Classification Efficiency of Multinomial Logistic Regression Relative to Ordinal Logistic Regression

原文摘要

Classification procedures are useful for the prediction of a response (or outcome) as a result of knowledge of the levels of one or more independent (or predictor) variables. The procedure is said to classify the (possibly multivariate) observation to a level of the response variable. An example might be the prediction of whether an individual will be well, suffer a nonfatal heart attack, or suffer a fatal heart attack. This prediction might be made on the basis of the levels of various independent variables, such as weight, blood pressure, and serum cholesterol, to name a few. The three response categories of the aforementioned example are ordinal. An example of three nonordered response categories might be as follows: well, death from heart attack, and death from cancer. There is some recent interest in ordinal classification procedures. It is reasonable to assume that, when the response variable is ordinal, inclusion of ordinality in the classification model to be estimated should improve model performance. It is, however, also true that, if ordinality is indeed the case, it will be evident in the parameters estimated by the usual (unordered) models. If there may be applications where use of the ordinal models could lead to bias, it becomes important to evaluate the magnitude of any advantage these models may have in ordinal situations. That is to say, if ordinal models are measurably superior in ordinal situations, the benefit of using them may outweigh the risk of their misuse. The purpose of this research was to quantify the impact of incorporating an ordinality assumption into a classification model in the case in which ordinality is indeed a correct assumption. We have chosen to compare Anderson's ordinal logistic regression model (Anderson 1984; Greenland 1985) with the multinomial logistic model. The former is a special case of the latter, having been developed by imposing ordinality constraints on the latter. Therefore, their inherent relationship as ordered and unordered versions of essentially the same model makes them attractive to compare; differences between their performances may be attributed to the ordinality assumption rather than other differences. In this article, they are compared on the basis of their asymptotic rates of misclassification error. The ordinal model was found to be more efficient when efficiency was measured in terms of the asymptotic rate of excess classification errors due to estimation of parameters. The relative classification efficiency of the usual multinomial model to the ordinal logistic model was shown to decrease as the number of response categories increases, as the Mahalanobis distance separating response populations decreases, or as the number of independent variables increases.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）