Beginner Researcher Here:
I am using the 10-Item Personality Inventory (Gosling, Rentfrow, & Swann, 2003) that measures the Big-5 traits . My preliminary analysis reveal that the data is not normal even after eliminating outliers and doing necessary transformations. Could the nature of the scale be an issue?
My DV's are also on a 7-point Likert scale that assesses likelihood of showing different types of behavior on Snapchat.
I believe personality is a reflective construct. What is the best possible regression I can run in order to see how personality traits influence such behaviors. Do I need to ensure normality before moving ahead?, which could mean that I re-run the survey on an entirely different sample (My original sample is of undergraduate students)
Thanks in advance.
There re usually not any regression assumptions for the distributions of independent variables. The assumptions of normality in some regressions is of the residuals. Still, if the variables are very skewed you may want to think whether the difference between say 6 and 7 is the same as between 4 and 4. As far as removing outliers, I would be careful doing this unless you know you these cases are not part of the population in which you are interested. For example, if am doing a reaction time study and somebody sneezes, I would remove that. Just removing, for example, cases that are +- 3 sd away from the mean affects how you would do subsequent statistics. Rand Wilcox, in his textbooks and monographs, discusses this.
Agree with Daniel, if you are talking about the IV as skewed, this is not a needed assumption in MLR. The normality assumptions is required for the DV.
And the normality assumption is of the residuals, not the IV or the DV.
Thank you for you answers Daniel and Muayyad. I am not achieving normality on the residuals either. Does this mean that my model is a non-linear one?
No, the distribution of the residuals is not about whether a straight line is a model for the data. These are different issues.
The problem with many non-normal sets of residuals is that they are tail heavy, and in procedures that use (or effectively use) least squares these tails are weighted highly, and thus a few points can greatly affect your results. Some people use more robust methods if the tails are heavy (and some people just ignore it and put up with lower power and accept that they may miss some effects). As above, I think the Wilcox textbooks are a good place to start.
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