Logit Formulation Research Articles

GEV-based destination choice models that account for unobserved similarities among alternatives

This paper investigates the destination choice problem in transportation planning processes. Most models assume a Multinomial Logit (MNL) form for the problem. The MNL cannot account for unobserved similarities which exist among choice alternatives. The purpose of this paper is to investigate alternative destination choice model structures, focusing on closed-form models. The paper reviews recent GEV formulations and discusses the adaptation of these models to destination choice situation. In addition the paper presents a new model structure composed of three hierarchical levels: it assumes a choice process composed of a broad selection of zones based on a specific land use characteristic (in this case, presence of shopping center) and then a finer selection of zones based on a geographical characteristic (in this case, adjacent zones). To illustrate the similarity measures of selected GEV formulations and the new model structure the paper specifies, estimates and compares destination choice models for weekday shopping trips based on a revealed preference survey. The paper discusses the structure of the proposed choice models, similarity measures and implementation issues related to the GEV destination choice models.

Random Utility Location, Production, and Exchange Choice; Additive Logit Model; and Spatial Choice Microsimulations

A land use modeling system has been developed and applied on the basis of random utility theory. The system abstracts the decisions of the actors located in and traveling around a city or region as a series of logit models: (a) the choice of where to locate the home; (b) the choice of technology, lifestyle, or production option, being the choice of the quantities of “commodities” (consisting of goods, services, labor, and space categories) to consume or produce and hence what interactions will occur; and (c) the location of the “exchange” (transaction or interaction) for each commodity consumed or produced (i.e., for each interaction). These logit models can be combined in a nesting structure, but an additive logit formulation is required because the exchange choices are not mutually exclusive. The additive logit model, which is developed by combining the central limit theorem with random utility theory, can be applied to any choice situation in which several independent choices are conditional on a higher level choice. The resulting choice probabilities can be applied in an aggregate allocation system (as in software for the Production Exchange Consumption Allocation System, PECAS) and result in supply-and-demand equations for each commodity in each exchange that can be solved for a short-term equilibrium. In future research, microsimulation versions of the system could allow a fully integrated and dynamic representation of land use-transport interactions.

Estimation of the time-dependency of values of travel time and its reliability from loop detector data

Although the effects of travel time and its reliability have been addressed in a variety of papers concerning pricing policies, most of the existing research is based on the assumption that travelers’ preferences are static over a given time interval, such as the morning commuting period. Here, we relax this assumption, assuming rather that travelers’ tastes toward the travel time and its reliability vary with time, and examine their time-dependent effects on traveler’s route choice decisions. We adopt a mixed logit formulation of route choice behavior as a function of travel time, reliability, and cost. To uncover the values of travel time and its reliability, we introduce an alternative approach to the use of traveler surveys to estimate the model coefficients by determining the parameter set that produces the best match between the aggregated results from the travelers’ route choice model and the observed time-dependent traffic volume data from loop detectors. We apply the methodology to loop detector data obtained from the California State Route 91 value-pricing project, and use a genetic algorithm to identify the parameters. The time-dependent values of travel time and values of reliability for the morning commuting period are estimated and their implications on the toll pricing policy are discussed. The results indicate that, under the time-dependent formulation, travel-time savings may be more important than uncertain travel time when departure time is close to such time constraints as work-start time.

Link function selection in stochastic multicriteria decision making models

A stochastic formulation of the Analytic Hierarchy Process (AHP) using an approach based on Bayesian categorical data models has been developed. However, in categorical data models it is known that the selection of the link function may have an impact on the model estimates. In particular, the selection of the probit link implies an assumption that model error terms are normally distributed and this normality assumption is regularly utilized in other related methods such as the multiplicative AHP. We examine model performance with respect to the choice of two model link functions. With regard to point estimates, it is found that the logit formulation is better able to replicate the estimates obtained by the eigenvector decomposition associated with the original formulation of the AHP. By contrast, the probit link produces priorities which are consistently more moderate than those of the AHP. The results suggest that the logit formulation will be preferred by decision makers who wish to replicate the AHP priorities as closely as possible. The results also suggest that the unexamined use of the normality assumption in other stochastic AHP methods may have an impact on priority estimates and thus is worthy of further attention.

