Question

What are the differences between MANOVA and discriminant analysis? What situations best suit each multivariate technique?

Answer 1

def:

1. Multivariate Analysis of Variance (MANOVA)

Multivariate analysis of variance, or MANOVA, like univariate analysis of variance is aimed at testing the null hypothesis that the means of groups of observations are identical. Rejection of this hypothesis is generally accompanied by the scientific conclusion that the groups of observations are indeed different, or were generated by some different process, or come from different underlying populations.

2. Discriminant Analysis

Discriminant analysis has several interrelated objectives that include:

• identification of how one or more groups of observations differ as discribed by one or more, usually several, interrelated variables
• identification of which variables best distinguish among the different groups
• assignment or classification of new observations to one or another of the groups based on the values of the variables

Illustration

When you aplly discriminant analys is when you want to discover the best variables that distinguish groups. Sometimes it is better to use categorical models, because demand less pressuposts.

When you apply Manova is when you have several quantitative dependent variables that are to be explained by several qualitative independent variables.

1) MANOVA is basically a canonical correlation and its output is comparable to the descriptive results of discriminant analysis. Logistic regression and discriminant analysis accomplish the same task through different means. Logistic regression "relates" the predictor variables to the groups using the maximum likelihood procedure while discriminant analysis uses predictor variables to distinguish groups using variances/co-variances.

2) If you do choose to go with discriminant analysis, please note that this tool has strict conditions regarding number of groups (g), number of discriminating variables (p), number of cases in group i' (ni), and total number of cases across all groups (n.). This is over and above the requirements for multivariate normality.

or

Discriminant analysis, MANOVA and regression have different purposes of applications and should be used according to the aim of the analysis. In particular, regression analysis should be carried out before even proceeding with morphometric variation analyses given that patterns of morphometric relationships can be influenced by the effect of allometric growth and size in species of undetermined age. I think in your case, dealing with 3 groups, discriminant analysis would be efficient enough to to determine which of the variables discriminate between groups. The relative contributions of each variable would be assessed on the basis of the structure correlations (discriminant loadings), rather than the discriminant coefficients, as the former are considered more valid in interpreting the discriminating power of the independent variables. MANOVA would consider all examined variable to depict significant differences among tested populations or groups.