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In statistics, ordinal regression is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant. It can be considered an intermediate problem in between (metric) regression and classification. Ordinal regression turns up often in the social sciences, for example in the modeling of human levels of preference (on a scale from, say, 1–5 for "very poor" through "excellent"), as well as in information retrieval. In machine learning, ordinal regression may also be called ranking learning. ==Linear models for ordinal regression== Ordinal regression can be performed using a generalized linear model (GLM) that fits both a coefficient vector and a set of ''thresholds'' to a dataset. Suppose one has a set of observations, represented by length- vectors through , with associated responses through , where each is an ordinal variable on a scale . To this data, one fits a length- coefficient vector and a set of thresholds with the property that . This set of thresholds divides the real number line into disjoint segments, corresponding to the response levels. The model can now be formulated as : or, the cumulative probability of the response being at most is given by a function (the inverse link function) applied to a linear function of . Several choices exist for ; the logistic function : gives the ordered logit model, while using the probit function gives the ordered probit model. A third option is to use an exponential function\ : which gives the proportional hazards model. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「ordinal regression」の詳細全文を読む スポンサード リンク
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