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Because univariate normality, i. Stevens points out that because a multivariate normal distribution entails that all subsets of variables have normal distributions, one way to assess multivariate normality is to determine whether all pairs of variables are bivariate normal. It should be noted that LDA may still discriminate between groups even if the assumption of multivariate normality does not hold. On the other hand, multivariate normality does not necessarily mean that LDA will effectively discriminate between the groups.
If this assumption is violated, a quadratic discriminant analysis QDA can be used instead. In a review of several Monte Carlo studies, Stevens concluded that, provided that the sample sizes are equal, even moderate heterogeneity of the covariances does not substantially affect type I error.
Unequal sample sizes, on the other hand, are potentially very problematic if the covariances are unequal. Monte Carlo studies have shown that if the sample size is not large compared to the number of variables, the standardized discriminant function coefficients and correlations obtained in LDA are unstable Stevens, He further cautions that a small n:p ratio i. The analysis of cross-classified categorical data. Longitudinal analysis of categorical epidemiological data: A study of three mile island.
Environmental Health Perspectives, 63, — The analysis of cross-classified data having ordered categories. London: Harvard University Press. Google Scholar Gonul, F. Modeling multiple sources of heterogeneity in multinomial logit models: Methodological and managerial issues.
Marketing Science, 12, — Methods for categorical longitudinal survey data: Understanding employment status of Australian women. Victoria: University of Melbourne. Google Scholar Lipsitz, S.
Analysis of repeated categorical data using generalized estimating equations. Statistics in Medicine, 13, — Statistical analysis of categorical data. A panel multinomial logit analysis of elderly living arrangements: Evidence from aging in Manitoba longitudinal data, Canada.
Analysis of repeated ordered categorical outcomes with possibly missing observations and time-dependent covariates. Journal of the American Statistical Association, 83, — Dynamic mixed models for familial longitudinal data.
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