Remedies for multivariate nonnormality in SEM

Nonnormality influence chi squre goodness-of-fit statistics, parameter estimates, and standard errors
Estimation-based redeies

• ADF--doesn't assume multivariate normality of the measured variable, ADF estimator produces asymtotically (large sample) unbiased estimates of the chi squre goodness-of-fit test, parameter estimates, and standard errors. With more than 20 to 25 measured variables, implemetation of ADF becomes impractical, even give modern high speed computers. ADF requires a large sample size. ADF can be trusted only at the largest (>5000) sample size. Hoyle and Panter (1995) recommend against ADF in favor of distribution-based adjustments to results of ML estimation.
• Satorra-Bentler scaled chi square statistic--scaled chi square statistic corrct or rescale the ML chi square statistic. However, it has a tendency to overreject true models at smaller sample size.
• Robust standard errors-- robust standard erros adjust standard error for the degree of multivariate kurtosis.
• Bootstrapping-- the bootstrap distribution will follow a noncentral chi squre distribution, rather than the usual central ch squre distribution specified by statistical theory

Reexpression of variables

• item parcels--Item parcels usually exhibit distributions that more closely approach a normal distribution than the original items. Item parcels produce composite variabels that more closely approximate normal distributions. Fewer parameters will need to be estimated in the measurement model. However, parcels may obscure the fact that more than on factor may underlie any given item parcel. The use of too few parcels as indicators of construct yields less stringent test of the proposed structure of confirmatory factor model. Identification problems are also more likely to occur if too few item parcels are used per factor,i.e, fewer than 3.
• Transformation of variables-- power function, logarithimic, squre root. Transformed data should be examined for univariate and multivariate normality to compare with the original data to see the improvement of normality.