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Applied Methods of Valuation of Water-related Ecosystem Services
Published in Robert A. Young, John B. Loomis, Determining the Economic Value of Water, 2014
Robert A. Young, John B. Loomis
Repeated observations of choices from a sample of respondents can provide evidence on how the various characteristics affect the probability of choice. The distributional assumptions made regarding the random term influence the choice of analytic technique. For example, the binary probit model follows from an assumption of normal distribution. If just a status quo and one action alternative is asked of respondents then a binary logit or probit model can be used. This format is gaining in adherents due to its potential incentive compatibility. However, not much information is obtained per respondent. To obtain more information, asking three to four alternatives are common. With more than two alternatives, a multinomial logit model can be applied if the random term takes on a Gumbel distribution (Hensher et al. 2005). To obtain even more information per respondent a new innovation of asking respondents to indicate their best choice alternative and worst choice alternative has emerged (see Scarpa et al. 2011 for a recreation example). Maximum likelihood methods are typically required to estimate the model. Econometric packages are available to perform the statistical analysis. For a primer on statistical analysis of choice experiments see Hensher et al. (2005).
Subway station dwell time prediction and user-induced delay
Published in Transportmetrica A: Transport Science, 2021
Matthew Volovski, Evangelia S. Ieronymaki, Cara Cao, John Paul O’Loughlin
The binary Probit model is a discrete outcome model that estimates the probability that a given observation will have one of the two distinct outcomes; in the context of the current research, the outcomes are; (i) there will or (ii) there will not be a user-induced delay. The underlying assumption of the Probit model is a normal distribution of errors. The probability of given outcome 1, P(1), is the probability that there will be user-induced delay and it is equal to the cumulative normal distribution, Φ, of the estimated function (web.mta.info) where B0 is the constant term and Biis a vector of the estimated coefficients for the xi vector of the independent variables. Therefore, the estimated parameters in the binary Probit model are not the change in P(1), rather they are the change in the z-score of P(1). The marginal effect of each independent variable on P(1) can be determined by evaluating the cumulative distribution function (cdf) before and after a one-unit change in the variable while keeping all other independent variables equal to their mean values.
Driver behavior analysis on rural 2-lane, 2-way highways using SHRP 2 NDS data
Published in Traffic Injury Prevention, 2018
The most widely used method for driver behavior prediction is the negative binomial, a logistic model (Russo et al. 2016). However, logistic models cannot handle a binary response model very well (James et al. 2013). In this research, macrolevel driver behaviors were divided into 2 types: Driver behavior fault and normal driver behavior (no fault), which have binary responses. A probit model is a popular specification for an ordinal or binary response model. Suppose that a response variable Y is binary; that is, it can have only 2 possible outcomes, which we will denote as 1 and 0. We also have a vector of regressors X, which are assumed to influence the outcome Y. Specifically, we assume that the model takes the form of Equation (2): where Pr denotes probability, and Φ is the cumulative distribution function of the standard normal distribution. The parameters β are typically estimated by maximum likelihood.
Traffic accident severity analysis in Barcelona using a binary probit and CHAID tree
Published in International Journal of Injury Control and Safety Promotion, 2022
Table 2 depicts how the model is significant. All likelihood ratio, score, and Wald are statistically significant with p-values less than 0.0001 for the applied probit model. Table 3 presents the significance of the classification variables that are used in the model. This table is showing the hypothesis tests for each variable individually. Weekday, the daytime, gender, age, and user are significantly improving the model-fit based on their Chi-square test and their p-values.