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Nonnormality of Data in Structural Equation Models

With the use of census block group data on sociodemographics, land use, and travel behavior, the cutoffs suggested in the literature for trustworthy estimates and hypothesis-testing statistics were tested, and the efficacy of deleting observations as an approach to improving multivariate normality in structural equation modeling was evaluated. It was found that the deletion of enough cases to achieve multivariate normality yielded results that were substantively different from those for the full sample and required that 17% of the sample be discarded. Alternatively, after only a few true outliers were deleted (0.8% of the sample), the measures of uni-variate and multivariate nonnormalities fell into the acceptable range for maximum likelihood estimation to be appropriate. The pursuit of a multivariate normal distribution by the deletion of observations should be consciously weighed against the loss of model power and generalizability in the interpretation of the results. That is, the analyst should proactively find the balance between the two extremes of (a) a model on the full sample that is unreliable because of extreme nonnormality and (b) a model on a sample that has discarded so many cases to achieve multivariate normality that it is no longer fully representative of the desired population. It is further argued that the process of finding that balance should be exposed to the audience rather than ignored or suppressed.