Multiple Discrete-continuous Choice Research Articles

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.

A new closed form multiple discrete-continuous extreme value (MDCEV) choice model with multiple linear constraints

Traditional multiple-discrete continuous choice models that have been formulated and applied in recent years consider a single linear resource constraint, which, when combined with consumer preferences, determines the optimal consumption point. However, in reality, consumers may face multiple resource constraints, such as those associated with time, money, and storage capacity. Ignoring such multiple constraints and instead using a single constraint can, and in general will, lead to poor data fit and inconsistent preference estimation, which can then have a serious negative downstream effect on forecasting and welfare/policy analysis. Unlike earlier attempts to address this multiple constraint situation, we formulate a new multiple-constraint (MC) multiple discrete continuous extreme value (MDCEV) model (or the MC-MDCEV model) that retains a closed-form probability structure and is as simple to estimate as the MDCEV model with one constraint. We achieve this by assuming a type-I extreme value distribution for the error term in its minimization form in the baseline utility preference of each good rather than a maximization form as in Bhat's (2005; 2008) original MDCEV formulation. The statistical foundation of the proposed model is based on the fact that the difference between a minimal type-I extreme value random variable with scale σ and the weighted sum of the exponential of standardized minimal type-I extreme value random variables (scaled up by σ) leads to an apparently new multivariate distribution that has an elegant and closed-form survival distribution function. Results from a simulation experiment show that our proposed model substantially outperforms single-constraint models; the results also highlight the serious mis-estimation that is likely to occur if only a subset of active constraints is used. The proposed model is applied to a case of week-long activity participation where individuals are assumed to maximize their utility from time-use subject to time and money budgets.It is hoped that our proposed simple closed-form multi-constraint MDCEV model will contribute to a new direction of application possibilities and to new research into situations where consumers face multiple constraints within a multiple discrete-continuous choice context.

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.

An integrated choice and latent variable model for multiple discrete continuous choice kernels: Application exploring the association between day level moods and discretionary activity engagement choices

In the recent years, multiple discrete continuous (MDC) models have emerged as a popular framework to simultaneously model the choice of multiple goods (that are imperfect substitutes to one another) and the associated consumption quantities. The paper presents a new integrated choice and latent variable (ICLV) model implementation called the Hybrid Multiple Discrete Continuous (HMDC) model that is capable of incorporating the influence of psychological factors (modeled as latent constructs) on MDC choice behaviors. Estimation of ICLV models (with single discrete choice kernels and MDC kernels) has been a challenge owing to the high dimensional integrals involved in the likelihood function. The typically used maximum simulated likelihood estimation (MSLE) approach becomes cumbersome when the dimensionality of integration increases. In this research, a composite marginal likelihood (CML) based estimation approach is proposed for parameter estimation of the HMDC framework. Unlike the ICLV model implementations with single discrete choice kernel, the dimension of the integral to be decomposed in the HMDC varies across observations. This necessitated the use of weights when decomposing the likelihood function using the CML approach. A simulation study was conducted using synthetic datasets to demonstrate the superiority of the weighted CML approach over its unweighted counterpart in the presence of MDC choice kernel. The applicability of the proposed model formulation and associated estimation routine was demonstrated using an empirical case study with data from the 2013 American Time Use Survey (ATUS). The empirical study identifies interesting association between day level moods and discretionary activity participation decisions.

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.

Analysis of long-distance vacation travel demand in the United States: a multiple discrete–continuous choice framework

This study analyzes the annual vacation destination choices and related time allocation patterns of American households. More specifically, an annual vacation destination choice and time allocation model is formulated to simultaneously predict the different vacation destinations that a household visits in a year, and the time (no. of days) it allocates to each of the visited destinations. The model takes the form of a multiple discrete–continuous extreme value (MDCEV) structure. Further, a variant of the MDCEV model is proposed to reduce the prediction of unrealistically small amounts of vacation time allocation to the chosen destinations. To do so, the continuously non-linear utility functional form in the MDCEV framework is replaced with a combination of a linear and non-linear form. The empirical analysis was performed using the 1995 American Travel Survey data, with the United States divided into 210 alternative destinations. The model estimation results provide several insights into the determinants of households’ vacation destination choice and time allocation patterns. Results suggest that travel times and travel costs to the destinations, and lodging costs, leisure activity opportunities (measured by employment in the leisure industry), length of coastline, and weather conditions at the destinations influence households’ destination choices for vacations. The annual vacation destination choice model developed in this study can be incorporated into a larger national travel modeling framework for predicting the national-level, origin–destination flows for vacation travel.

