Discrete-continuous Choice Model Research Articles

Modelling activity patterns of wild animals - An application of the multiple discrete-continuous extreme value (MDCEV) model

Advanced econometric models used in the field of transport or marketing are becoming increasingly sophisticated and able to capture complex decision making and outcomes. In this paper, we apply state-of-the-art discrete-continuous choice models to the field of Ecology, in particular to model activity engagement of the population of Swedish Brown bears. Using data from GPS collars that track wild animals over time, we estimate a Multiple Discrete-Continuous Extreme Value (MDCEV) model to understand activity engagement and duration as a function of both bear characteristics and other external factors. We show that the methodology is not only suitable to address this aim, but also allows us to produce insights into the connection between the animal's age and gender and activity engagement as well as the links with climate variables (temperature and precipitation) and human activity (hunting).

Probit-Based Discrete-Continuous Choice Model to Explore the Relationship Between Car Ownership and Commuters’ Non-Work Activity Durations in Xiaoshan District of Hangzhou, China

In China, a developing country, the car ownership level is much lower than that in developed countries, but transportation policies have been implemented to discourage car ownership and mitigate traffic congestion. However, car ownership (considered as car availability in this paper, meaning that an individual has access to a household private car) may influence travelers’ well-being. To highlight the interrelation between car ownership and travelers’ well-being, this paper develops a probit-based discrete-continuous model to analyze the relationship between car ownership and the duration of commuters’ three major non-work outdoor activities (Act1: shopping and dining; Act2: leisure and entertainment; and Act3: visiting relatives or friends) in Xiaoshan District, Hangzhou, China. Empirical results indicate strong effects of individual and household socio-demographics, built environment attributes, and work-related characteristics on the car ownership decision and the duration of three non-work activities. The analysis shows positive correlations in unobserved factors between the car ownership decision and the duration of Acts1–3, indicating a mutually promotive relationship. Similarly, negative correlations among the duration of Acts1–3 show that non-work activities’ duration is mutually substitutive. These findings will help to better understand commuters’ car ownership decisions and non-work outdoor activity behavior restricted by fixed work schedules in developing countries, which can, in turn, better evaluate the impact of transportation policies (such as car ownership restriction) on travel demand as well as well-being, and provide decision support for the formulation of transportation policies.

Impact of the COVID-19 Pandemic on Activity Time Use and Timing Behavior in Switzerland

This paper analyzes the impact of the COVID-19 pandemic on activity time use and timing behavior in Switzerland. The evaluation is based on mobility tracking data collected in Switzerland during the COVID-19 pandemic. The pandemic has affected how people spend their time and schedule their activities throughout the day, subsequently creating new activity patterns. Because of the rare occurrences of pandemics in the recent past, little is known about their implications on the behavioral choices of affected people. This paper analyzes these implications by applying a multiple discrete-continuous choice model on mobility tracking data from Switzerland. The applied model is consistent with the results of the descriptive analysis and shows that the different stages of the pandemic drove changes in the activity patterns. During the lockdown, an increase in home activities comes along with decreases in the other activity types. With progressive relaxation of the measures in the following phases, the trends slowly return to the initial state before the pandemic. In addition, it can be seen that the impact of main drivers such as age, gender, household size, income and weather on time use and activity scheduling varies between phases, activity types, and time of day.

Multiple discrete-continuous choice models with additively separable utility functions and linear utility on outside good: Model properties and characterization of demand functions

In this paper, we enhance the current understanding of the properties of multiple discrete-continuous (MDC) choice models with additively separable (AS), independent and identically distributed (IID) utility functions, and linear utility form on the essential outside good. First, we highlight that the prior implementations of this model in the literature ignore primal feasibility conditions related to the budget constraint and the essential nature of outside good in formulating the model likelihood function. Second, we evaluate the suitability and performance of the model for alternative consumption patterns relative to the budget. In addition, we provide a systematic comparison of the performance of MDC choice models with the linear outside good utility form (i.e., the Lγ-profile model) and those with the non-linear outside good utility form (i.e., the NLγ-profile model). Third, for the Lγ-profile model with infinite budgets (i.e., when a very small proportion of the budget is allocated to inside goods), we derive the distributions of the resulting optimal demand functions and analytic expressions for the corresponding first and second moments, and identify a property that makes it easy to estimate the utility function parameters of an inside alternative even when consumption data is not available for other alternatives. In addition, perhaps for the first time in the literature, we show how an independent system of Tobit models can be derived as a restricted version of the utility-theoretic Lγ-profile MDC model structure. Finally, we apply the model for an empirical analysis of expenditure patterns of leisure trips from a domestic tourism survey sample of households in India.

