 
Summary: Airoldi, J.P., Salvioni, M. & Flury, B. (1995). Discrimination between two species of Microtus
using both classified and unclassified observations. J. Theor. Biol. 177 : 247262.
We analyze a set of morphometric data obtained from the skull of 288 specimens of Microtus
subterraneus and M. 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 "discriminant analysis with partially classified data", has the potential to greatly
improve the estimation of classification rules, as we illustrate using the Microtus data. Like finite
mixture analysis, Discrimix requires iterative computations to estimate the parameters, but has
the advantage of fully using the information contained in both the classified and unclassified
observations to construct the classification rule. We illustrate both traditional discriminant
analysis and Discrimix in the univariate and multivariate case, and use a bootstrap method to
show that the estimates obtained from Discrimix are more stable (that is, have less variability)
than those obtained from discriminant analysis.
