I am training a logistic regression model on some continuous numeric data with binary labels, and I have access to an auxiliary variable (discrete, numeric). This auxiliary variable represents the ordinal position of an item on a web page. Each item has an 𝑜𝑟𝑑𝑖𝑛𝑎𝑙𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛∈ℤ+ denoting it was either the first item, second from the top, third from the top, and so on.
This auxiliary variable is NOT available in our production environment, but I would still like to train the model in such a way that the ordinal position does not bias our results (i.e., normalize by ordinal position). How might this be done?
I have thought about aggregating records by 𝑜𝑟𝑑𝑖𝑛𝑎𝑙𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛, finding the average score by group, finding the grand-mean, deleting records in above-grand-mean groups (to lower group's mean to grand-mean), and artificially adding records to below-grand-mean groups (to raise group's mean to grand-mean). However, I am concerned this will skew the results.