Solved – How to interpret a predictor with a positive structure coefficient and a negative standardised coefficient in discriminant function analysis

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I am doing a discriminant function analysis and I have four continous independent variables
and one categorical dependent variable (that has 3 groups). I have
chosen to do this analysis to see how these groups
can be predicted by the four independent variables.

  • Firstly, when we are interpreting the results, do we look at standardised coefficients or the structure matrix coefficients? From my reading of the literature,
    I have found contradictory opinions. Some say that structure
    coefficients are better since they are more stable while others say
    that both standarized and structure coefficients should be looked at.

  • Secondly, when I do look at both structure and standardized
    coefficients, two of my dependent variables have the opposite signs
    for their standardized and structure coefficients (for both of them
    the structure coefficient is positive and more than .30 whereas the
    standardized coefficient is negative and has a very small value).
    I have read up some stuff on it and I think these are suppressor
    variables (they are related to the other IV's but do not directly
    predict the DV). How are we supposed to handle these suppressor
    variables?

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The main difference between the coefficients and the correlations (elements of structure matrix) is not that these are less stable than those. Coefficient shows partial (i.e. unique) contribution of the variable to the discriminant function score, it is like regression coefficient. Correlation shows omnibus (i.e. unique + shared with other variables) contribution of the variable to the score, it is in fact usual zero-order correlation. You may look at both coefficients and correlations, keeping in mind the above differences. If you plan to interpret discriminant functions like you interpret factors in factor analysis, I think you better look at coefficients, which are formally similar to loadings of factor pattern matrix, with one important distinction though, that in factor analysis factor "loads" variable, while in discriminant analysis variable "loads" discriminant function.

I would not hurry to call the two variables with sign disagree between coefficients and correlations "suppressor variables". Yes, suppressors often show such a pattern, yet there are suppressors apart from it. Also, other things than suppresorness can cause it, for example collinearity. The definition of suppressor variable within multiple regression is that it rises R-square by greater amount than its own squared Pearson r with the DV. In the context of discriminant analysis, mean squared canonical correlation will stand for R-square, I believe. But what can stand for squared Pearson r? – at this point I'm not sure [Pillai's trace, I suspect?]; so, I'm not clear about how to define suppressor in discriminant analysis.

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