Discriminant function analysis: Difference between revisions

Revision as of 00:39, 26 April 2012

Revision as of 00:41, 26 April 2012

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*[[Normality|Multivariate normality]]: Independent variables are normal for each level of the grouping variable.<ref name="buy"/><ref name="green"/>

*Homogeneity of Variancevariance/Covariancecovariance ([[homoscedasticity]]): Variances among group variables are the same across levels of predictors. Can be tested with BoxesBox's M statistic .<ref name="green"/>.{{pn}} It has been suggested, however, that [[linear discriminant analysis]] be used when covariances are equal, and that [[quadratic classifier#quadratic discriminant analysis|quadratic discriminant analysis]] may be used when covariances are not equal.<ref name="buy"/>

*[[Multicollinearity]]: Predictive power can decrease with an increased correlation between predictor variables.<ref name="buy"/>

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*[[statistical independence|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.<ref name="buy"/><ref name="green"/>

It has been suggested that discriminant analysis is relatively robust to slight violations of these assumptions,<ref>Lachenbruch, P. A. (1975). ''Discriminant analysis''. NY: Hafner</ref> and it has also been shown that discriminant analysis may still be reliable when using dichotomous variables (where multivariate normality is often violated).<ref>Klecka, William R. (1980). ''Discriminant analysis''. Quantitative Applications in the Social Sciences Series, No. 19. Thousand Oaks, CA: Sage Publications.</ref>.

==Discriminant functions==