The literature has suggested that individuals employ more simplified decision making rules than the compensatory rule represented by the linear-in-attributes utility function. However, the parameter estimation of such simplified decision rules is not necessarily simpler than that of the compensatory rule because of a high non-linearity of the model.

The empirical estimability of the semi-ordered lexicographic model is examined in this study. Three methods are compared in this study: the conventional maximum likelihood estimation, the sequential estimation procedure by applying a data mining algorithm, and the hybrid estimation procedure of above two alternatives. The three methods are examined using the synthetic data with three alternatives and three attributes, where 1000 hypothetical individuals are postulated to make decisions via semi-ordered lexicographic rule. Conventional multinomial logit models are also estimated with the same data for comparison purpose. The result shows that the convergence rate of the semi-ordered lexicographic model is low especially for the case with negative correlation of the attributes. On the other hand, data mining algorithm has no problem in convergence, but it sometimes generates wrong order of compared attributes for the case with positive correlation. And, the hybrid methods improve the estimability only for the case with small heterogeneity in the thresholds.