# Regression with some observations having more than one factor level

I have data I want to analyze using multiple regression or machine learning: the response is cells for which I measured viability (a continuous response) and the independent variables are the genes in the genome where each can have 21 types of mutations. In other words, each gene is a categorical factor with 21 levels. The thing is that while 90% of the genes have only a single type of mutation the remaining 10% have multiple types of mutations. So in practice there are 612 combinations of mutations. One option is to have the 21 mutation types for each gene as a binary factor, meaning I'll have 20,000*21 = 420,000 factors. Another option is to have 612 levels for each of the 20,000 genes.

Which option is better given that I only have 500 cells and are there better options than those two?

• Would it help to have 21 predictor variables (called a, b, ..., u) each zero or one depending on whether that level is present for this case? – mdewey Jun 26 '16 at 15:57
• Thanks mdewey. I edited my text to clarify my problem. Hope it helps. – dan Jun 26 '16 at 16:13
• So to get this straight, you have 20k predictors that each represents if a particular gene has a particular type of mutation? Of the bat, I would suggest you aggregate the mutation type you see in a smaller number of categories. Also aggregate the genes in some kind of families/group. Having 500 cells and more than 20000 explanatory variables is just asking to overfit. Finally use LASSO or Elastic Net for fitting your model so you can induce some sparsity to your estimates. – usεr11852 Jun 26 '16 at 17:54
• If one only knew how to aggregate genes in a way that is relevant to the response.. – dan Jun 26 '16 at 18:19
• Do you have any idea of the effect you expect from an observation with two mutations? will the effects of the separate mutations add, or maybe "almost add" (like in effect =0.8(a+b)), or combine in some other way? with some such information, maybe we could taylormake a model? – kjetil b halvorsen Mar 19 '17 at 21:28