Thijs Dekker | Searcharxiv

arXiv2026

Statistical significance in choice modelling: computation, usage and reporting

This paper offers a commentary on the use of notions of statistical significance in choice modelling. We review the reasons for uncertainty in parameter estimates, provide a precise discussion on the computation of measures of uncertainty and confidence intervals, and discuss the use of statistical tests. We argue that, as in many other areas of science, there is an over-reliance on 95\% confidence levels, and misunderstandings of the meaning of significance. We also observe a lack of precision in the reporting of measures of uncertainty in many studies, especially when using $p$-values and even more so with \emph{star} measures. The paper also stresses the importance of considering behavioural or policy significance in addition to statistical significance. Finally, we stress a number of points that are specific to choice modelling and which require special attention, notably in relation to derived measures such as willingness-to-pay, the treatment of random heterogeneity, and the use of repeated choice data.

econ.EM↗

arXiv2023

Revisiting McFadden's correction factor for sampling of alternatives in multinomial logit and mixed multinomial logit models

In this paper, we revisit McFadden (1978)'s correction factor for sampling of alternatives in multinomial logit (MNL) and mixed multinomial logit (MMNL) models. McFadden (1978) proved that consistent parameter estimates are obtained when estimating MNL models using a sampled subset of alternatives, including the chosen alternative, in combination with a correction factor. We decompose this correction factor into i) a correction for overestimating the MNL choice probability due to using a smaller subset of alternatives, and ii) a correction for which a subset of alternatives is contrasted through utility differences and thereby the extent to which we learn about the parameters of interest in MNL. Keane and Wasi (2016) proved that the overall expected positive information divergence - comprising the above two elements - is minimised between the true and sampled likelihood when applying a sampling protocol satisfying uniform conditioning. We generalise their result to the case of positive conditioning and show that whilst McFadden (1978)'s correction factor may not minimise the overall expected information divergence, it does minimise the expected information loss with respect to the parameters of interest. We apply this result in the context of Bayesian analysis and show that McFadden (1978)'s correction factor minimises the expected information loss regarding the parameters of interest across the entire posterior density irrespective of sample size. In other words, McFadden (1978)'s correction factor has desirable small and large sample properties. We also show that our results for Bayesian MNL models transfer to MMNL and that only McFadden (1978) correction factor is sufficient to minimise the expected information loss in the parameters of interest. Monte Carlo simulations illustrate the successful application of sampling of alternatives in Bayesian MMNL models.

stat.ME↗