Mixed Multinomial Logit Research Articles

Who is Overeducated and Why? Probit and Dynamic Mixed Multinomial Logit Analyses of Vertical Mismatch in East and West Germany

Who is Overeducated and Why? Probit and Dynamic Mixed Multinomial Logit Analyses of Vertical Mismatch in East and West Germany

Comparative study on mode split discrete choice models

Discrete choice model acts as one of the most important tools for studies involving mode split in the context of transport demand forecast. As different types of discrete choice models display their merits and restrictions diversely, how to properly select the specific type among discrete choice models for realistic application still remains to be a tough problem. In this article, five typical discrete choice models for transport mode split are, respectively, discussed, which includes multinomial logit model, nested logit model (NL), heteroscedastic extreme value model, multinominal probit model and mixed multinomial logit model (MMNL). The theoretical basis and application attributes of these five models are especially analysed with great attention, and they are also applied to a realistic intercity case of mode split forecast, which results indicating that NL model does well in accommodating similarity and heterogeneity across alternatives, while MMNL model serves as the most effective method for mode choice prediction since it shows the highest reliability with the least significant prediction errors and even outperforms the other four models in solving the heterogeneity and similarity problems. This study indicates that conclusions derived from a single discrete choice model are not reliable, and it is better to choose the proper model based on its characteristics.

Demand for Primary Health Care in Rural North India: Jointly Modelling Revealed Preference and Qualitative Choice Intentions

The combined analysis of revealed preference and qualitative choice data offer complementary features in addressing data shortages and reliability constraints faced in many low-middle income countries. The lack of data for rural north India’s primary health care market provides a context in which this joint modelling is advantageous. This paper specifically highlights the benefits of jointly modelling data to help overcome a lack of price data for non-utilised health care providers. The flexibility of the Mixed Multinomial Logit error component model to apply random draws from non-normal distributions and account for data set specific scaling is compelling.

An investigation of household interactions in daily in-home and out-of-home maintenance activity participation and social behavior in Cairo, Egypt

This study is an empirical investigation of household interactions in joint in-home and out-of-home daily maintenance activity participation. Intra-personal trade-offs between solo and joint in-home and out-of-home maintenance activity participation decisions, and the possible substitution and/or complementary patterns between them were examined. Additionally, inter-personal trade-offs between solo and joint “with whom” out-of-home maintenance activity participation decisions were explored. Finally, the role of social roles, mobility resources, and internet availability in individuals’ daily joint maintenance activity participation was analyzed. The analyses included the following two dimensions: (1) modeling the choice behavior of solo and joint in-home and out-of-home maintenance activity participation, and (2) modeling the choice behavior of solo and joint “with whom” out-of-home maintenance activity participation. Two mixed multinomial logit (MMNL) models were developed using two-day activity and travel diary data from Cairo, Egypt. The MMNL model structure offers several advantages over other types of discrete choice models. First, it can accommodate intra-individual variations (i.e. heterogeneity) in joint activity participation. Also, it is capable of determining possible sources of any solo and joint preference heterogeneity that may exist. Finally, correlations due to shared unobservable factors among solo and joint activity participations can be captured within the model. Empirical evidences support many of the research hypotheses regarding joint “with whom” maintenance activity participations. Household traditions, social roles, and life style were found to be the main factors that affect joint activity participation.

Migration in Arctic Alaska: Empirical evidence of the stepping stones hypothesis

This paper explores hypotheses of hierarchical migration using data from the Alaskan Arctic. We focus on migration of Inupiat people, who are indigenous to the region, and explore the role of income and subsistence harvests on migration. To test related hypotheses we use confidential micro-data from the US Census Bureau’s 2000 Decennial Census of Population and Income and generate migration probabilities using a mixed multinomial and conditional logit model. Our findings are broadly consistent with Ravenstein’s (1885) early hypothesis of step-wise migration; we find evidence of step-wise migration, both up and down an urban and rural hierarchy. We also find that where migrants choose to live is a function of place, personal, and household characteristics.

