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Discriminant function analysis is a statistical analysis to predict a categorical dependent variable (called a grouping variable) by one or more continuous or binary independent variables (called predictor variables). The original dichotomous discriminant analysis was developed by Sir Ronald Fisher in 1936.〔Cohen et al. Applied Multiple Regression/Correlation Analysis for the Behavioural Sciences 3rd ed. (2003). Taylor & Francis Group.〕 It is different from an ANOVA or MANOVA, which is used to predict one (ANOVA) or multiple (MANOVA) continuous dependent variables by one or more independent categorical variables. Discriminant function analysis is useful in determining whether a set of variables is effective in predicting category membership.〔Green, S.B. Salkind, N. J. & Akey, T. M. (2008). Using SPSS for Windows and Macintosh: Analyzing and understanding data. New Jersey: Prentice Hall.〕 Discriminant analysis is used when groups are known a priori (unlike in cluster analysis). Each case must have a score on one or more quantitative predictor measures, and a score on a group measure.〔BÖKEOĞLU ÇOKLUK, Ö, & BÜYÜKÖZTÜRK, Ş. (2008). Discriminant function analysis: Concept and application. Eğitim araştırmaları dergisi, (33), 73-92.〕 In simple terms, discriminant function analysis is classification - the act of distributing things into groups, classes or categories of the same type. Moreover, it is a useful follow-up procedure to a MANOVA instead of doing a series of one-way ANOVAs, for ascertaining how the groups differ on the composite of dependent variables. In this case, a significant F test allows classification based on a linear combination of predictor variables. Terminology can get confusing here, as in MANOVA, the dependent variables are the predictor variables, and the independent variables are the grouping variables.〔 ==Assumptions== The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables.〔 *Multivariate normality: Independent variables are normal for each level of the grouping variable.〔〔 *Homogeneity of variance/covariance (homoscedasticity): Variances among group variables are the same across levels of predictors. Can be tested with Box's M statistic.〔 It has been suggested, however, that linear discriminant analysis be used when covariances are equal, and that quadratic discriminant analysis may be used when covariances are not equal.〔 *Multicollinearity: Predictive power can decrease with an increased correlation between predictor variables.〔 *Independence: Participants are assumed to be randomly sampled, and a participant’s score on one variable is assumed to be independent of scores on that variable for all other participants.〔〔 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「Discriminant function analysis」の詳細全文を読む スポンサード リンク
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