# Multinomial Logistic Regression- goodness of fit and alternatives

I am trying to do future 2 year value prediction at an individual customer level. Originally I tried to use a linear regression for this prediction, but was getting really poor r-squared value. (0.31) Hence, I converted to problem into a classification problem and used multinomial logistic model. (multinom from R's nnet package)

I converted the 2 year value into 5 classes, the relative proportion of the classes in the training sample is as follows:

Class 1 (not transacted)- 72%
Class 2 (< 10K )- 19%
Class 3 (10K- 25K)- 5%
Class 4 (25K-50K) - 3%
Class 5 (>=50K)- 2%

The code and results for the multinomial logistic model are pasted below:

Call: multinom(formula = REV_DEC13_NOV15_5_bands_factor ~ REV_DEC12_NOV13 + VISITS_IN_DEC12_NOV13 +QUANTITY_VISIT_DEC12_NOV13 + DISTINCT_Category_IN_DEC12_NOV13 + DISTINCT_Subcategory_IN_DEC12_NOV13 + TENURE_TILL_NOV13 , data = data_Single_Trans) While, they are not included here, I have also got a p-values for all variables and categories.

Questions: 1. How do I know whether the model is a good one? What are the goodness of fit metrics for a multinomial logistic model?

1. Is multinomial logistic model a good way to address this kind of a problem? What are other techniques I could think of?

2. Does multinom take care of the interaction effects if any?

3. I scored the model to get the 5 probabilities. For doing the class-assignment, I picked the class with the highest predicted probability. Is there any other way of doing this?

• This question has been asked on the website previously. Here is one of the links: stats.stackexchange.com/questions/83899/…. Translating a regression problem (by its nature) to classification just because regression does not give good results is not a very sound strategy. If I were you, I would spend more time on identifying why regression did not turn out as well as expected, rather than switching to classification. – Zhubarb Dec 29 '15 at 9:23
• Thanks @Zhubarb for the quick revert. I had already gone through the earlier question, and one of my team members is pursuing the linear model. However, on the multinomial logistic model, I would still like to have answers to the questions 3 & 4 from my list above. Also, Would be great if someone could Someone could point me to R-implementations for: Hausman or Small-Hsiao tests of the IIA Various scalar measures of fit (like McFadden's R2) Wald or LR tests for combining alternatives – TAK Dec 29 '15 at 9:34
• I agree with @Berkan and don't think multinomial regression is ideal here (among other things, your discretized variable is now ordinal, not categorical). But as for your question #3, the model cannot 'take care of' interaction effects if they have not been specified in its structure. – mkt Apr 3 '18 at 11:27