# Finding the most important product feature for a customer

Looking at a data of the format given below, I am asked to find the (top 3) feature(s) that affect a customer's purchase preference the most.

In the dataset below, each customer row contains the break-down of purchases of a single product by various features of the product. Fi stands for the i'th product feature (e.g. colour, material) and Catj stands for the j'th value that a feature can take on (e.g. Purple, Woolen, etc). All features are categorical and they can take on different number of categories, e.g. F1 below can take on 3 categories, F2 can take on 2.

 Customer  |  F1,Cat1  | F1,Cat2 | F1,Cat3 | F2,Cat1 | F2,Cat2 |...  | Fi, Catj|
1      |    100    |    800  |   100   |   1200  |   1200  |...  |   ...   |
2      |    300    |    300  |   300   |    100  |    900  |...  |   ...   |
3      |    250    |    250  |   250   |    200  |    100  |...  |   ...   |
...    |    ...    |    ...  |   ...   |    ...  |    ...  |...  |   ...   |


I don't have a statistical background. However, I can visually interpret that Customer 1 is highly selective on F1, and majorly prefers Cat2 over other categories of this feature. On the other hand, her purchases wrt Feature 2 show that she is not very selective about the binary F2 feature. The situation is reversed for Customer 2.

Q1. What is the most suitable formal method to carry out an analysis like this? (I thought this may be achieved by analysing the variances per feature.)

Q2. Is it OK to assume a multinomial distribution for each categorical feature? If so, we get covariance matrices per each feature, and I am not sure how to interpret them.

Any comments or pointers to relevant online sources will be greatly appreciated!