Discriminant function analysis in marine ecology: some oversights and their solutions

Marine ecologists commonly use discriminant function analysis (DFA) to evaluate the similarity of distinct populations and to classify individuals of unknown origin to known populations. However, investigators using DFA must account for (1) the possibility of correct classification due to chance alone, and (2) the influence of prior probabilities of group membership on classification results. A search of the recent otolith chemistry literature showed that these two concerns are sometimes ignored, so we used simulated data sets to explore the potential pitfalls of such oversights. We found that when estimating reclassification success for a training data set, small sample sizes or unbalanced sampling designs can produce remarkably high reclassification success rates by chance alone, especially when prior probabilities are estimated from sample size. When using a training data set to classify unknown individuals, maximum likelihood estimation of mixture proportions and group membership afforded up to 20% improvement over DFA with uninformative priors when groups contributed to the sample unequally. Given these results, we recommend the use of (1) randomization tests to estimate the probability that reclassification success is better than random, and (2) maximum likelihood estimation of mixture proportions in place of uninformative priors.