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I want to estimate the parameters of a discrete choice model for an item (let's say a piece of stone). In the end, I want to predict a stone's attractivity or utility. Let's say there are 4 variables that determine the item's utility (weight, hardness, strength and weathering). Is there a way to estimate the parameters for each variable if I only have data on previous items that have been sold, with each unique variable values? So I'd have the values of the 4 variables for all stones sold in the past, but not of stones not sold. Or is it necessary to make an estimation of all stones out there?

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