I am trying to build a multiple regression model where I have 7 independent variables(predictors), out of which 3 are numerical and 4 are categorical(with each of factor levels upto 80). I need to filter the best possible predictors(variable selection) from these. Is there any way I can do this? I read about Lasso but I guess it can be applied only if all the predictors are of numerical in nature. Step wise selection is generally not advisable. Please help me with your ideas. Thanks.
Decision trees and Random forests are known to be useful to do feature selection. If you train your data on any of those at the end you'll be able to sort features by importante. The nature of those methods works by kind of splitting data based on the gain of information when a particular feature is used to split data. If you split the data with a good feature you'll will gain more information than if you split data with a bad feature.
Check this reference using R on the examples: http://freakonometrics.hypotheses.org/19835
The thing with lasso is that l1 regularization can produce 0 coefficients so people often refers to that property as a 'builtin feature selector'. If the coefficient is 0 it means that this feature it's not relevant to describe the data. It's also a popular way to do feature selection.