Posted by
Poes, Matthew Joseph on
Jan 05, 2012; 4:57pm
URL: http://spssx-discussion.165.s1.nabble.com/Question-about-the-linearity-assumption-for-Discriminant-Analysis-tp5121318p5123356.html
I believe this is due to a misunderstanding of what these two terms are dealing with, and what a DFA actually is. DFA can be thought of as an upside down ANOVA, it is an extension of the GLM. In an anova, you take a set of linear variables, and make a sample means comparison between groups, across those variables. The variables need not be linearly related to each other, they simply need to be linear continuous variables. This means normally distributed, equal error variance, etc. You can't use standard DFA to discriminate groups via categorical variables, even if they are ordinal, because it would break this assumption, just like it does for ANOVA.
Variables can also be linearly related within a DFA as well, this would just mean they have common variance. It may or may not be associated with their ability to help discriminate groups. To be honest, this is unimportant, other than, as you say, you want to have variables which are not overly highly correlated, but which have some meaningful reason to be in the DFA.
The end interpretation, as you probably know, is that you take a set of variables, which you believe can be used to discriminate amongst these groups, and are then able to quantify this ability in terms of their relative discriminant effect.
Matthew J Poes
Research Data Specialist
Center for Prevention Research and Development
University of Illinois
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of TomSnider
Sent: Wednesday, January 04, 2012 5:58 PM
To:
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Subject: Question about the linearity assumption for Discriminant Analysis
I'd appreciate an clarification of the linearity assumption for discriminant analysis. I am told that the model requires a linear relationship among the predictor variables within each group. At the same time, it would seem that we would prefer to reduce redundancy among the predictors -- i.e., have them be unrelated. I can't seem to reconcile these two demands. Could someone help?
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