A Non-Compensatory Random Utility Choice Model based on Choquet Integral
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We present a random utility maximisation (RUM) based discrete choice model to simultaneously consider three behavioural aspects of the decision-maker - i) evaluation of each attribute (e.g., constant marginal utility beyond attribute thresholds), ii) aggregation of attributes in the systematic part of the indirect utility, and iii) flexible substitution patterns between alternatives. Corresponding to each aspect, we use i) fuzzy membership functions to capture how the decision-maker evaluates a range of attributes, ii) replace the weighted-sum aggregation function in the indirect utility with the Choquet integral (CI) to capture non-linear interactions between attributes, and iii) adopt multinomial probit (MNP) choice probability kernel to represent flexible substitution patterns between alternatives. We estimate the proposed model using a constrained maximum likelihood estimator. A comprehensive Monte Carlo study is performed to establish the statistical properties of the estimator and demonstrate the superiority of the proposed model over the traditional MNP model with weighted sum indirect utility in terms of goodness of fit and recovery of marginal effects. Note that the proposed CI-based specification provides complementarity between pairs of attributes coupled with their individual importance ranking as a by-product of the estimation. This information could potentially help policymakers in making policies to improve the preference level for an alternative. The advantages of considering attribute cut-off based non-compensatory behaviour and a flexible aggregation function are illustrated in an empirical application to understand New Yorkers' preferences towards mobility-on-demand services.
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