Profit or patients’ health benefit? Exploring the heterogeneity in physician altruism

This paper investigates physician altruism toward patients’ health benefit using behavioral data from Hennig-Schmidt et al.'s (2011) laboratory experiment. In the experiment, medical students in the role of physicians decide on the provision of medical services. The experimental setup allows us to identify the influence of profits and patients’ health benefit on the choice of medical treatment. We estimate physician altruism, the weight individuals attach to patients’ health benefit, by fitting mixed logit and multinomial logit regression models to the experimental data. Estimation results provide evidence for physician altruism. We find, however, substantial variation in the degree of physician altruism. We also discuss some implications of our results for the design of physician payment schemes in the light of the theoretical literature.

Price Competition Under Mixed Multinomial Logit Demand Functions

In this paper, we postulate a general class of price competition models with mixed multinomial logit demand functions under affine cost functions. In these models, the market is partitioned into a finite set of market segments. We characterize the equilibrium behavior of this class of models in the case where each product in the market is sold by a separate, independent firm. We identify a simple and very broadly satisfied condition under which a pure Nash equilibrium exists and the set of Nash equilibria coincides with the solutions of the system of first-order-condition equations, a property of essential importance to empirical studies. This condition specifies that in every market segment, each firm captures less than 50% of the potential customer population when pricing at a specific level that, under the condition, is an upper bound for a rational price choice for the firm irrespective of the competitors' prices. We show that under a somewhat stronger, but still broadly satisfied, version of the above condition, a unique equilibrium exists. We complete the picture by establishing the existence of a Nash equilibrium, indeed a unique Nash equilibrium, for markets with an arbitrary degree of concentration, under sufficiently tight price bounds. We discuss how our results extend to a continuum of customer types. A discussion of the multiproduct case is included. The paper concludes with a discussion of implications for structural estimation methods. This paper was accepted by J. Miguel Villas-Boas, marketing.

Evaluating alternate discrete outcome frameworks for modeling crash injury severity

This paper focuses on the relevance of alternate discrete outcome frameworks for modeling driver injury severity. The study empirically compares the ordered response and unordered response models in the context of driver injury severity in traffic crashes. The alternative modeling approaches considered for the comparison exercise include: for the ordered response framework-ordered logit (OL), generalized ordered logit (GOL), mixed generalized ordered logit (MGOL) and for the unordered response framework-multinomial logit (MNL), nested logit (NL), ordered generalized extreme value logit (OGEV) and mixed multinomial logit (MMNL) model. A host of comparison metrics are computed to evaluate the performance of these alternative models. The study provides a comprehensive comparison exercise of the performance of ordered and unordered response models for examining the impact of exogenous factors on driver injury severity. The research also explores the effect of potential underreporting on alternative frameworks by artificially creating an underreported data sample from the driver injury severity sample. The empirical analysis is based on the 2010 General Estimates System (GES) data base—a nationally representative sample of road crashes collected and compiled from about 60 jurisdictions across the United States. The performance of the alternative frameworks are examined in the context of model estimation and validation (at the aggregate and disaggregate level). Further, the performance of the model frameworks in the presence of underreporting is explored, with and without corrections to the estimates. The results from these extensive analyses point toward the emergence of the GOL framework (MGOL) as a strong competitor to the MMNL model in modeling driver injury severity.

On Locally Optimal Criterion for a Logit Model with Random Parameters

Mixed logit is a highly flexible model that can approximate any random utility model. In this paper, two kinds of mixed multinomial logit models were considered. The main aim was to introduce a locally D-optimal criterion to obtain an optimal combination of the levels of attributes for producing alternatives and an optimal combination of alternatives in choice sets. Thus, a design including choice sets as the support points was designed.

