Mixed Multinomial Logit Research Articles

Simulation error in maximum likelihood estimation of discrete choice models

Maximum simulated likelihood is the preferred estimator of most researchers who deal with discrete choice. It allows estimation of models such as mixed multinomial logit (MXL), generalized multinomial logit, or hybrid choice models, which have now become the state-of-practice in the microeconometric analysis of discrete choice data. All these models require simulation-based solving of multidimensional integrals, which can lead to several numerical problems. In this study, we focus on one of these problems – utilizing from 100 to 1,000,000 draws, we investigate the extent of the simulation bias resulting from using several different types of draws: (1) pseudo random numbers, (2) modified Latin hypercube sampling, (3) randomized scrambled Halton sequence, and (4) randomized scrambled Sobol sequence. Each estimation is repeated up to 1 000 times. The simulations use several artificial datasets based on an MXL data generating process with different numbers of individuals (400, 800, 1 200), different numbers of choice tasks per respondent (4, 8, 12), different number of attributes (5, 10), and different experimental designs (D-optimal, D-efficient for the MNL and D-efficient for the MXL model). Our large-scale simulation study allows for comparisons and drawing conclusions with respect to (1) how efficient different types of quasi Monte Carlo simulation methods are and (2) how many draws one should use to make sure the results are of “satisfying” quality – under different experimental conditions. Our study is the first to date to offer such a comprehensive comparison. Overall, we find that the number of the best-performing Sobol draws required for the desired precision exceeds 2 000 in some of the 5-attribute settings, and 20,000 in the case of some 10-attribute settings considered.

A dynamic mixed logit model with agent effect for pedestrian next location choice using ubiquitous Wi-Fi network data

Abstract Large scale automated data collection on the movement and activities of pedestrians is a challenging problem. In a previous work we developed a network of cheap sensors that can perform larger scale data collection of pedestrian movements using WiFi signals emitted by WiFi-enabled devices (such as smartphones). The devices are deployed during an entire summer (4 months period) on a pedestrianized street spanning 14 intersections. This data is then processed to produce indicators describing the pedestrians’ behaviours, such as time spent, pedestrian density variations through time, flow of pedestrians and the tracking of trajectories and destinations over time. The use of street-level land usage data allows further conclusions to be made about the reasons for these behaviours. The indicators developed, in addition to facility usage information, are then used to develop and estimate three different dynamic next location choice models. The three models compared are a multinomial logit model (MNL), a mixed multinomial logit model (MMNL) and a mixed multinomial logit model with agent effect (MMNL-AE). The latter model is determined to be the most representative of the observed pedestrian behaviours. It can forecast the next location, within the detected area, any individual pedestrian chooses, conditioned upon its previous and current locations. The model can subsequently be used to predict future events in similar places, and help with the planning, promotion and optimization of such events.

Acceptability and Predictors of Uptake of Anti-retroviral Pre-exposure Prophylaxis (PrEP) Among Fishing Communities in Uganda: A Cross-Sectional Discrete Choice Experiment Survey.

We used a discrete choice experiment to assess the acceptability and potential uptake of HIV pre-exposure prophylaxis (PrEP) among 713 HIV-negative members of fishing communities in Uganda. Participants were asked to choose between oral pill, injection, implant, condoms, vaginal ring (women), and men circumcision. Product attributes were HIV prevention effectiveness, sexually transmitted infection (STI) prevention, contraception, waiting time, and secrecy of use. Data were analysed using mixed multinomial logit and latent class models. HIV prevention effectiveness was viewed as the most important attribute. Both genders preferred oral PrEP. Women least preferred the vaginal ring and men the implant. Condom use was predicted to decrease by one third among men, and not to change amongst women. Oral PrEP and other new prevention technologies are acceptable among fishing communities and may have substantial demand. Future work should explore utility of multiple product technologies that combine contraception with HIV and other STI prevention.

