I am trying to build a regression model where I have 25 independent variables(predictors) all of which 5 point Likert items and 1 dependent variable which is a mean score of a 7 point Likert scale (aggregated score). I need to filter the best possible predictors(variable selection) from these 25. I was wondering what type of regression should I use, linear or ordinal ?
I think I get it, too many questions. However, obtaining answers to them is important for a good recommendation.
One approach to answering your regression question would be to use the Lasso, a regularizing method, for variable selection. That said, every statistician and their sibling has a "favorite" variable selection method. The Lasso has the advantage of being called out by Larry Wasserman on his defunct Normal Deviate blog as one of the 10 best contributions to statistics in the last 10 or 20 years. The Lasso would reduce 25 variables down to a more manageable fewer number.
Then, there are plenty of heuristics for ranking variables by their relative importance, i.e., identifying the "drivers." A bad choice to avoid is using the betas or regression coefficients since they are not scale invariant. A better choice would be to rank the absolute values of the t-statistics associated with each variable. An "optimal" choice to relative variable importance would be to read Ulrike Groemping's papers on this area of statistical modeling and implement her own approach called RELAIMPO... https://prof.beuth-hochschule.de/groemping/relaimpo/.