Multiple discrete-continuous choice models with bounds on consumptions

This paper derives a multiple discrete–continuous (MDC) choice model formulation with constraints that specify upper bounds on consumption. To do so, considering the conventional utility maximization problem of a consumer, the Karush-Kuhn-Tucker (KKT) conditions are laid out for the MDC model with a general set of linear constraints that include inequalities. Subsequently, we derive a model with constraints that accommodate upper bounds on consumptions and an additive utility structure that accommodates lower bounds on consumptions. The likelihood expression for the proposed model takes a closed form. Furthermore, we extend the formulation to impose bounds on an MDC choice model with activity episode-level choice alternatives that accommodates a logical ordering among different episodes of an activity. The proposed models are derived for two different specifications of the outside good utility – (1) nonlinear utility with respect to consumption and (2) linear utility with respect to consumption. The proposed models are applied to an empirical context to analyze activity-level as well as episode-level activity participation and time allocation while considering bounds on time allocations. Empirical results suggest that the models that consider upper bounds on consumption offer a better fit to data, avoid predictions of unrealistically large time allocations, and result in overall better predictions than those from models without bounds. The proposed models are useful in situations, such as microsimulation models of travel demand, where it is crucial to avoid unrealistically large predictions.

Sensitivity of Water Price Elasticity Estimates to Different Data Aggregation Levels

The empirical literature on residential water demand employs various data aggregation methods, which depend on whether the aggregation is over consumption, sociodemographic variables, or both. In this study, we distinguish three dataset types—aggregated data, disaggregated data, and semi-aggregated data—to compare the consequences of using a large sample of semi-aggregated data vis-à-vis a small sample of fully disaggregated data on the water price elasticity estimates. We also analyze whether different aggregation levels in the sociodemographic variables affect the water price elasticity estimates when the number of observations is fixed. We employ a discrete-continuous choice model that considers that consumers face an increasing block price structure. Our results demonstrate that the water price elasticities depend upon the level of aggregation of the data used and the sample size. We also find that the water price elasticities are statistically different when comparing a large semi-aggregated sample with a small disaggregated sample.

Computationally efficient forecasting procedures for Kuhn-Tucker consumer demand model systems: Application to residential energy consumption analysis

This paper proposes simple and computationally efficient forecasting algorithms for random utility maximization-based multiple discrete-continuous (MDC) choice models with additively separable utility functions, such as the Multiple Discrete-Continuous Extreme Value (MDCEV) model. The algorithms build on simple yet insightful, analytical explorations with the Karush Kuhn-Tucker (KKT) conditions of optimality that shed new light on the properties of the models. The MDCEV model and the forecasting algorithms proposed in this paper are applied to a household-level energy consumption dataset to analyze residential energy consumption patterns in the United States. Further, simulation experiments are undertaken to assess the computational performance of the proposed and existing KT demand forecasting algorithms for a range of choice situations with small and large choice sets.

Modeling workers’ daily out-of-home maintenance activity participation and duration

Abstract This paper applies a multiple discrete–continuous choice model to determine worker’s decisions on interdependencies of maintenance activity participation and duration over different time periods in a worker’s day. To accommodate household effect, each time period is further defined according to whether the maintenance activities were conducted independently or jointly with other household members. Using the household survey data from the New York metropolitan area, the worker’s participation and duration decisions were jointly estimated for four time periods, including the morning commute, midday, evening commute, and after evening commute. To account for the censored nature of the duration data, a “censored system of equations” proposed by Shonkwiler and Yen was adopted and modified to increase asymptotic efficiency of the parameter estimates. Despite simplicity of the model and its ease of implementation, the estimation results offer valuable insights into the effects of socio-demographics, land use density, transportation service, and work duration characteristics on worker’s daily scheduling of maintenance activities and travel in a highly urbanized environment.