Modeling Household Fleet Choice as Function of Fuel Price by Using a Multiple Discrete–Continuous Choice Model

In this paper a new model of fleet choice for households uses the multiple discrete–continuous extreme value (MDCEV) model as a framework. The aim is to establish a model to allocate car types to activity-based microscopic agent-based transport simulations. What is new in the presented model is that choice is influenced by fuel price in addition to socioeconomic attributes of households. To model a range of fuel prices up to US$20/gal, a database from a sophisticated stated adaption survey about residential mobility choice in approximately 400 Swiss households was used. The model had a choice set of 17 alternatives distinguishing car type and drivetrain. In the MDCEV model, a household chooses multiple car types and distributes an overall budget of vehicle miles traveled to chosen alternatives. The model shows that fuel price has a much greater influence on the selection of the car type than on the use (vehicle miles traveled) of a car. In a certain range of fuel prices, households tend to switch from gasoline to diesel cars. When fuel prices become too high, alternative fuel technologies are considered.

Generalized extreme value (GEV)-based error structures for multiple discrete-continuous choice models

This paper formally derives the class of multiple discrete-continuous generalized extreme value (MDCGEV) models, a general class of multiple discrete-continuous choice models based on generalized extreme value (GEV) error specifications. Specifically, the paper proves the existence of, and derives the general form of, closed-form consumption probability expressions for multiple discrete-continuous choice models with GEV-based error structures. In addition to deriving the general form, the paper derives a compact and readily usable form of consumption probability expressions that can be used to estimate multiple discrete-continuous choice models with general cross-nested error structures. The cross-nested version of the MDCGEV model is applied to analyze household annual expenditure patterns in various transportation-related expenses using data from a Consumer Expenditure Survey in the United States. Model estimation results and predictive log-likelihood based validation tests indicate the superiority of the cross-nested model over the mutually exclusively nested and non-nested model specifications. Further, the cross-nested model was amenable to the accommodation of socio-demographic heterogeneity in inter-alternative covariance across decision-makers through a parameterization of the allocation parameters.

When Pavarotti Meets Harry Potter at the Super Bowl

This study aims to assess the magnitude of the interdependencies across leisure activities. Such interdependencies can be due not only to the time and budget constraints, but also to correlation in preferences across these activities as well as the need to pay travel costs for out-of-home activities.To capture these effects we introduce a multiple discrete-continuous choice model in which consumers have heterogeneous preferences over a latent attribute space and pricing is non-linear. The combination of multiple discrete-continuous choice with non-linear pricing makes the estimation challenging. We overcome this obstacle by using a powerful genetic algorithm in the estimation.Using structural estimation and individual level data on the allocation of time of Americans in 2003 we find that there are significant interdependencies across leisure activities and that travel costs as well as correlated preferences play an important role in creating them.These interdependencies have important implications to various strategic decisions such as pricing, bundling and mergers.

A forecast of household ownership and use of alternative fuel vehicles: A multiple discrete-continuous choice approach

The paper analyzes how adding alternative fuel passenger cars to the market will affect patterns in demand for passenger cars. We use conjoint analysis and a multiple discrete-continuous choice model to estimate consumer preferences regarding alternative fuel vehicles, and based on the estimates we conduct a simulation to analyze changing rates of ownership and use of variously fueled passenger cars under the effect of the introduction of alternative fuel passenger cars. In addition, we estimate changes in overall fuel consumption and the emission of pollutants. The results show that gasoline-fueled cars will still be most consumers' first choice, but alternative fuel passenger cars will nevertheless compete and offer a substitute for the purchase and use of gasoline-fueled or diesel-fueled cars. Finally, results show that adding alternative fuel cars to the market would effectively lower gasoline and diesel fuel consumption and the emission of pollutants.