anita_jiu
hi, there
I'm struggling at the moment about Discriminant Function Analysis. There are 2 primary assumptions about this technique; one of them is to assume that the variance/covariance matrices of variables are homogeneous across groups. Like ANOVA/MANOVA, Box's M test is used to test this assumption. In my sample, the test shows a statistical significance at the p level of 0.0001. In other words, my data seems to be violating the assumption of equal covariance among groups.
I'm wondering, having known that the M test is sensitive to deviations from multivariate normality while the result from my sample does show a statistical significance, is it appropriate to carry on the rest of the analysis? Would you have any thoughts regarding the above, pls?
Much appreciation for your interactions and feedbacks.
ilikemath
maybe your sample is heteroscedastic, make a transformation first .
anita_jiu
Hi, Ilikemath
Thanks for the reply. To a large extent, my sample shares homogeneity. This is why I'm confused by the Box's M text...
anita_jiu
啊，这个Box's M test，终于搞清楚了。由于这个测试对样本人数特别敏感，我随机挑选了９０人（３０各一组，共３组）去做测试。最后发现这个test doesn't show significant results on 3 independent variables but significant on the other 2 independent variables.
我还找到其他的文献，说明在使用discriminant analysis时，Box's M test只是测试其中一种assumption. But it's not the unique test 'justifying' whether your data is appropriate to use discriminant analysis. When your dependent variable group sizes are unequal and the whole sample is also large, it's very common that the M test would show significant result. However, researchers shouldn't decide to/not to apply discriminant analysis solely depending on the M test result. Rather, other assumption criterion should be considered, e.g. normality, multicollinearity, etc. This is what I have found so far.
