Date of Award
Doctor of Philosophy
When outcome is ordinal, it would be expected that classification procedures which assume ordering will be superior to classification procedures which do not assume ordering. The objective of this research was to quantify this advantage in terms of reduced classification errors. The assumptions of ordinality of y and multivariate normality of x were imposed. The problem was approached geometrically. Equations were derived to express the asymptotic error rate of a classification procedure in terms of the deviation of the estimated classification boundaries from Fisher's optimal boundaries. The asymptotic relative efficiency of two procedures was defined in terms of asymptotic classification error rate. These equations can only be applied to procedures whose classification boundaries are estimates of Fisher's optimal boundaries. Some theoretical limits of asymptotic relative classification efficiency were derived and some evaluations were performed for pairwise combinations of the normal discriminant procedure, the multinomial logistic procedure, the ordinal logistic procedure (Anderson, 1984) and an ordinal normal discriminant procedure (proposed in this thesis). A commonly referenced ordinal procedure is the proportional odds procedure (McCullagh, 1980). The classification boundaries of the proportional odds model are not estimates of Fisher's boundaries, therefore this model could not be compared to the above models in terms of relative classification efficiency. However some theoretical properties of the proportional odds procedure and its classification boundaries were investigated. Specifically, the boundaries associated with two classification procedures associated with the proportional odds model were investigated for properties under the conditions of pooling of adjacent outcome categories.
Campbell, Martha Karen, "Asymptotic Error Rates Of Classification Procedures When The Response Variable Is Ordinal" (1986). Digitized Theses. 1541.