Discriminant analysis has the assumption of normal distributions, homogeneity of variances, and correlations between means and variances. If those assumptions are not fullfilled, is there any non-parametric method that can be used as a "substitute" for Discriminant analysis?
Many thanks in advance.
Discriminant analysis is robust to violation of normality when (1) data are randomly sampled, (2) sample sizes are large, and (3) groups have equal sample sizes. Also, Log or probit transformations of data can help make the data more normally distributed.
If all else fails, ordinal logistic regression will work (if the DV is ordinal). Otherwise, multinomial logistic regression (if the DV is nominal).
@Blaine Tompkins sorry but DA is not robust to non normality. I wrote my dissertation on robust DA lo those many years ago. Google Booth and Isenhour Robust Partial Discriminant Analysis. Computers and Biomedical Research. David Booth
David Booth. Although not optimal, DA is fairly robust to normality violations with an adequately large and random sample. This has been well-established. However, if one already has a large sample with non normal data, they may as well using logistic regression anyways.
Multicollinearity and unequal variance-covariance matrices are much bigger problems.
Jorge W. Moreno-Bernal ,, literarily in respect of your question, (not wanting to quess much on why you need alternatives to LDA, or not considering Quadratic Discriminant Analysis, QDA), testing of data prior to analysis is necessary, and atimes "classification trees" are recommended either as a replacement for LDA or as a supplement by Feldesman M. R. (2002), and whenever data do not meet relevant assumptions. Expecially, whenever the data set contains important cases with missing predictor variables.
I want to draw attention to this: alternative methods have prices, (loss of certain information), and do not necessarily answer the same research questions as that we wish alternative for. For instance, while logistic regression is very similar to discriminant [function] analysis, the primary question LR addressed is “How likely is the case to belong to each response group (i.e., DV)” whereas, DFA helps with “which response group is the case most likely to belong to, (given a creterion?)”.
Reference Feldesman M. R. (2002). Classification trees as an alternative to linear discriminant analysis. American journal of physical anthropology, 119(3), 257–275. https://doi.org/10.1002/ajpa.10102
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