I am working on a case to finish my (not so advanced) data scientist course and I have already been helped a lot by topics here, thanks! Unfortunately now I am stuck again and cannot find an existing answer.

My data comes from a bike shop and I want to see if products bought during customers' first registered purchase are related to/have impact on how important they will become to the shop in the future. I have grouped customers into 5 clusters (from those who registered and made never any registered purchase again, through these who made 2-3 purchases for little money, those who made a few purchases for a lot of money to those who purchase stuff regularly and really bring a lot of money to this bike shop), I have ordered them into an ordinal dependent variable.

As the independent variables I have prepared 20+ binary variables that identify products/services bought during the first purchase from this shop (first purchase as a registered customer). One row per customer. So I want to check the idea if there are combinations of products (probably "extras" to the bike purchase) that can increase the chance that a customer would register and hopefully stay as a loyal customer for the future.

The dream would be be able to say, for example, if you buy a cheap or middle-cheap bike during this first purchase you probably don't contribute so much to the bike shop in a long term so you have low grade on the dependent variable. But those who bought a middle-cheap bike AND a helmet AND a lock (probably to special price) are more likely to become one of the loyal registered customers bringing money for a longer time.

There might be no relation like that but I want to test that anyways. Implementation of the result could be being able to recommend an extra product during a purchase (with a good price on it).

I am learning R during this course. We went through some techniques and first I was imagining it would be possible to work with the neural networks (just cause it sounded most fun to try), having all these products as input in the sparse matrix and the customers clusters as the output (I hoped it was similar to the examples I read about with sparse matrix with pixels from a picture as the input and numbers 1-9 as the output) but then I was told that this actually is based on pictures and real patterns and in my case I don't even know if there is any.

Then I was thinking I could try with the ordinal forest. But it doesn't predict my clusters well, not at all (2 out of 5 clusters get no predictions). But that is OK, I don't expect the first purchase to be able to predict all the customers future. But I would really want to see if there are combinations of products that might increase the chance that a customer ends up in one of the "higher" clusters on the loyalty scale.

I am not sure if this was clear enough. :) Do you think that there is any way of testing my idea? What could I try to do? Let me know if you need more information.