Sample size requirements for stated choice experiments

Stated choice (SC) experiments represent the dominant data paradigm in the study of behavioral responses of individuals, households as well as other organizations, yet in the past little has been known about the sample size requirements for models estimated from such data. Traditional orthogonal designs and existing sampling theories does not adequately address the issue and hence researchers have had to resort to simple rules of thumb or ignore the issue and collect samples of arbitrary size, hoping that the sample is sufficiently large enough to produce reliable parameter estimates, or are forced to make assumptions about the data that are unlikely to hold in practice. In this paper, we demonstrate how a recently proposed sample size computation can be used to generate so-called S-efficient designs using prior parameter values to estimate panel mixed multinomial logit models. Sample size requirements for such designs in SC studies are investigated. In a numerical case study is shown that a D-efficient and even more an S-efficient design require a (much) smaller sample size than a random orthogonal design in order to estimate all parameters at the level of statistical significance. Furthermore, it is shown that wide level range has a significant positive influence on the efficiency of the design and therefore on the reliability of the parameter estimates.

Does Homeownership Lead to Longer Unemployment Spells? The Role of Mortgage Payments

This paper examines the impact of housing tenure choice on unemployment duration in Belgium using EU‐SILC micro data. We contribute to the literature in distinguishing homeowners with mortgage payments and outright homeowners. We simultaneously estimate unemployment duration by a mixed proportional hazard model, and the probability of being an outright homeowner, a homeowner with mortgage payments or a tenant by a mixed multinomial logit model. To be able to correctly identify the causal influence of different types of housing tenure on unemployment duration, we use instrumental variables. Our results show that homeowners with a mortgage exit unemployment first. Outright owners stay unemployed the longest. Tenants take an intermediate position. Moreover, our results reveal the different share of mortgage holders within the group of homeowners as a possible explanation for the discrepancy between former contributions to this literature.

Mixed Multinomial Logit Model for Out-of-Home Leisure Activity Choice

The design and the results of a study of the factors that influence the choice of out-of-home leisure activities are presented. Influencing factors appear to be related to sociodemographic characteristics, personal preferences, characteristics of the built environment, and other aspects of the activities themselves, such as transport mode and day of the week. The Dutch continuous time–use research data on leisure activities for 2008 to 2009 were used for estimating a mixed multinomial logit model that accounts for heterogeneity in individuals’ preferences. The model formulation also allows analysis of substitution and complementarity between the types of activities. Results indicate differences in behavior between people with different sociodemographic characteristics, especially regarding the life-cycle stage, which is a variable composed by age and household composition. The built environment exerts a slight influence on the choice of leisure activity purpose, whereas travel party has a strong influence. For substitution and complementary relationships between activity purposes, although outdoor leisure decreases the propensity to perform sports or hobbies–courses activities, such leisure increases the propensity to perform fun shopping and going-out or cultural activities. Limitations of the study are discussed.

Accounting for attribute non-attendance and common-metric aggregation in a probabilistic decision process mixed multinomial logit model: a warning on potential confounding

Latent class models offer an alternative perspective to the popular mixed logit form, replacing the continuous distribution with a discrete distribution in which preference heterogeneity is captured by membership of distinct classes of utility description. Within each class, preference homogeneity is usually assumed, although interactions with observed contextual effects are permissible. A natural extension of the fixed parameter latent class model is a random parameter latent class model which allows for another layer of preference heterogeneity within each class. A further extension is to overlay attribute processing rules such as attribute non-attendance (ANA) and aggregation of common-metric attributes (ACMA). This paper sets out the random parameter latent class model with ANA and ACMA, and illustrates its application using a stated choice data set in the context of car commuters and non-commuters choosing amongst alternative packages of travel times and costs pivoted around a recent trip in Australia. What we find is that for the particular data set analysed, in the presence of attribute processing together with the discrete distributions defined by latent classes, that adding an additional layer of heterogeneity through random parameters within a latent class only very marginally improves on the statistical contribution of the model. Nearly all of the additional fit over the fixed parameter latent class model is added by the account for attribute processing. This is an important finding that might suggest the role that attribute processing rules play in accommodating attribute heterogeneity, and that random parameters within class are essentially a potentially confounding effect. An interesting finding, however, is that the introduction of random parameters increases the probability of membership to full attribute attendance classes, which may suggest that some individuals assign a very low marginal disutility (but not zero) to specific attributes or that there are very small differences in the marginal disutility of common-metric attributes, and this is being accommodated by random parameters, but not observed under a fixed parameter latent class model.

