# Inference on survey results

I have user responses to different types of surveys (e.g. "car survey", "lifestyle survey",...). Most of the users have answered just a very small number of surveys. I would like to predict the response on the remaining unanswered surveys based on all the data available (answered surveys and user demographics). The surveys have categorical variables and numerical variables as well as single and multiple responses.

The approach I have begin with is to treat the problem as a recommender system, where the items are the different questions. However I am not sure this is the best possible approach. Specifically I am having troubles dealing with categorical variables and the multiresponse questions as most of the literature about recommender systems focus on the rating user-item problem.

I am also experimenting creating a glm model for each question. It gives me good results but it is slow and it does not scale very well. I have ~150k users and 200 questions.

Do you know any better approach to the problem? How can I manage the problems with the recommender system approach (categorical variables, multiple response)?

Thank you!

I would see this as a missing data problem. One very common approach for such problem in surveys is imputation. In your case, since you have multiple variables to impute, but also multiple fully observed variables, you could try using a Multivariate Imputation by Chained Equations (MICE) approach, which is implemented in R in the mice package. A similar approach is the Sequential Regression Imputation Method (SRIM), which is implemented in IVEware available both in a stand-alone and SAS version.