My independent variables are on a 7-point Likert scale, and despite of log transformations, they still didn't achieve normality. My dependent variables are also on a seven-point Likert scale.
What regression method would suit this? (I'm studying influences of Big-Five personality traits on Snapchat use among millennials. My sample size is 280)
Please check this article:
http://www.theanalysisfactor.com/the-distribution-of-independent-variables-in-regression-models/
There is no requirement that IVs be normal. The IVs are fixed. If the IVs aren't fixed, see errors in variable models. As far as DVs go you might look at limited dependent variable models. See below. Best, David
https://www.google.com/#q=limited+dependent+variable+models+
https://www.google.com/#q=errors+in+variables+models+
Because your outcome is ordered I suggest that you use ordered logistic regression
http://stats.idre.ucla.edu/stata/dae/ordered-logistic-regression/
http://web.pdx.edu/~newsomj/da1/ho_levels.pdf
Ordered logistic regression can be quite complicated. If your Likert-scored variables are part of a scale, then you should assess the extent to which they do indeed form a scale, and if so, then use that scale as a linear variable.
Because there have been so many questions here about Likert-scored items and scaling, I have collected a set of resources on this topic:
https://www.researchgate.net/post/How_can_one_help_people_create_simple_scales_from_Likert-scored_items
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