Numerical optimization for mixed logit models and an application
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In this thesis an algorithm (MLOPT) for mixed logit models is proposed. Mixed logit models are flexible discrete choice models, but their estimation with large datasets involves the solution of a nonlinear optimization problem with a high dimensional integral in the objective function, which is the log-likelihood function. This complex structure is a general problem that occurs in statistics and optimization. MLOPT uses sampling from the dataset of individuals to generate a data sample. In addition to this, Monte Carlo samples are used to generate an integration sample to estimate the choice probabilities. MLOPT estimates the log-likelihood function values for each individual in the dataset by controlling and adaptively changing the data sample and the size of the integration sample at each iteration. Furthermore, MLOPT incorporates statistical testing for the quality of the solution obtained within the optimization problem. MLOPT is tested with a benchmark study from the literature (AMLET) and further applied to real-life applications in the automotive industry by predicting market shares in the Low Segment of the new car market. The automotive industry is particularly interesting in that understanding the behavior of buyers and how rebates affect their preferences is very important for revenue management. Real transaction data is used to generate and test the mixed logit models developed in this study. Another new aspect of this study is that the sales transactions are differentiated with respect to the transaction type of the purchases made. These mixed logit models are used to estimate demand and analyze market share changes under different what-if scenarios. An analysis and discussion of the results obtained are also presented.