Estimation of Logit and Probit models using best, worst and best-worst choices

Paolo Delle Site, Karim Kilani, Valerio Gatta, Edoardo Marcucci () and André de Palma ()
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Paolo Delle Site: UNICUSANO - University Niccolò Cusano = Università Niccoló Cusano
Karim Kilani: LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM]
Valerio Gatta: ROMA TRE - Università degli Studi Roma Tre = Roma Tre University
Edoardo Marcucci: Molde University College - Molde University College

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Abstract: The paper considers models for best, worst and best-worst choice probabilities, that use a single common set of random utilities. Choice probabilities are derived for two distributions of the random terms: i.i.d. extreme value, i.e. Logit, and multivariate normal, i.e. Probit. In Logit, best, worst and best-worst choice probabilities have a closed form. In Probit, worst choice probabilities are simply obtained from best choice probabilities by changing the sign of the systematic utilities. Strict log-concavity of the likelihood, with respect to the coefficients of the systematic utilities, holds, under a mild necessary and sufficient condition of absence of perfect multicollinearity in the matrix of alternative and individual characteristics, for best, worst and best-worst choice probabilities in Logit, and for best and worst choice probabilities in Probit. The assumption of substitutability between best and worst choices is tested with data on mode choice, collected for the assessment of user responses to urban congestion charging policies. The numerical results suggest significantly different preferences between best and worst choices, even accounting for scale differences, in both Logit and Probit models. Worst choice data exhibit coefficient attenuation, less pronounced in Probit than in Logit, and higher mean values of travel time savings with larger confidence intervals.

Keywords: Probit; Congestion charge; Strict log-concavity; Logit; Random utility model; Best-worst choices (search for similar items in EconPapers)
Date: 2018-12-13
New Economics Papers: this item is included in nep-dcm, nep-tre and nep-upt
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