Identification of Dynamic Discrete-Continuous Choice Models, with an Application to Consumption-Savings-Retirement

This paper studies the non-parametric identification of the discount factor and utility function in the class of dynamic discrete-continuous choice (DDCC) models. In contrast to the discrete-only model we show the discount factor is identified. Our results further highlight why Euler equation estimation approaches that ignore agents' discrete choices are inconsistent. We estimate utility and discount factors for a consumption- savings-retirement choice problem using the Panel Study of Income Dynamics (PSID). We show that the relative risk aversion parameter and the intertemporal elasticity of substitution are separately identified, and that the latter varies across agents due to the wealth-dependence of the surplus from the discrete choice. This surplus also implies that the value function may be locally convex in wealth, and we find that a simulated Universal Basic Income (UBI) policy counterintuitively benefits wealthier working households more than poorer ones due to this effect.

The relationship between length of stay and land transportation mode in the tourism sector: A discrete–continuous framework applied to Swiss data

This study aims to investigate the relationship between travel mode and length of stay decisions in the context of domestic trips in Switzerland, formulating a discrete–continuous choice model. The adoption of this method allows us to explicitly recognize the interrelated nature of such decisions while testing and measuring the underlying correlation effects. The data source employed for the empirical analysis refers to the Household Budget Survey, which gathers information with regard to the 642 trips undertaken by Swiss resided tourists in 2010 and in particular to the most recent nonbusiness sojourn in this regard. The estimated correlation parameters reveal that tourists are likely to stay longer at the destination when travelling by train and appear to be less inclined to spend more extended sojourns when heading to the destination by car.

The impact of socioeconomic characteristics and land use patterns on household vehicle ownership and energy consumption in an urban area with insufficient public transport service – A case study of metro Manila

Understanding the impact of household characteristics and land use attributes on household vehicle ownership and usage decision is an efficient way of crafting strategic approaches having negative impacts on private vehicle dependency toward a sustainable urban transportation system. This empirical study applied the Gaussian copula-based discrete-continuous choice model to develop an integrated household vehicle ownership and energy consumption model using the unique data sample of 1795 households gathered in 2017 through various areas in Metro Manila, Philippines. The findings necessarily reported that household income is the main factor of household vehicle ownership and energy consumption decision. Households with the presence of older and well-educated household heads are found to be willing to acquire more vehicles. Encouraging urban densification, improvement of road public transport line density, reduction of distance from a residential area to the shortest railway station, and increasing mixture of integral facilities in neighborhoods (i.e., hospitals, markets, schools, and recreation centers) have considerable contributions to build a metropolis with less private vehicle dependency. The developed model was then applied to simulate percentage changes of the vehicle fleet and energy consumption based on various scenarios, and the policy implications based on the empirical findings were also discussed to help policymakers.

Testing the behavior of rationally inattentive consumers in a residential water market

Rationally inattentive consumers tend to apply simplified heuristics when making decisions. We test the hypothesis of rational inattention in the context of residential water usage where water bills typically account for a small fraction of household expenditures and only attract casual attention. We begin by rigorously testing whether or not residential water customers exhibit evidence of rational inattention. We then propose a heuristic water demand model to explore the decision-making of rationally inattentive consumers and validate the model by comparing the model with the discrete-continuous choice model on attentive and fully informed decision makers in out-of-sample predictions.

Exit dynamics of start-up firms: Structural estimation using indirect inference

We estimate by means of indirect inference a structural economic model where firms’ exit and investment decisions are the solution to a discrete–continuous stochastic dynamic programming problem. Our method solves the main difficulty of simulation-based inference in structural discrete–continuous choice models, namely that the simulated trajectories are discontinuous functions of the structural parameters. Estimating the model on all start-up firms in the Norwegian manufacturing sector, we find that if the expected value of continuing production is persistently low relative to the expected value of exit, the firm has a high probability to exit.