An analysis of different types of advertising media and their influence on consumer preferences and purchase intentions for digital cameras

This study analyzes consumer preferences for different types of advertising media: print media, the Internet, salespersons, and a new type of media1– an innovative information delivery device based on Microsoft's multi-touch screen and a single-touch sensor bar. We chose three kinds of digital cameras for our study and analyzed how different types of advertising media influence purchase intention. We used mixed logit model and multinomial logit–OLS two-stage estimation method for this analysis. Our results show that the Internet had the highest influence on consumers' purchase intentions. The new type of media had the second highest influence. This study reveals that advertisements which use new types of media can positively influence consumers. These findings can inspire companies to use new types of advertising media to develop their advertising strategy portfolios. This proposed model is applicable to other products and types of advertising media in order to analyze consumer preferences and purchase intentions.

Travel mode choice and transit route choice behavior in Montreal: insights from McGill University members commute patterns

In developed countries such as Canada and United States, a significant number of individuals depend on automobile as their main mode of transport. There has been a stronger push towards analyzing travel behavior at the individual level so that transportation agencies can formulate appropriate strategies to reduce the auto dependency. Towards this pursuit of enhancing our understanding on travel behavior, we examine individual home to work/school commute patterns in Montreal, Canada with an emphasis on the transit mode of travel. The overarching theme of this paper is to examine the effect of the performance of the public transportation system on commuter travel mode and transit route choice (for transit riders) in Montreal. We investigate two specific aspects of commute mode choice: (1) the factors that dissuade individuals from commuting by public transit and (2) the attributes that influence transit route choice decisions (for those individuals who commute by public transit). This study employs a unique survey conducted by researchers as part of the McGill University Sustainability project. The survey collected information on commute patterns of students, faculty and staff from McGill University. In addition, detailed socio-demographic and residential location information was also collected. The analysis was undertaken using multinomial logit model for the travel mode choice component and a mixed multinomial logit model for the transit route choice component. The model estimation results were employed to conduct policy sensitivity analysis that allows us to provide recommendations to public transportation and metropolitan agencies.

Discrete choice with large choice sets

Modeling product demand with discrete choice models requires specifying how all competing products rate on various attributes, which becomes difficult when the choice set is large. As a result, this paper approximates the ratings for the various product offerings with a parameterized distribution. When applied to the mixed multinomial logit model with a Gaussian parameterized distribution, this leads to an easily estimable, ‘anti-ideal point’ choice model.

A simulation of the simple Mohring model to predict patronage and value of resources consumed for enhanced bus services

Choosing between the competing approaches to providing enhanced bus services requires the ability to predict the effects on patronage and overall benefits to society in terms of Value of Resources Consumed (VRC) of any proposed change. One common approach uses the Mohring model of 1972 and its successors to optimise one or more aspects of the supply of transit services given various level of demand. This paper simulates the operation of a simple circular bus route using the equations of a basic Mohring type model and a Decision Support System (DSS) to endogenise demand under the assumption that there is a fixed demand for travel but commuters can choose between the bus and private vehicle. The selected approach recognises that demand for a particular mode of travel is predicated on the speed of the vehicle in service which is itself determined by the demand for that vehicle (in this model or boarding and alighting time) rather than being determined exogenously. This creates an iterative feedback mechanism whereby changes to the attributes of the bus and car alter mode choice and the speed in service of the bus which, in turn, alters mode choice. The simulation is used to predict changes to patronage and VRC under scenarios regarding changes to the transport network (in terms of fares and running costs, frequency and spacing of bus stops) using parameters from both a Multinomial Logit (MNL) and a Mixed Multinomial Logit (MMNL). The results demonstrate that there are large differences in the size and, in some cases, direction of predicted changes to patronage, VRC and revenue, depending on whether the parameters of the MNL or MMNL model are used.

