The selection of optimal discriminant procedures for discrete data.

The statistical literature contains a wide variety of reports on procedures for discriminant analysis. They range from the classical linear discriminant and logistic model at one end of the spectrum through to the recent recursive partitioning and neural network based procedures in the field of pattern recognition at the other extreme. By contrast the literature offers little advice concerning choice of procedure especially for discrete data. This thesis therefore addresses the problem of selection of optimal discriminant procedures for discrete data.The problem is approached by identifying key determinants of procedure choice such as prior information about the data, sample size and the performance expected of the procedure. Two new ways of assessing performance of a discriminant are suggested for the discrete data situation. The first of these, the n- criterion, is a weighted sum of posteriors for correctly allocated and misallocated objects. The second consists of analysing performance in relation to the distribution of relative differences between the two largest posteriors. A selection tree is constructed on the basis of these two approaches.The results indicate that the n-criterion exhibits low variance as well as low bias but also has the ability to differentiate better than the customary error rate. The use of classification thresholds proves particularly useful in the detection of optimal procedures for discrete data. A structured approach using a selection tree is demonstrated and evaluated.Integration of the developed techniques into statistical software packages is recommended.