A Model for Evaluation of Transport Policies in Multimodal Networks with Road and Parking Capacity Constraints

This paper presents a model for evaluation of transport policies in multimodal networks with road and parking capacity constraints. The proposed model simultaneously considers choices of travelers on route, parking location and mode between auto and transit. In the proposed model, it is assumed that auto drivers make a simultaneous route and parking location choice in a user equilibrium manner, and the modal split between auto and transit follows a multinomial logit formulation. A mathematical programming model with capacity constraints on road link and parking facilities is proposed that generates optimality conditions equivalent to the requirements for multimodal network equilibrium. An augmented Lagrangian dual algorithm embedded by partial linearization approach is developed to solve the proposed model. Numerical results on two example networks are presented to illustrate the proposed methodology. The results show that the service level of transit, parking charges, road link and parking capacities, and addition of a new parking location may bring significant impacts on travelers’ behavior and network performance. In addition, transport policies may result in paradoxical phenomenon.

Analysis of U.S. Catfish Fillet Market Share Using a Flexible Logistic Model

This paper forecasts market share for U.S. frozen, farm-raised catfish fillets using alternative logit formulations. Results suggest the log inverse power transformation (IPT) performs better than the simple logit and IPT logit models, and had the smallest percentage errors for out-of-sample forecast. Estimates from the log-IPT model indicated higher price premiums of U.S. catfish fillets negatively affected market shares. As domestic fillet wholesale price levels increased relative to imported fillet price, buyers would substitute domestic catfish with imported catfish, assuming undifferentiated products. Catfish is found to be a necessity with a negative relationship between income and shares, equating sales values to consumer expenditures. Total market demand for catfish appears relatively stable following changes in the economy, typical of necessities. It suggests caution in price setting policies. A pricing strategy based on higher sales volumes to address the declining market share situation could be an effective policy measure for optimal long-run sustainability and profitability of the industry.

Do Black Bears Respond to Military Weapons Training?

The primary function of military training areas is to support military missions; however, management of natural resources that is compatible with that function has become a focal issue on many military installations. We investigated the relationship between black bear (Ursus americanus) habitat use and weapons-firing exercises at 3 spatial scales on the western portion of U.S. Marine Corps Base Camp Lejeune (Camp Lejeune), North Carolina. In 2000 and 2001, we collected 1,494 telemetry locations for 14 bears (6 males, 8 females). We used spatial contours of human auditory disturbance levels based on the noise generated from firing activities to establish high-, medium-, and low-disturbance noise zones for each firing range. We used the multinomial logit form of discrete choice analysis to examine whether bears exhibited a spatial (i.e., general avoidance of areas associated with military activity) or temporal response (i.e., avoidance of military training areas but only when firing exercises occurred). Except for small areas near the firing positions, differences in bear use among the 3 noise zone areas was mostly a function of the prevalence of selected vegetation types and not a response to military activity. Our temporal analysis further suggested that bears did not respond to weapons exercises; the distance of bears to the nearest high-disturbance noise zone was not associated with the occurrence of weapons exercises.

Modeling the bilateral micro-searching behavior for urban taxi services using the absorbing markov chain approach

This paper develops a mathematical model that is based on the absorbing Markov chain approach to describe taxi movements, taking into account the stochastic searching processes of taxis in a network. The local searching behavior of taxis is specified by a logit form, and the O-D demand of passengers is estimated as a logit model with a choice of taxi meeting point. The relationship between customer and taxi waiting times is modeled by a double-ended queuing system. The problem is solved with a set of non-linear equations, and some interesting results are presented. The research provides a novel and potentially useful formulation for describing the urban taxi services in a network.

Risk factors for heart disease and stroke among diabetic persons, by disability status