Product-Line Pricing Under Discrete Mixed Multinomial Logit Demand

We study a product-line price optimization problem with demand given by a discrete mixed multinomial logit (MMNL) model. The market is divided into a finite number of market segments, with product demand in each segment governed by the multinomial logit (MNL) model. We show that the concavity property with respect to the choice probability vector shown for the MNL model breaks down under MMNL even for entirely symmetric price sensitivities. In addition, the equal markup property identified for the MNL model no longer holds under MMNL, suggesting that heterogeneity in customer population justifies non-equal-markup pricing. In this paper, we characterize the profit function under MMNL as the sum of a set of quasiconcave functions and present efficient optimization algorithms. We demonstrate the application of our methods using data from Intel Corporation. Our results show that the optimal prices exploit segment differences through redistribution of sales and profit among customer segments. In addition, we use our methods to generate the profit-share efficient frontier, helping the firm to set prices that effectively balance these two measures. The tools developed in this research function in three important ways at Intel: (1) they provide a new alternative for market share prediction among Intel products for different customer segments, adding to the suite of independent demand forecasting tools; (2) they optimize product prices based on segment-specific customer preferences revealed through sales data, a capability that Intel’s current pricing tools include only heuristically; (3) they quantify the trade-off between profit and market share, adding a new decision support capability to the company. The online appendix is available at https://doi.org/10.1287/msom.2017.0675 .

A Conceptual Framework for Forecasting Car Driver’s On-Street Parking Decisions

Abstract This paper describes a conceptual framework of a behavioral model, well able to predict the parking choice decision process of car drivers’ while driving in a city center. The model assumes that parking choice decisions are mainly based on features associated to road conditions that a car driver faces while entering a street. A stated preference experiment was designed to collect respondents’ preferences related to preferred parking facility. A set of hypothetical road conditions were presented in the form of choice tasks. The collected data is analyzed using mixed multinomial logit model. The results from the model estimation show that almost all the presented attributes such as parking costs, payment options, expected parking duration, speed limit, level of parking convenience, space availability and surrounding activities play a considerable role when determining car drivers’ parking preferences. Moreover, the model highlights relatively important road related attributes which can induce search traffic. Therefore, cruising for parking can be reduced by avoiding certain road conditions, this information is valuable for the local authorities to design efficient parking policies.

Informal and formal care preferences and expected willingness of providing elderly care in Germany: protocol for a mixed-methods study

IntroductionIn Germany, the number of elderly people in need of care is expected to increase from 2.4 million in 2015 to 3.2 million in 2030. The subsequent rise in demand...

Motorcycle door crashes: An evaluation of crash characteristics in Taipei City, Taiwan.

ObjectivesCrashes due to motorcyclists colliding with an open car door can cause devastating injuries. In Taiwan, such crashes typically occur when the motorcyclist is travelling alongside a row of parallel-parked cars, and a driver suddenly opens the door in front of or next to the motorcycle without determining whether it is safe to do so. Injuries resulting from motorcycle door crashes tend to be severe. This study examined the factors that contribute to motorcycle door crashes.MethodsBy using linked data from the National Traffic Crash Dataset and Emergency Medical Service for Taipei City for the years 2010–2015, this study estimated a mixed multinomial logit model to predict the likelihood of three types of door crashes: driver-door crashes, left passenger-door crashes, and right passenger-door crashes.ResultsData on 8237 motorcycle door crashes were extracted from the two datasets and matched. The results from the mixed multinomial logit model revealed that illegal parking, older car occupants, teenage car occupants, intoxicated car occupants and motorcyclists, and motorcycle speeding contribute to driver-door crashes; and female passengers and taxis as the type of vehicle involved in crash are associated with left passenger-door crashes.ConclusionsOur study suggested that controlling motorcycle speed, and prosecuting illegal parking and drink driving/riding may constitute effective countermeasures. The “Dutch Reach” intervention measure, which is commonly adopted in Europe for bicycle door crashes, should be applied in Taiwan to curb motorcycle door crashes, especially for elderly car occupants.

