Discrimination Between Two Species ofMicrotususing both Classified and Unclassified Observations

We analyse a set of morphometric data obtained from the skulls of 288 specimens ofMicrotus subterraneusandM. multiplex. The chromosomes of 89 specimens were analyzed to identify the species; species is unknown for the remaining 199 specimens. In this situation one may either use the classified observations to estimate a discriminant function (this is the traditional approach of discriminant analysis), or one may attempt to use the unclassified observations as well to improve parameter estimation. The latter case, which we refer to as Discrimix is a combination of discriminant analysis and finite mixture analysis which appears to be essentially unknown among biologists. Yet the method, the statistical theory of which is fairly well developed under the name “discriminate analysis with partially classified data“, has the potential to greatly improve the estimation of classification rules, as we illustrate using theMicrotusdata. Like finite mixture analysis,Discrimixrequires iterative computations to estimate the parameters, but has the advantage of fully using the information contained in both the classified and the unclassified observations to construct the classification rule. We illustrate both traditional discriminant analysis andDiscrimixin the univariate and the multivariate case, and use a bootstrap method to show that the estimates obtained fromDiscrimixare more stable (that is, have less variability) than those obtained from discriminant analysis.