Please note, the consumer market is oblivious to me. I know more about SARS-CoV-2 than commonly understood consumer brands (I've heard of Coca Cola).
Therefore - because I've not a clue how this data will behave - I'd use an algorithm robust against variance, imbalance and sparse data. Thus its got to be XGBoost. Still I wouldn't be aware if a transformation would be needed. It looks like standard ordinal data to me, so no.
Question If you want to identify what products/brands are most sensitive to post-code variation and from those brand types which are connected with other brand choices:
- XGBoost - accuracy, AUC-ROC, precision/recall/F1
- feature selection
- interaction analysis.
The postcode is the training target trained against brand preference. There's going to be missing data, could be lots of missing data - it will work regardless. So like washing machines might top the list and max out on the associated weight, simply rich postcodes buy high-end machine brands, other post-codes buy economy brands. That might form an interaction with other domestic appliances like cookers and fridges.
The data type might be 'brand' so just switch my term "cooker" for a given "cooker/domestic appliance brand" (I don't know any cooker nor appliance brands).
The concern with brand choice is there will be a frequency issue within each brand, so the variance will not be homogeneous for certain parts of the data but homogenous for other parts. I dunno, cars - post codes in certain areas are going to buy loads of cars more frequently. On the other hand, essentials like washing powder or tooth paste are probably exempt. It would need some thought.
If there are thousands of postcodes this isn't going to work, there would need to be an external criteria - like house price - to group equivalent postcodes together. If that approach was used there would need to be a control against geographic bias. If there were a limited number postcodes thats fine.
Once you've got your weights then certain consumer choices have stronger classification power in identifying a post-code, enabling targeting of a specific consumer choice in the future, targeted ads stuff like that.