Hi All,
I am in between running either MANCOVA/MANOVA or Multiple Regression on some data but none of my DV's (outcome variables) are normally distributed. In all actuality, they are predictably highly and negatively skewed as I used a 33-item scale to assess resilience. I am looking for some scholarly sources to validate that I can still run and report my statistical analysis even though my DVs are not normally distributed. I see some people arguing that the assumption of normality is outdated but others still stand by it.
*UPDATE*: I compared my measures of central tendency and all of them are nearly the same. For instance, for my overall resilience DV here are the scores:
Mean = 4.56
Median = 4.61
Mode = 4.55
Is this enough validation to still run a parametric test?
You can use the generalized estimating equation technique, which does not depend on the distribution of the data. The previous discussion can also be helpful: https://www.researchgate.net/post/What_do_I_do_if_my_data_distribution_is_not_Normal
Try article suggested by Md. Belal Hossain it will help greatly.
Hello Nuchelle,
Do recognize that the normality assumption associated with linear models applies to the errors after fitting the model, not the observed scores themselves. With that caveat mentioned, you can:
1. Use methods which don't require assumptions of normality. These generally include: (a) rank-based methods; (b) exact/permutation tests; (c) bootstrap tests.
2. Attempt to ameliorate the degree of departure from normality, via transformation. However, there are often data sets for which this approach simply won't work "perfectly."
While the generalized estimation equation (GEE) approach is mentioned above, my understanding is that it fares better at coping with variance/covariance heterogeneity than with non-normality.
Below are some links that introduce non-parametric multivariate methods which you may find helpful.
Good luck with your work.
https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=2072&context=jmasm
Article Nonparametric MANOVA approaches for non-normal multivariate ...
Nuchelle -
Normality for multiple regression refers to the estimated residuals, or the random factors of the estimated residuals in weighted least squares (WLS) regression, not to any of the variables, and is not a strict requirement. (Perhaps you were thinking about the 'not strict requirement' part? But this does not refer to the variables at all.)
If you plot predicted y on the x-axis, and estimated residuals on the y-axis, for a "graphical residual analysis," you can evaluate your model fit. Some kind of "cross-validation," considering held out or removed data, might help you study whether you have overfit to your particular sample. You might want to research "model selection" first.
A graphical residual analysis is also the first step to looking into heteroscedasticity in regression. (See examples in https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity. References there may be of some interest or perhaps lead to other references of possible use to you.)
Cheers - Jim
Nuchelle -
You asked about multiple regression, but did you mean multivariate regression? Perhaps you are just looking at a series of regressions, each with one independent variable and a dependent variable? I was just wondering if you needed to realize that you might be looking at the need for polynomial linear regression, or nonlinear regression, or even poisson regression. In multiple regression you could have polynomial terms. There may be many possibilities to explore.
At any rate, I think you will learn more from the regression approach because you can plot your data and see what relationships look like.
Cheers - Jim
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