Hi all,
My data exhibits univariate non-normality. I am using SPSS Amos 26. I am reading conflicting information. Some papers say that ML is robust to non-normality. Byrne says that Kurtosis must not be greater than 7, which is no in my case. A professor told me not to worry too much about normality, but the literature sometimes suggests evaluating normality before a CFA is performed.
I was thinking if expecting normal data for a survey is always reasonable. For example, if we ask respondents about how honest they are, most results will be skewed towards honesty. I am using a previously validated instrument. I have established discriminant and convergent validity as well as construct reliability using alpha, AVE, and CR. My model fit is border line. I am using a previously proposed model and just evaluating it against a different population.
I read the following in Blunch (2017):
"Since the consequences generally lie more with test statistics than with parameter values, you can use GLS or ML, and then regulate the test statistics using so-called robust statistics (see e.g. Chou, Bentler, & Satorra, 1991). This may in many cases be the best way to solve the problem, but it is not available in the present version (19) of AMOS."
Just confused!
Thanks,
Sal
You can remove multivariate outliers through the mahalanobis distance in the "Tests for normality and outliers" option in AMOS and remove all those evaluated with p values of .000 to improve multivariate normality
Look at this paper
Article Addressing non-normality: A taxonomy of approaches, reviewed...
Hello Sal,
If none of the usual remedies for non-normal data work or are acceptable to you, you should definitely consider bootstrapped estimates of model parameters when you run AMOS.
Good luck with your work.
You can expect that your data do not follow a normal distribution. This is ok for most statistical methods whenever the sample size is big enough - think on the central limit theorem which works in this case. For other application, e.g. regression, you would transform variables, e.g., log(honesty) instead of honesty before fitting the model.
However, outliers might be a problem.
There is some papers available, for example, in survey statistics:
M. Templ, J. Gussenbauer, P. Filzmoser: "Evaluation of robust outlier detection methods for zero-inflated complex data"; Journal of Applied Statistics, 0 (2019), 1; S. 1 - 24.
I would not use a kurtosis because it can be highly influence by outliers, and ML is not robust.
Sal -
You said "I was thinking if expecting normal data for a survey is always reasonable." You are correct, it often isn't reasonable. Normality in data is not really so ... normal. The Gaussian ("normal") distribution comes up often because of the Central Limit Theorem, with regard to the distribution of means, and "normality" is somewhat desirable for estimated residuals, but people often overemphasize normality.
For regression, the data need not be "normally" distributed. It is nice if the estimated residuals, or better, for weighted least squares (WLS) regression, the random factors of the estimated residuals, are not far from "normally" distributed, but you don't have to have that.
Note that the establishment survey data with which I worked for many years were highly skewed.
When data cover a large range of values, heteroscedasticity in regression can be particularly important. See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and updates.)
Cheers - Jim
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