Location Type Choice for Face-to-Face Interactions in Business Centers

Business centers offer flexible shared workspaces and facilities to multiple organizations, which provide more freedom in where to interact with others. However, knowledge on where different types of organizational interactions take place in business centers and how this behavior is influenced is still lacking. Therefore, the aim of this study is to analyze the location choice for different types of face-to-face interactions. Data, collected by means of an experience sampling method (ESM), were analyzed using a mixed multinomial logit (MMNL) model. Results showed that interorganizational interactions take place less frequently at workspaces or formal meeting spaces and more frequently at shared spaces such as the coffee corner or canteen. These interactions are also more likely to be influenced by the physical work environment, as these interactions were found to be mainly coincidental. Results of this study could help office designers with regard to stimulating face-to-face interactions among organizations.

Crash severity analysis of rear-end crashes in California using statistical and machine learning classification methods

Investigating drivers’ injury level and detecting contributing factors that aggravate the damage level imposed on drivers and vehicles is a critical subject in the field of crash analysis. In this study, a comprehensive vehicle-by-vehicle crash data set is developed by integrating 5 years of data from California crash, vehicles involved, and road databases. The data set is used to model the severity of rear-end crashes for comparing three analytic techniques: multinomial logit, mixed multinomial logit, and support vector machine (SVM). The results of the crash severity models and the role of contributing factors to the severity outcome of rear-end crashes are extensively discussed. In terms of prediction performance, all three models yielded comparable results; although, the SVM performed slightly better than the other two methods. The results from this study will inform aspects of our driver safety education and design, either vehicle or roadway design, required to be improved to alleviate the probability of severe injuries.

Public preferences towards bicycle sharing system in developing countries: The case of Mashhad, Iran

Bicycle Sharing System (BSS) has been introduced as an alternative mode of urban transportation which can mitigate the consequences of excessive motor vehicle usage and contribute to sustainable urban development. Adoption of BSS within transport networks relies on their key attributes such as safety, accessibility, cost and convenience to meet the public needs. Yet, the required infrastructure is often developed without much explicit knowledge about the public preferences. The consequence of this lack of knowledge is more acute in developing countries where there are economic and cultural constraints in adopting new modes of urban transportation.This study aims to provide more insight on the key attributes that are considered by the public in selecting BSS as the primary mode of urban transportation against the other alternatives in a developing country. First, a thorough literature review is conducted to find common BSS attributes that have been investigated within developed countries in North America, Europe, Asia and Australia. An empirical list of BSS attributes is then explored for the current bicycle sharing system in the city of Mashhad, the second most populated city in the developing country of Iran, based on frequent costumers’ judgment and experts’ opinion. A Stated Choice Experiment (SCE) survey is then designed and public preference data are collected from a sample of 90 randomly selected residents in Mashhad. Multinomial logit (MNL), mixed multinomial logit (MMNL) and latent class multinomial logit (LCMNL) models are used to investigate factors contributing to selection of BSS against other transport modes.We found that the MMNL model outperformed the other models in terms of statistical fit. More importantly, we found that bicycle fare, separated bicycle lane, bicycle quality, pavement quality, proximity of bicycle stations to bus stops, bicycle training programs, gender and employment status of respondents significantly influence public preferences towards BSS in Mashhad. People are willing to pay substantially more than the current bicycle fare to have safety, accessibility and convenience. The impact of gender and employment status on the public preferences is not homogeneous across individuals. Overall, the findings of the study have important implications to cost-benefit analysis of bicycle sharing system development plans in Mashhad.

Modelling route choice of Dutch cyclists using smartphone data

This paper analyzes the GPS traces recorded by cyclists in the framework of the Mobile Mobility Panel throughout the Netherlands. The objective of this paper is to analyze bicycle route choice via network attributes and trip length over a sequence of trips by approximately 280 bicycle users, who were asked to register their trips by means of a specific smartphone application. Approximately 3,500 bike trips were recorded throughout the Netherlands over a four-week period in 2014. The bike trips have been matched to a specific bicycle network built and updated by a Dutch cyclists’ union. Route choice models were estimated, using both the binomial logit model and the mixed multinomial logit model with Path-size logit model formulation. The chosen alternatives were part of the choice set for the mixed multinomial logit model. Also, the shortest route was generated for each origin-destination pair. 
 