Objective To determine whether disabled diabetic persons have a higher prevalence of risk factors for heart disease and stroke than do diabetic persons without disability. Research, design, and methods Data were analyzed for noninstitutionalized adults in 27 states and the District of Columbia that participated in the Behavioral Risk Factor Surveillance System (BRFSS) in 2001 and/or 2003. Logistic regression analysis was used to estimate the adjusted prevalence and odds ratios of disabled diabetic persons, by sociodemographic characteristics. The logit form of each model was used to estimate conditional marginal probabilities of risk factors for heart disease and stroke among diabetic persons, by disability status. Results Diabetic persons with disability were more likely than those without disability to have more risk factors for heart disease and stroke, including insufficient leisure-time physical activity or inactivity (adjusted prevalence: 75.2% vs. 63.3%; P<.001), obesity (58.9% vs. 43.3%; P<.001), hypercholesterolemia (52.6% vs. 48.4%; P=.038), and hypertension (63.9% vs. 56.6%; P<.001). They were also more likely to have one or more, two or more, three or more, and four or more risk factors (97.2% vs. 95.6%, 83.5% vs. 74.0%, 56.5% vs. 41.1%, and 22.2% vs. 13.6%, respectively; P≤.005). Conclusions Diabetic persons with disability are more likely than those without disability to have clusters of risk factors for heart disease and stroke. Health care guidelines specifically targeting diabetic patients with disability may be needed to aid health care providers in addressing these risk factors.

A Dynamic Kernel Logit Model for the Analysis of Longitudinal Discrete Choice Data: Properties and Computational Assessment

This paper focuses on the application of the kernel logit formulation to model dynamic discrete choice data. A dynamic kernel logit (DKL) formulation with normal errors is presented to model unordered discrete choice panel data. Investigating the theoretical foundations of the kernel logit model, it is demonstrated that the mixed logit error structure converges in distribution asymptotically to a suitable multivariate normal error structure. This result provides support for both cross-sectional kernel logit (CKL) and DKL models with normal errors. The calibration, identification, and specification issues associated with the latter model are also discussed. The performance of the proposed DKL model is assessed from the perspective of computational efficiency and estimate accuracy relative to the multinomial probit (MNP) model using a series of numerical experiments. Complexity analysis reveals that the DKL has a lower computational complexity than the MNP frequency simulator, which has an exponential complexity. Thus, for choice situations with a large number of alternatives (J) in each time period, and/or large number of time periods (T), the DKL model is faster than the corresponding MNP by more than an order of magnitude. This is also confirmed by computational experiments conducted using 32 synthetic data sets. The computational performance of the DKL relative to MNP appears to be the result of a trade-off between the number of Monte-Carlo draws required, and the computational cost of each draw. With fewer than 25 alternatives (JT), the results suggest that it is more advantageous to use the probit model (MNP) compared to the DKL. There appears to be little advantage in applying the kernel logit formulation relative to the MNP to cross-sectional data with a few alternatives. Regarding computational accuracy, the numerical results suggest that the parameter estimates of both models (MNP and DKL) are comparable and close to the true values from which the data sets were generated. However, both DKL and MNP formulations may lead to the maximization of a nonconcave objective function, resulting in flat log-likelihood functions, and identification problems.

On distinguishing between physically active and physically passive episodes and between travel and activity episodes: an analysis of weekend recreational participation in the San Francisco Bay area

This paper examines the out-of-home recreational episode participation of individuals over the weekend, with a specific focus on analyzing the determinants of participation in physically active versus physically passive pursuits and travel versus activity episodes (travel episodes correspond to recreational pursuits without any specific out-of-home location, such as walking, bicycling around the block, and joy-riding in a car, while activity episodes are pursued at a fixed out-of-home location, such as playing soccer at the soccer field and swimming at an aquatics center). The above disaggregation of recreational episodes facilitates the better analysis and modeling of activity-travel attributes, such as travel mode, episode duration, time-of-day of participation and location of participation. From a broader societal standpoint, the disaggregation of recreational episodes provides important information to encourage active participatory recreational pursuits, which can serve to relieve mental stress, improve the physical health of the population, and contribute to a socially vibrant society through increased interactions among individuals. The paper employs a mixed multinomial logit formulation for examining out-of-home recreational episode type participation using the 2000 San Francisco Bay area travel survey. A variety of variables, including individual and household sociodemographics, location attributes, and day of week and seasonal effects, are considered in the model specification. Individual-specific unobserved factors affecting the propensity to participate in different types of recreational episodes are also accommodated.

A mixed multinomial logit model analysis of weekend recreational episode type choice

This paper presents a model for the type of recreational activity episodes that individuals pursue during the weekend. The choice set characterizing the type of recreational episode includes in-home, out-of-home, and pure recreational episodes (pure recreation refers to recreation trips pursued for the sole purpose of the recreational value obtained from the trip, such as walking, bicycling, and joy driving). The paper estimates a mixed multinomial logit formulation using the 2000 San Francisco Bay Area Travel Survey. The effects of household and individual sociodemographics, land-use and density variables, and episode participation attributes are examined. Inter-individual and intra-individual variation in unobserved determinants of episode type choice are also analyzed. Finally, the implications of the results for land-use and transportation planning are identified.

