I conducted a study using three dependent variables, which were self-esteem, social identity and life satisfaction. I plan to use a multiple regression. When I looked at the histograms and shapiro wilks test, I found that the data for self-esteem and life-satisfaction was significantly skewed. As this is the case, what would my next step be?
Would I conduct a spearman's rho correlation followed by the multiple regression?
Or would I need to transform my self-esteem and life satisfaction variables to make them normally distributed and then conduct a Pearson's correlation followed by a multiple regression?
Also, if I needed to transform my variables how would I do this on SPSS?
Thank you
Multiple regression doesn't assume that your variables are normally distributed, only that your model residuals are. As you have three dependent variables you would have three models (with other independent variables explaining variation in those variables I guess). You can run the multiple regressions to see if your residuals are normally distributed.
If not then you can look into generalized linear-models, box-cox transformations or others.
If you are interested in analysing the three dependent variables concurrently, then you may want to consider the multivariate analysis approach.
Linear regression assumes normality of residuals, not independent or dependent variables. Most popular transformations are square root extraction (for moderate skewness), calculation of the logarithm (for high skewness) and the reciprocal transformation (1/x, for extremely high skewness). You can perform they by choosing Transform... - Compute variable in SPSS menu,
After fitting your regression model you have to check all the three assumptions on residuals, normality, independence (lack of cycles or other kind of patterns) and homoscedasticity (a.k.a. equal variance). Forget transformations, if residuals are not normal your model does not fit well. The logic behind is that after you have taken all the significant variables into account what is left (the error) must be WHITE NOISE, just something that is unpredictable (it is only in statistical terms - +/- Epsilon) and the most important, unexplainable by using a few additional variables.
Be aware of using 'traditional' multivariate regression methods, such as PCAR or PLS. Most people do not know they are based on the assumption of the multivariate normal distribution. They are based on the covariance matrix. They extract the factors/principal components, based on the assumption of variance/covariance, which is a symmetrical assumption.
See (it is an open access book):
Rencher, A. C. “Methods of Multivariate Analysis: Third Edition.” Methods of Multivariate Analysis, 3rd ed., Wiley, 2012, pp. 1–758, doi:10.1002/9781118391686.
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