Hello, I have not normally distributed data and wonder if I should use and report the standard Maximum Likelihood Model Fit Indices such as CFI, TLI etc. or if I cannot use them due to non-normality. I'm also unsure if I went correctly in the SEM procedure regarding non-normality.
This is the order I proceeded:
Model: UTAUT2, n=120, Software: AMOS 23, SPSS 23
1. Exploration
1.1 Eye-Inspection of data in SPSS for outliers (straight-liners)
1.2 KMO & Bartletts test -> both suggest data fitness for FA
2. CFA:
2.1 Construct reliability and validity -> good after modification
2.2 Model Fit Indices (based on MLE) -> acceptable
2.3 normality test -> items are not normally distributed
2.4 Bollen-Stine Bootstrap -> p not significant, which means model should NOT be rejected
2.5 Bootstrap -> Bias-corrected percentile Method -> all items load significantly
3. Structural Model:
3.1 Bollen-Stine -> p not significant -> model is not rejected
3.2 Model Fit Indices (based on MLE) -> acceptable
3.3 Bootstrap -> Make assumptions
I'd be very thankful for any help and recommendations.
You can perform mahalanobis distance to delete data to typical .000 (AMOS or SPSS). You can also consider another estimator such as ULS for non-normal data.
Cristian Ramos-Vera Thanks for your help. I tried to delete the biggest outliers but it didn't change too much. I also tried to estimate with ULS but it seems there are no standard errors being estimated with ULS and I need to know the significance of the estimates. But I could use ULS to obtain model fit indices and then use ULS bootstrap to get significance levels of the estimates. What do you think about it?
Preliminary analyses should be done for confirming adequate sample size with free of outliers and missing data. Normality, homoscedasticity and multicollinearity should be checked. Then god for CFA to see the factor loading and of course fitness of CFA. If it permits then go for initial or theoretical model. Check the fitness of the initial model and if needed you can modify or adjust within the fitness but no need to change the theoretical shape just for finding significance. When the latent variables are more than 7 and model is more complex with second or third degree relation it's really quite challenging to find everything like the theoretical model.
You can read more from the book.
Hair JF, Black WC, Babin BJ, Anderson RE. Structural equations modeling overview. Multivariate Data Analysis, 7th edition. United Kingdom: Prentice Hall PTR; 2013.
Muhammed Ashraful Alam Hello, thanks for your response and recommendations. Modification was needed due to some very low loading items but the theoretical shape has not been changed. I am now wondering if it would be adequate to conduct a ULS estimation for Model Fit and ULS bootstrap to estimate the significance. Would you consider this adequate for a non-normal distributed sample?
Preliminary analyses should be done for confirming adequate sample size with free of outliers and missing data. Normality, homoscedasticity and multicollinearity should be checked. Normality and non normal distribution are not the same thing. You have to ensure normality for SEM.
Please go through the book mentioned previously.
ULS estimation can be applied for data with non-normal distribution unlike the ML estimator.
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