Quantifying the transport-related impacts of parental school choice in England

School travel is becoming increasingly car-based and this is leading to many environmental and health implications for children all over the world. One of several reasons for this is that journey to school distances have increased over time. This is a trend that has been reinforced in some countries by the adoption of so-called ‘school choice’ policies, whereby parents can apply on behalf of their child(ren) to attend any school, and not only the school they live closest to. This paper examines the traffic and environmental impacts of the school choice policy in England. It achieves this by analysing School Census data from 2009 from the Department for Education. Multinomial logit modelling and mixed multinomial logit modelling are used to illustrate the current travel behaviour of English children in their journey to school and examine how there can be a significant reduction in vehicle miles travelled, CO2 emissions and fuel consumption if the ‘school choice’ policy is removed. The model shows that when school choice was replaced by a policy where each child only travelled to their ‘nearest school’ several changes occurred in English school travel. Vehicle Miles Travelled (VMT) by motorised transport fell by 1 % for car travel and 10 % for bus travel per day. The reduction in vehicle miles travelled could lead to less congestion on the roads during the morning rush hour and less cars driving near school gates. Mode choice changed in the modelled scenario. Car use fell from 32 to 22 %. Bus use fell from 12 to 7 %, whilst NMT saw a rise of 17 %. With more children travelling to school by walking or cycling the current epidemic of childhood obesity could also be reduced through active travel.

Embedding Risk Attitudes in a Scheduling Model: Application to the Study of Commuting Departure Time

In traditional travel time reliability valuation studies, the value of travel time savings and the value of travel time reliability (or reduced time variability) are estimated within a linear utility functional form, which assumes risk-neutral attitudes for decision makers. In this paper, we develop nonlinear scheduling models to address both risk attitude and preference in the context of a stated choice experiment of car commuters facing risky choices where the risk is associated with the trip time. We also investigate unobserved between-individual heterogeneity in time-related parameters and risk attitudes using a mixed multinomial logit model. The willingness-to-pay values for reducing the mean travel time and variability (earlier/later than the preferred arrival time) are also estimated within the nonlinear scheduling framework. The model is then used to estimate preferred departure times for commuters, assuming that random link capacities are the source of travel time variability. Results show that the more variable travel times are, the earlier commuters depart and that the nonlinear scheduling model predicts earlier optimal departure times than the linear scheduling model does. The application in this paper helps to bridge the gap between theory and practice.

Accounting for Systematic Influences on Preference Heterogeneity in Air Travel

Modeling passengers' itinerary choice behavior helps in understanding the increasingly competitive airline market and in predicting air travel demand. Recently, investigation of the variation in passengers' preferences with regard to factors influencing their choice through estimation of the mixed multinomial logit model has received attention. An extended form of the model identifies sources of heterogeneity and consequently makes the choice models less restrictive in considering both systematic and random preference variation across individuals. This research investigates the existence of significant interactions between passengers' preference heterogeneity around the mean of random parameters in estimated utility functions and observed sociodemographic or trip-related attributes in the case of air travel. Unlike previous research in the literature that has focused on choice behavior modeling in mature markets with relatively high per capita rates of air travel activity, this study centers on a survey of travelers in Tehran, Iran, a low-propensity air travel market. Several distributions for random parameters are considered to test the impacts of restricting distributions to allow only normality. The potential to improve model fit with alternative distributions was confirmed. The findings suggest that differences in the marginal utilities can be explained mostly by differences in travel experience. More experienced passengers are less sensitive to fare and more sensitive to flight level-of-service attributes. Furthermore, the estimated distributions of willingness-to-pay (WTP) measures confirm the value of accounting for interactions between preference heterogeneity and observed variables and in this case yield higher mean WTP values than does analysis that omits these interaction effects.