 The results show that trip lengths and trip distribution over time reveal a population sample much used to cycling, frequently and over long distances. Furthermore, when considering the composition of chosen routes in terms of link type, the usage of cycleway links is frequent. For repeated trips, the shortest route option tends to be chosen more; frequent cyclists, on systematic trips, tend to optimize their trip and prefer the shortest routes. This is even truer for males and for non-leisure trips. The estimated probabilities for both multinomial and binomial models show that the binomial model tends to overestimate the probabilities of choosing the shortest route. This result is stronger in non-leisure trips, where people tend to choose a more personalized route, instead of the shortest. This research contributes to the generation of a more efficient distribution of bicycle trips over the network. Future research can more specifically address the intrapersonal variation in route—destination choice given the availability of longitudinal data.

The Monetary Value of Informal Care: Obtaining Pure Time Valuations Using a Discrete Choice Experiment

Interventions in health care often not only have an effect on patients, but also on their informal caregivers. Caregiving can have a profound impact on the health and wellbeing of carers. Ignoring these spillovers in economic evaluations risks labelling interventions mistakenly as cost-effective, at the expense of informal caregivers. This paper investigates willingness-to-accept (WTA) values for an hour of informal care, corrected for positive and negative impacts of informal care, to facilitate the inclusion of informal care hours on the cost side of economic evaluations without double-counting spillover effects. A discrete choice experiment (DCE) was conducted among a representative sample of the adult population in the Netherlands (n = 552) in September 2011. An experimental design minimizing the D-error was used to construct choice sets with two unlabelled alternatives with the attributes 'hours caregiving', 'monetary compensation for caregiving' and seven impacts of caregiving. To operationalize the random utility model, we used a panel mixed multinomial logit (MMNL) parameter model. For calculation of WTA, we used both population-level parameters and individual-level parameters. The mean WTA for an additional hour of informal care, corrected for positive and negative impacts of informal care, was €14.57. The signs of the coefficients were all in the expected directions. This study reports a preference-based monetary value for informal care, corrected for other impacts. This valuation facilitates the inclusion of informal care hours on the cost side in economic evaluations without double-counting any spillover effects included on the effects side.

Technical Note—A Conic Integer Optimization Approach to the Constrained Assortment Problem Under the Mixed Multinomial Logit Model

We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.

Impact of Built Environment on First- and Last-Mile Travel Mode Choice

The paper studies the impacts of built environment (BE) on the first- and last-mile travel modal choice. We select Singapore as a case study. The data used for this work is extracted from the first- and last-mile trips to mass rapid transit (MRT) stations in the Household Interview Travel Survey of Singapore in 2012 with nearly 24,000 samples. The BE indicators are quantified based on four “D” variables: Density, Diversity, Design, and Distance to transit. We also take into account sociodemographic and trip-specific variables. Mixed logit (ML) modeling frameworks are adopted to estimate the impact of BE and the heterogeneity of taste across the sample. Based on the availability of light rail transit (LRT) in different areas, two modeling structures are implemented with binary ML models for non-LRT areas where “walk” and “bus” are the available travel modes, and multinomial ML models for areas where LRT is an additional alternative. The modeling results shed light on the following findings: BE—especially distance to MRT station, transportation infrastructures, land-use mix, and socioeconomic activities—significantly influences the first- and last-mile travel behaviors. Those who live or work close to MRT stations and in an area with high socioeconomic activities and land-use mix may have stronger preferences to walk for the first- and last-mile trips. The impact of physical BE (i.e., distance, infrastructures) is relatively homogeneous among the sample, while the impact of socioeconomic BE factors (i.e., floor space density, entropy) tends to vary across the sample.