Accommodating Heterogeneity and Heteroscedasticity in Intercity Travel Mode Choice Model: Formulation and Application to HoNam, South Korea, High-Speed Rail Demand Analysis

Multinomial logit models and nested logit models are limited in that they cannot accommodate unobserved variations in travelers' taste and they do not have flexible substitution patterns among alternatives because of the independence of irrelevant alternatives property. Taking this background into account, traffic demand analysts have recently used the mixed logit model in many studies. Unfortunately, most of the studies in the literature for joint analysis of revealed-preference (RP) and stated-preference (SP) data could not simultaneously resolve the two limitations just mentioned. The mixed logit framework is used to formulate an intercity travel mode choice model for joint RP-SP analysis that accommodates the following behavioral considerations: ( a) observed and unobserved heterogeneity across individuals in response to level-of-service (LOS) factors, ( b) heteroscedasticity across alternatives, and ( c) scale differences between the RP and SP choice contexts. The mixed logit formulation is estimated with the maximum simulated likelihood method that employs quasi-random Halton draws. The formulation is applied to examine the travel behavior responses of users of the HoNam, South Korea, high-speed rail to changes in travel conditions. The empirical results show that there is a significant heteroscedasticity across alternatives and a significant heterogeneity in response to LOS attributes based on both observed and unobserved individual characteristics. There is an improvement in the data-fit statistics when one introduces heterogeneity and heteroscedasticity. These results highlight the need to include heterogeneity and heteroscedasticity within the context of intercity travel mode choice modeling to assist policy decision making.

An illustration of Cox's non-nested testing procedure for logit and probit models

Empirical and methodological issues arising when the Cox test statistic for non-nested models is used to test the probit vs. logit specifications are discussed. As an example, the models in Bardasi and Monfardini (European University Institute Working Paper ECO No. 97/9, 1997) for the occupational choice by Italian workers among the private, public and self-employed options is considered. Different versions of the test are compared. The bootstrap technique is then used to control for the actual properties of the test. The results indicate the probit to be the more adequate model, providing evidence against the independence of the irrelevant alternatives assumption imposed by the logit formulation.

Migration and regional labor market adjustment: Chile 1977-1982 and 1987-1992

The main objective of this paper is to evaluate the migration processes that have been occurring in Chile between 1977–1982 and 1987–1992, as a market mechanism to re-allocate labor among regions. Using traditional consumer theory, a model is developed for a migrant who is evaluating migration. Secondly, this model is estimated, with cross section aggregate data, for both periods using a logit formulation. The results indicate that there is a strong force in the Chilean regional labor market, which serves to concentrate the workforce around the largest populated region of the country. Finally, regional labor markets are simulated to show that migration forces are very weak to arbitrage regional wages and unemployment rate and specific policy is required to promote balanced development across Chilean regions.

Injury Severity Analysis with Variable and Correlated Thresholds: Ordered Mixed Logit Formulation

An ordered mixed logit (OML) formulation is proposed to model injury severity, given a crash. The proposed formulation extends the ordered probit/logit models by accommodating variable, random, and correlated injury severity thresholds associated with various severity levels. The proposed model is calibrated using a sample from the 1996 National Automotive Sampling System General Estimates System data set. Chi-square tests indicate that the more general OML formulation provides a statistically superior representation of observed injury severity data than corresponding ordered logit models. Model results indicate that injury severity thresholds vary systematically depending on individual, traffic, crash-related, and vehicle characteristics. Further, significant unobserved variability in thresholds is found, and the thresholds are correlated within a given individual. The results suggest drastically increased chances of fatal injury due to certain factors including tripped rollovers and injuries sustained by moped riders. These findings suggest that targeting these drivers, behaviors, and conditions with suitable countermeasures including education, enforcement, or curfews is likely to result in substantial safety benefits. The model and results have important implications for developing effective safety countermeasures and more accurate assessment of their impacts.

