I would like to use R to do the following analysis:

A bank has 5 different investment products and I want to do an analysis to see the characteristics of individuals who are buying the investment products.

So I have Product A, Product B, Product C, Product D and Product E which are my dependent (target) variable.

I have the following independent variables of the individuals: - Age - Gender - Occupation - Geographical Area (of residence) - Marital Status

I would like to know the type of model that I can use in R so that I will be able to predict the type of investment product that would be bought by a 36-year old married woman who lives in Province A and is an Accountant. Please note that the dependent variable is nominal and has more than 2 levels.

I would also want to know how best I can validate the model in R

  • $\begingroup$ You could try search on multinomial regression. $\endgroup$ – user20650 May 11 '18 at 9:52
  • $\begingroup$ Here is an article that walks through an example in R. $\endgroup$ – Joel May 11 '18 at 15:22

A log-linear model from the nnet package (function ?multinom) can estimate the 4 simultaneous logistic regression models comparing the risk of opting for products B, C, D, or E vs A (as a referent). This will also give rise to absolute probabilistic predictions for each of the 5 products.

The space of all possible log-linear models might be too large. You describe 5 possible features: aside from age, gender, and marital status, we know nothing of geographic area or occupation. If each factor has over, say, 20 levels, then the number of parameters in the saturated model could be as large as $2^{(20 \times 20)} - 1$ which is probably singular. Even feature selection techniques like LASSO are ignorant to the fact that, say, "statistician" and "biostatistician" are somehow related careers.

If I were presented with this data analysis problem, I would first consider using some statistical or by-hand methods to aggregate down these factors into usable data.

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