Water resource management and public preferences for water ecosystem services: A choice experiment approach for inland river basin management

The concept of ecosystem services provides a valuable approach for linking humans and nature and for supporting the protection of natural ecosystems. River water services, which influence public health and daily routines, have both social and ecological benefits to a surrounding area. However, river networks and their services have suffered extensive destruction due to urbanization and industrialization, especially in China. An assessment of river system benefits and recognition of public preferences are crucial for sustainable river management and effective river system restoration. The objective of this study was to assess a household's willingness to pay using a choice experiment (CE) with mixed logit and multinomial logit models. This technique was applied to evaluate a respondent's preferences regarding water service attributes such as upper basin, middle basin and lower basin ecological water distribution; water quality; and payment and the possible source of heterogeneity in these attributes. The estimated likelihood ratio test demonstrated that random parameter logit model (RPL) models had considerably more explanatory power than multinomial logit (MNL) models. It was also revealed that the RPL-II model was the most powerful among all the models, demonstrating the capability of that model to predict the choices of the respondents. Furthermore, the findings show that water quality was the most preferred river attribute, and households were willing to pay more for the water quality attribute that derives the highest marginal value. Household income level, residential location, education level, and sex were the main factors influencing willingness to pay. These assessments provide guidance, policy recommendations and a reference for researchers and policy makers to improve and enhance current river water services in the future.

A finite mixture modeling approach to examine New York City bicycle sharing system (CitiBike) users’ destination preferences

Given the recent growth of bicycle-sharing systems (BSS) around the world, it is of interest to BSS operators/analysts to identify contributing factors that influence individuals’ decision processes in adoption and usage of bicycle-sharing systems. The current study contributes to research on BSS by examining user behavior at a trip level. Specifically, we study the decision process involved in identifying destination locations after picking up the bicycle at a BSS station. In the traditional destination/location choice approaches, the model frameworks implicitly assume that the influence of exogenous factors on the destination preferences is constant across the entire population. We propose a finite mixture multinomial logit (FMMNL) model that accommodates such heterogeneity by probabilistically assigning trips to different segments and estimate segment-specific destination choice models for each segment. Unlike the traditional destination choice based multinomial logit (MNL) model or mixed multinomial logit (MMNL), in an FMMNL model, we can consider the effect of fixed attributes across destinations such as users’ or origins’ attributes in the decision process. Using data from New York City bicycle-sharing system (CitiBike) for 2014, we develop separate models for members and non-members. We validate our models using hold-out samples and compare our proposed FMMNL model results with the traditional MNL and MMNL model results. The proposed FMMNL model provides better results in terms of goodness of fit measures, explanatory power and prediction performance.

A Comparative Empirical Study of Discrete Choice Models in Retail Operations

Demand estimation is a fundamental task in retail operations and revenue management, providing the necessary input data for inventory control, assortment and price optimization models. The task is particularly difficult in operational contexts when product availability varies over time and customers may substitute. In addition to the classical multinomial logit (MNL) model and its variants (e.g., nested logit, mixed MNL), new demand models have been proposed (e.g., the Markov chain model) and others have been revisited (e.g., the rank-based and exponomial models). At the same time, new computational approaches were developed to ease the estimation function (e.g., column generation, EM algorithms). In this paper, we conduct a systematic, empirical study of different demand models and estimation algorithms, spanning both maximum likelihood and least squares criteria. Through an exhaustive set of numerical experiments on synthetic and real data, we provide comparative statistics of the quality of the different choice models and estimation methods, and characterize operational environments suitable for different model/estimation implementations.

Patient Preferences for Managing Insomnia: A Discrete Choice Experiment.

