the factors over and beyond the covariates are diminished.

There is a term called Step down MANOVA which can also be called Roy-Bargman Stepdown F test.  Step down MANOVA in multivariate GLM is used to perform a significance test of the main effects in order to prevent the inflation of Type I errors.

Basically, MANOVA in multivariate GLM is a two-step procedure which involves the significance test and the post hoc test.

There are certain significance tests in MANOVA. These are the Hotelling’s T square test, the Wilk’s lambda U test, and the Pillai’s trace test.

There are certain assumptions of Multivariate GLM.  These assumptions are as follows:

• The independent variables are categorical in nature.
• The dependent variables are continuous and interval in nature.
• The covariate variables are assumed to be measured without error.
• The residuals in multivariate GLM are randomly distributed.
• There should be no outliers as MANCOVA is highly sensitive to outliers in the covariates.

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Resources

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Hand, D. J., & Taylor, C. C. (1987). Multivariate analysis of variance and repeated measures. London: Chapman and Hall.

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Huynh, H., & Mandeville, G. K. (1979). Validity conditions in a repeated measures design. Psychological Bulletin, 86(5), 964-973.

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Olson, C. L. (1976). On choosing a test statistic in multivariate analyses of variance. Psychological Bulletin, 83(4), 579-586.

Powell, R. S., & Lane, D. M. (1979). CANCOR: A general least-squares program for univariate and multivariate analysis of variance and covariance. Behavior Research Methods & Instrumentation, 11(1), 87-89.

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Smith, H. F. (1958). A multivariate analysis of covariance. Biometrics, 14, 107-127.

Related Pages:

Conduct and Interpret a One-Way MANOVA

Conduct and Interpret a One-Way MANCOVA

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