An Expectation-Maximization Algorithm To Estimate The Parameters Of The Threshold Utility Model

This essay introduces an efficient expectation-maximization algorithm to estimate the parameters of the Threshold Utility Model,proposed and studied by Ruxian Wang and Guillermo Gallego in 2019.TUM is a multiple-product model which means the customer might buy more than one product in a purchase.Under the TUM,the customer would buy those products whose actual utility is higher than the threshold value.We assume that the utility function obey uniform distribution or exponential distribution for solvability.And because of the missing of some data,we introduces the EM method into our algorithm.Different from simple-product model,the data sets of TUM are quietly complicated.Thus we need some special optimization methods such as minorize-maximize to deal with the complicated log-likelihood function.At the end of our essay,we make a program in Python to test the algorithm.Besides,we make a comparison between our algorithm and the classic estimation method under MNL model.Our numerical experiments promote the application of TUM in the future research or management.