I am planning to analyze my data through SEM. However, my data is not normally distributed and some variables are heavily negatively skewed. I have tried transform my data using log transformation, square root and inverse transformation but normality tests still indicate a non normal distribution. What else can I do to arrive to a normal distribution? Noting that I have tried to run the data through AMOS and I keep getting very large numbers for CMIN/DF fit indicators. I have a sample of over 500 cases.
Non-normality mostly affects the test statistics (chi-square test of model fit) and parameter standard errors when using maximum likelihood estimation in SEM. To obtain adjusted ("robust") test statistics, standard errors, and p-values with non-normal data, you can use the Bollen-Stine bootstrap option in AMOS.
You may use composite distribution which will take care of heavy tails.
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