Dear Chandrika

I agree with Rana and Helena. 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.

Good luck! 

Hello Chandrika

many researchers treat two as interchangeable, for studying groups differences in multiple variables, discriminant analysis DA used to pursuant MANOVA to identify dimensions of differences for groups. 

DA has two main purposes, predictive and descriptive, while MANOVA helps you to understand differences between groups

my opinion to use DA it will be more interpretable because you have 21 V's so your MANOVA table might be complex. DA will introduce 2 discriminant equations which is might be easier to interpret. Note that all this depends on your research questions and what your goal

Also see Tatsouka 1974 and Pedhazur1997 they will help you. 

Rana

Dear Chandricka, 

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.

When you aplly regression is when you want to explain a quantitative dependente variable as a function of quantitative independentes variables. In regression you could add as independent variables some qualitative variables ie dummies.

Helena

Dear Chandrika

I agree with Rana and Helena. 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.

Good luck! 

Dear Chandrika

You had better tried several methods systematically as follows.

1. Check the scatter plots indicating three groups. Do you know Fisher's iris data that consists of three species having 4 variables. By scatter plots, you can find setosa is separated by other species. This means the analysis is very simple. You can  discriminate two classes except Setosa and choose the best model (predictor variables).

2. Check 21 box-whisker plots by three classes. I skip this procedure and lost three years to resolve third problem of discriminant analysis (See my papers in 2014),

3. Try to the partition and the nominal logistic regression.

4. SPSS support the discrimination methods over three variables. However, I do not recommends the discrimination over 3-classes. 

5. You try the discriminate analysis and the regression analysis ( you use dummy variable y=1/-1 as the plug-in rule). You can choose the proper predictor variables.

6. By MANOVA, it is slightly difficult to find predictor variables.

Hi, Chandrika

All the answers that you've been given are quite useful.

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.

3) If using SPPS, also note that the variable selection criteria and estimation procedure are immensely important and have to match your research design (e.g. exploratory vs. confirmatory).