Despite the rapid development of effective treatments, both pharmacological and non-pharmacological, insomnia management remains suboptimal at the practice interface. Patient preferences play a critical role in influencing treatment outcomes. However, there is currently a mismatch between patient preferences and clinician recommendations, partly perpetuated by a limited understanding of the patients' decision-making process. The aim of our study was to empirically quantify patient preferences for treatment attributes common to both pharmacological and non-pharmacological insomnia treatments. An efficient dual-response discrete choice experiment was conducted to evaluate patient treatment preferences for managing insomnia. The sample included 205 patients with self-reported insomnia and an Insomnia Severity Index≥14. Participants were presented with two unlabelled hypothetical scenarios with an opt-out option across 12 choice sets. Data were analyzed using a mixed multinomial logit model to investigate the influence of five attributes (i.e. time, onset of action, maintainability of improved sleep, length of treatment, and monthly cost) on treatment preferences. Treatments were preferentially viewed if they conferred long-term sleep benefits (p<0.05); had an ongoing, as opposed to a predefined, duration of treatment course (p<0.05); required some, as opposed to no, additional time commitment (p<0.05); and had lower monthly out-of-pocket treatment costs (p<0.001). However, treatment onset of action had no influence on preference. Age, help-seeking status, concession card status and fatigue severity significantly influenced treatment preference. Participants' prioritization of investing time in treatment and valuing the maintainability of therapeutic gains suggests a stronger inclination towards non-pharmacological treatment, defying current assumptions that patients prefer 'quick-fixes' for managing insomnia.

Impact of combined alignments on lane departure: A simulator study for mountainous freeways

Lane departures are responsible for many side-swipe, rear-end and single-vehicle run-off-road crashes. There is a dearth of research, however, on how lane departures are impacted by roadway alignments. The objective of this paper is to examine which geometric design characteristics, including road alignment at the current segment and the adjacent segments, have significant influence on lane departure. Lane departure data from a total 30 drivers were collected from a driving simulator study of a four-lane (two lanes in each direction) divided mountainous freeway. Lane departures were classified into lane keeping, lane departure to the left and lane departure to the right for all-alignments (Dataset I), and lane keeping, lane departure to the inside and lane departure to the outside for curves-only (Dataset II). A mixed multinomial logit model for each dataset was employed to examine the contributory factors. This approach allows for the possibility that the estimated model parameters can vary randomly to account for unobserved effects potentially relating to heterogeneous driver behaviors. Fixed parameters that had a significant increase on lane departure were horizontal curvature at the current segment, and the difference (max-min) in horizontal curvature within the 300-m adjacent upstream alignment. Downward slope and upward slope with fixed parameters significantly decreased lane departure. Estimated parameters related to the direction of the curve, driving lane (bordering median or hard shoulder) and driving speed had found to have randomly distributed over the drivers. This indicates that driver behavior is not consistent in the effect of these three variables on lane departure. These results can assist engineers in designing safer mountainous freeways.

Comparison of parametric and semiparametric representations of unobserved preference heterogeneity in logit models

The logit-mixed logit (LML) model is a very recent advancement in semiparametric discrete choice models. LML represents the mixing distribution of a logit kernel as a sieve function (polynomials, step functions, and splines, among many other variants). In the first part of this paper, we conduct Monte-Carlo studies to analyze the number of required parameters (e.g., polynomial order) in three LML variants to recover the true population distributions, and also compare the performance (in terms of accuracy, precision, estimation time, and model fit) of LML and a mixed multinomial logit with normal heterogeneity (MMNL-N). Our results indicate that adding too many parameters in LML may not be the best strategy to retrieve underlying taste heterogeneity; in fact, overspecified models generally perform worst in terms of BIC. We recommend to use neither minimum-BIC nor the most flexible specification, but we rather suggest to start with the same number of parameters as a parametric model (such as MMNL-N) while checking changes in the derived histogram of the mixing distribution. As expected, LML was able to recover bimodal-normal, lognormal, and uniform distributions much better than the misspecified MMNL-N. Computational efficiency makes LML advantageous in the process of searching for the final specification. In the second part of the paper, we estimate the willingness-to-pay (WTP) estimates of German consumers for different vehicle attributes when making alternative-fuel-car purchase choices. LML was able to capture the bimodal nature of WTP for vehicle attributes, which was not possible to retrieve using standard parametric specifications.