Stephane Hess, David Bunch, Andrew Daly
arXiv 3 Jun 2025 · Econometrics
arXiv:2506.02722 · PDF · DOI · OpenAlex · Extracted main text
Choice modellers routinely acknowledge the risk of convergence to inferior local optima when using structures other than a simple linear-in-parameters logit model. At the same time, there is no consensus on appropriate mechanisms for addressing this issue. Most analysts seem to ignore the problem, while others try a set of different starting values, or put their faith in what they believe to be more robust estimation approaches. This paper puts forward the use of a profile likelihood approach that systematically analyses the parameter space around an initial maximum likelihood estimate and tests for the existence of better local optima in that space. We extend this to an iterative algorithm which then progressively searches for the best local optimum under given settings for the algorithm. Using a well known stated choice dataset, we show how the approach identifies better local optima for both latent class and mixed logit, with the potential for substantially different policy implications. In the case studies we conduct, an added benefit of the approach is that the new solutions exhibit properties that more closely adhere to the property of asymptotic normality, also highlighting the benefits of the approach in analysing the statistical properties of a solution.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | McCullough, B.D., Vinod, H.D (2003) Verifying the solution from a nonlinear solver: A case study | 0.874 | 6 | 2 | 100% |
| 2 | Bunch, D.S (2024) Numerical methods for optimization-based model estimation and inference self | 0.737 | 3 | 2 | 100% |
| 3 | Daly, A., Hess, S., de Jong, G (2012) Calculating errors for measures derived from choice modelling estimates self | 0.644 | 2 | 2 | 100% |
| 4 | Davidson, R., MacKinnon, J.G (1993) Estimation and inference in econometrics | 0.644 | 2 | 2 | 100% |
| 5 | Hess, S., Palma, D (2019) Apollo: A flexible, powerful and customisable freeware package for choice model estimation and application self | 0.644 | 2 | 2 | 100% |
| 6 | Amemiya, T (1985) Advanced Econometrics | 0.405 | 1 | 1 | 100% |
| 7 | Armstrong, P., Garrido, R.A., Ortúzar, J.de D (2001) Confidence interval to bound the value of time | 0.405 | 1 | 1 | 100% |
| 8 | Axhausen, K.W., Hess, S., König, A., Abay, G., Bates, J.J., Bierlair… (2008) State of the art estimates of the swiss value of travel time savings self | 0.405 | 1 | 1 | 100% |
| 9 | Bierlaire, M., Thémans, M., Zufferey, N (2010) A heuristic for nonlinear global optimization | 0.405 | 1 | 1 | 100% |
| 10 | Sobol, I.M (1967) On the distribution of points in a cube and the approximate evaluation of integrals | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 15 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Statistical significance in choice modelling: computation, usage and reporting | 0.405 | 1 | 1 |