A unified mixed logit framework for modeling revealed and stated preferences: formulation and application to congestion pricing analysis in the San Francisco Bay area

This paper formulates and applies a unified mixed-logit framework for joint analysis of revealed and stated preference data that accommodates a flexible competition pattern across alternatives, scale difference in the revealed and stated choice contexts, heterogeneity across individuals in the intrinsic preferences for alternatives, heterogeneity across individuals in the responsiveness to level-of-service factors, state-dependence of the stated choices on the revealed choice, and heterogeneity across individuals in the state-dependence effect. The estimation of the mixed logit formulation is achieved using simulation techniques that employ quasi-random Monte Carlo draws. The formulation is applied to examine the travel behavior responses of San Francisco Bay Bridge users to changes in travel conditions. The data for the study are drawn from surveys conducted as part of the 1996 San Francisco Bay Area Travel Study. The results of the mixed logit formulation are compared with those of more restrictive structures on the basis of parameter estimates, implied trade-offs among level-of-service attributes, heterogeneity and state-dependence effects, data fit, and substantive implications of congestion pricing policy simulations.

Development of Microsimulation Activity-Based Model for San Francisco: Destination and Mode Choice Models

A tour-based microsimulation approach to modeling destination choice and mode choice of San Francisco residents is presented. These models were developed as part of an overall tour-based travel demand forecasting model (SF model) for the San Francisco County Transportation Authority to provide detailed forecasts of travel demand for various planning applications. The models described represent two of the nine primary components of the SF model. Both model components consist of multiple logit choice models and include both tour-level models (which refer to the primary activity of the tour) and trip-level models (other activities on the tour). A separate model was estimated for each tour purpose, including work, school, other, and work-based. The destination choice models combine the trip attraction and trip distribution components of the traditional four-step process and use a multinomial logit specification. The mode choice models utilize a nested logit formulation to capture the similarities among sets of similar modes. The two models are linked by incorporating the mode choice utility logsum in the destination choice models; the result is equivalent to a nested structure with a mode choice nest under destination choice. It is demonstrated that the microsimulation approach easily allows the inclusion of a number of key variables in destination and mode choice models that have a significant explanatory power compared with those in traditional models. It is also shown that this approach allows estimation of the effects of tour characteristics on the choice of destination and mode using widely available data and estimation procedures.

Investigation of the Stochastic Utility Maximization Process of Consumer Brand Choice by Semiparametric Modeling

ABSTRACT The se of nonparametric methods, which posit fewer assumptions and greater modelu flexibility than parametric methods, could provide useful insights when studying brand choice. It was found, however, that the data requirement for a fully nonparametric brand choice model is so greatthat obtaining such large data sets is difficult even in mar keting. Semiparametric methods balance model flexibility and data requirement by imposing some parametric structure on components that are not sensitive to such assumptions while leaving the essential component nonparametric. In this paper, the authors compare two semiparametric brand choice models that are based on the generalized additive models (GAM). One model is specified as a nonparametric logistic regression of GAM (Hastie and Tibshirani 1986) with one equation for each brand. The other model is a multinomial logit (MNL) formulation with a nonparametric utility function, which is derived by extending the GAM framework (Abe 1999). Both models assume a parametric distribution for the random component, but capture the response of covariates nonparametrically. The competitive structure of the logistic regression formulation is specified by data through nonparametric response functions of the attributes forthe competitive brands, whereas that of the MNL formulation is guided by the choice theory of stochastic utility maximization (SUM). Simulation study and application to actual scanner panel data seem to support the behavioral assumption of SUM. In addition, if we relax the SUM assumption by letting data specify the competitive structure, a substantially larger amount of data, perhaps an order of magnitude more, would be required. Therefore, if alternative brands are chosen carefully, nonparametric relaxation to capture cross effect (i.e., nonparametrization of the MNL structure) may not be warranted unless the size of database becomes substantially larger than the one currently used.

Understanding Supermarket Competition Using Choice Maps

In this paper we propose a model which combines the spatial interaction models with the latest developments in internal market structure analysis and allows us to infer supermarket competition from revealed preference data. Using a nested logit formulation we model consumers' store choice decisions to be a two stage process in which consumers choose first the suburb and then the store from which to buy groceries. Hence, our method allows retail managers not only to understand the advantage (or disadvantage) of having their store chain in a particular area but also assess the competition within that area. Comparisons to Factor Analytic Choice Map is made.