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Random Parameters Models
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
Estimation of the mixed logit model shown in Equation (16.4) by maximum likelihood is undertaken using simulation approaches due to the difficulty in computing the probabilities. Recall from Chapter 13 that the log-likelihood function is written as [see Equation (13.22) for comparison], () LL=∑n=1N∑i=1IδinLN[Pnm(i)]
Traffic Crash Analysis And Prevention
Published in Dušan Teodorović, The Routledge Handbook of Transportation, 2015
The mixed logit model requires a distributional assumption for the random parameters, but several such assumptions can be tested in terms of their results on goodness-of-fit. The normal distribution is a logical starting point in the absence of a priori information. With that distribution, each parameter can be described by a mean and a standard deviation. If the standard deviation for a random parameter is not found to be statistically significantly different from zero, it suggests the parameter should remain fixed and not random given that other distributional alternatives have been tested as well, such as the uniform distribution.
Pedestrian-injury severity analysis in pedestrian-vehicle crashes with familiar and unfamiliar drivers
Published in Transportmetrica A: Transport Science, 2022
Separate multinomial logit models and mixed logit models are developed for analysing injury severities of pedestrians in pedestrian-vehicle crashes with both familiar and unfamiliar drivers involved. Goodness of fit of the mixed logit and multinomial logit models is measured by the McFadden pseudo- values. The much higher McFadden pseudo- values (0.539 and 0.650 for mixed logit models of pedestrian-vehicle crashes with familiar drivers and unfamiliar drivers, respectively) suggest a better fit of the data by the mixed logit models. Therefore, in the following section, we present the parameter estimation results obtained from the mixed logit models. As discussed in Section 3, the injury severity outcomes of the pedestrians considered in the models include major injury, minor injury and possible/no injury. During model estimation, variables were included in the specification if they had t-statistics corresponding to the 90% confidence interval or above on a two-tailed t-test. However, the random parameters were included if their standard deviations had t-statistics corresponding to the 90% confidence interval or above.
Willingness to pay for the outcomes of improved stormwater management
Published in Urban Water Journal, 2022
Robert Gillespie, Jeff Bennett
The mixed logit (ML) specification of the utility function allows for the relaxation of the IID assumption of the CL specification as it allows for heterogeneity of preferences across individuals (Hensher, Rose, and Greene 2005) and across alternatives (Green and Hensher 2007). It can also account for correlations in unobserved factors over repeated choices by each individual (Revelt and Train1998). The ML specification is the same as the CL specification set out in equation 1 except one or more of the parameter estimates are represented as:
The influence of group decision-making on residents’ preferences for sustainable energy measures of dwellings
Published in Building Research & Information, 2022
Nick Tiellemans, Astrid Kemperman, Stephan Maussen, Theo Arentze
The mixed logit model is used as a framework to estimate the preference parameters based on the choice data. (e.g. Louviere et al., 2000; Lee et al., 2018; Revelt & Train, 1998; Train, 2003). The mixed logit model is an extension of the more basic multi-nominal logit model that allows for heterogeneity between individuals by assuming random parameters (a distribution rather than point estimates). In this section, we will first briefly introduce the mixed logit model and next specify the utility function that allows us to estimate the parameters of interest.