A. Serdar Simsek
Research
Publications
An Expectation-Maximization Algorithm to Estimate the Parameters of the Markov Chain Choice Model (with H. Topaloglu)
Abstract
We develop an expectation-maximization algorithm to estimate the parameters of the Markov
chain choice model. In this choice model, a customer arrives into the system to purchase a certain
product. If this product is available for purchase, then the customer purchases it. Otherwise, the
customer transitions between the products according to a transition probability matrix until she
reaches an available one and purchases this product. The parameters of the Markov chain choice
model are the probability that the customer arrives into the system to purchase each one of the
products and the entries of the transition probability matrix. In our expectation-maximization
algorithm, we treat the path that a customer follows in the Markov chain as the missing piece
of the data. Conditional on the final purchase decision of a customer, we show how to compute
the probability that the customer arrives into the system to purchase a certain product and
the expected number of times that the customer transitions from a certain product to another
one. These results allow us to execute the expectation step of our algorithm. Also, we show
how to solve the optimization problem that appears in the maximization step of our algorithm.
Our computational experiments show that the Markov chain choice model, coupled with our
expectation-maximization algorithm, can yield better predictions of customer choice behavior
when compared with other commonly used alternatives.
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