Increasing Block Tariffs in an Arid Developing Country: A Discrete/Continuous Choice Model of Residential Water Demand in Jordan

Arid developing countries face growing challenges from water scarcity, which are exacerbated by deficient piped water supply infrastructures. Increasing block tariffs (IBTs), charging higher rates with increasing water consumption, can potentially reconcile cost recovery to finance these infrastructures with an equitable and affordable sharing of the cost burden. A firm understanding of the impacts of varying prices and socio-economic conditions on residential water demand is necessary for designing IBTs that promote these objectives. Consistently estimating water demand under an IBT requires a discrete/continuous choice (DCC) model. Despite this, few econometric studies of arid developing countries have applied this state-of-the-art approach. This paper applies a DCC model to estimate residential water demand under IBTs in the severely water-stressed country of Jordan, using 15,811 country-wide household-level observations from five years up to 2013. We extend Hewitt and Hanemann’s original DCC formulation in order to accommodate IBTs featuring a linearly progressive tariff block. We then use the resulting demand function to assess Jordan’s 2013 IBTs and alternative IBT designs. Under the estimated price elasticities, very few IBT designs achieve a full recovery of the financial costs of water provision, but we still identify a potential to improve cost recovery and affordability.

A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior

Most multinomial choice models (e.g., the multinomial logit model) adopted in practice assume an extreme-value Gumbel distribution for the random components (error terms) of utility functions. This distributional assumption offers a closed-form likelihood expression when the utility maximization principle is applied to model choice behaviors. As a result, model coefficients can be easily estimated using the standard maximum likelihood estimation method. However, maximum likelihood estimators are consistent and efficient only if distributional assumptions on the random error terms are valid. It is therefore critical to test the validity of underlying distributional assumptions on the error terms that form the basis of parameter estimation and policy evaluation. In this paper, a practical yet statistically rigorous method is proposed to test the validity of the distributional assumption on the random components of utility functions in both the multinomial logit (MNL) model and multiple discrete-continuous extreme value (MDCEV) model. Based on a semi-nonparametric approach, a closed-form likelihood function that nests the MNL or MDCEV model being tested is derived. The proposed method allows traditional likelihood ratio tests to be used to test violations of the standard Gumbel distribution assumption. Simulation experiments are conducted to demonstrate that the proposed test yields acceptable Type-I and Type-II error probabilities at commonly available sample sizes. The test is then applied to three real-world discrete and discrete-continuous choice models. For all three models, the proposed test rejects the validity of the standard Gumbel distribution in most utility functions, calling for the development of robust choice models that overcome adverse effects of violations of distributional assumptions on the error terms in random utility functions.

Functional forms and price elasticities in a discrete continuous choice model of the residential water demand

AbstractDuring recent decades, water demand estimation has gained considerable attention from scholars. From an econometric perspective, the most used functional forms include log‐log and linear specifications. Despite the advances in this field and the relevance for policymaking, little attention has been paid to the functional forms used in these estimations, and most authors have not provided justifications for their selection of functional forms. A discrete continuous choice model of the residential water demand is estimated using six functional forms (log‐log, full‐log, log‐quadratic, semilog, linear, and Stone‐Geary), and the expected consumption and price elasticity are evaluated. From a policy perspective, our results highlight the relevance of functional form selection for both the expected consumption and price elasticity.

A Microeconomic Theory–Based Latent Class Multiple Discrete–Continuous Choice Model of Time Use and Goods Consumption

A microeconomic theory–based multiple discrete–continuous choice model was developed to accommodate ( a) both time allocation and goods consumption as decision variables in the utility function, ( b) both time and money budget constraints governing the activity participation and goods consumption decisions, ( c) a finite probability of zero consumption and zero time allocation (i.e., corner solutions), and ( d) technical constraints in the form of minimum consumption levels for any good that would be consumed and minimum time allocation for any activity conducted. The proposed model was applied in the form of a latent class model (to consider heterogeneity) on a Dutch data set to understand the determinants of weekly time use and goods consumption behavior.

Estimation of Annual Mileage Budgets for a Multiple Discrete-Continuous Choice Model of Household Vehicle Ownership and Utilization

This paper presents an empirical comparison of the following approaches to estimate annual mileage budgets for multiple discrete-continuous extreme value (MDCEV) models of household vehicle ownership and utilization: (a) a log-linear regression approach to model observed total annual household vehicle miles traveled (AH-VMT), (b) a stochastic frontier regression approach to model latent annual vehicle mileage frontier, and (c) other approaches used in the literature to assume annual household vehicle mileage budgets. For the stochastic regression approach, MDCEV and multiple discrete-continuous heteroscedastic extreme value (MDCHEV) models were estimated and examined. When model predictions were compared with observed distributions of vehicle ownership and utilization in a validation data sample, the log-linear regression approach performed better than other approaches. However, policy simulations demonstrate that the log-linear regression approach does not allow for AH-VMT to increase or decrease as a result of changes in vehicle-specific attributes, such as changes in fuel economy. The stochastic frontier approach overcomes that limitation. Policy simulation results with the stochastic frontier approach suggest that increasing the fuel economy of a category of vehicles increases the ownership and use of those vehicles. But this does not necessarily translate into an equal decrease in the use of other household vehicles, confirming previous findings in the literature that improvements in fuel economy tend to induce additional travel. In view of policy responsiveness and prediction accuracy, using the stochastic frontier regression (for estimating mileage budgets) in conjunction with the MDCHEV model for discrete-continuous choice analysis of household vehicle ownership and utilization is recommended.

The benefits of allowing heteroscedastic stochastic distributions in multiple discrete-continuous choice models

This paper investigates the benefits of incorporating heteroscedastic stochastic distributions in random utility maximization-based multiple discrete-continuous (MDC) choice models. To this end, first, a Multiple Discrete-Continuous Heteroscedastic Extreme Value (MDCHEV) model is formulated to allow heteroscedastic extreme value stochastic distributions in MDC models. Next, an empirical analysis of individuals' daily time use choices is carried out using data from the National Household Travel Survey (NHTS) for three geographical regions in Florida. A variety of different MDC model structures are estimated: (a) the Multiple Discrete-Continuous Extreme Value (MDCEV) model with independent and identically distributed (IID) extreme value error structure, (b) the MDCHEV model, (c) the mixed-MDCEV model that allows heteroscedasticity by mixing a heteroscedastic distribution over an IID extreme value kernel, (d) the MDC generalized extreme value (MDCGEV) model that allows inter-alternative correlations using the multivariate extreme value error structure, (e) the mixed-MDCEV model that allows inter-alternative correlations using common mixing distributions across choice alternatives, and (f) the mixed-MDCEV model that allows both heteroscedasticity and inter-alternative correlations. Among all these model structures, the MDCHEV model provided the best fit to the current empirical data. Further, heteroscedasticity was prominent while no significant inter-alternative correlations were found. Specifically, the MDCHEV parameter estimates revealed the significant presence of heteroscedasticity in the random utility components of different activity type choice alternatives. On the other hand, the MDCEV model resulted in inferior model fit and systematic discrepancies between the observed and predicted distributions of time allocations, which can be traced to the thick right tail of the type-1 extreme value distribution. The MDCHEV model addressed these issues to a considerable extent by allowing tighter stochastic distributions for certain choice alternatives, thanks to its accommodation of heteroscedasticity among random utility components. Furthermore, spatial transferability assessments using different transferability metrics also suggest that the MDCHEV model clearly outperformed the MDCEV model.

Stated response and multiple discrete-continuous choice models: Analyses of residuals

In sophisticated transport models, choice modelling is used to capture a wide range of behaviour, such as mode choice, vehicle choice and route choice. A newly developed approach to improving realism is the multiple discrete-continuous extreme value (MDCEV) model, which allows researchers to model the allocation of continuous amounts of a consumer good. Before implementing this model in overall frameworks, it is important to determine the accuracy of the forecasting. In this paper, an MDCEV model of household fleet choice based on data collected in a stated adaptation survey is presented. The model was used to predict the annual mileage of households with regard to 17 different types of cars, and the results of that forecast were compared to the actual data by calculating the residuals. The residual analysis showed that the model performed significantly better than a completely random model, but the share of wrongly allocated mileage, 70% of the total, remained high. However, the results of only one model were not sufficient to assess the procedure. The differences between two submodels, one with and one without public transport, regarding the distribution of the residuals indicated that model specification has a significant influence on performance. Therefore, more work on forecasting additional MDCEV models was necessary to have a basis for comparison. We compared two further MDCEV models to obtain a fuller understanding of their performance.