EXPONOMIAL MODEL FOR MULTIPLE DISCRETE-CONTINUOUS CHOICES: ANALYSIS OF ACTIVITY TIME-USE PATTERNS IN DUAL EARNER HOUSEHOLDS

ABSTRACT

In single choice modeling, methods like the popular multinomial logit (MNL) are focused on estimating the probability of each alternative to be chosen given specific conditions. This can be very limiting for scenarios where the decision makers consume more than one alternative. Multiple discrete-continuous (MDC) models address this issue by accounting for the allocation of a constrained budget (e.g., money or time) across a set of available alternatives, rather than a binary consumption or not.

The standard approach for MDC models is the Multiple Discrete-Continuous Extreme

Value (MDCEV) choice model and is based on a Gumbel distribution for the stochastic component. From a behavioral perspective of the consumers, the positive skewness of a Gumbel distribution does not accurately describe the expected nor observed rational consumption of goods. A negatively skewed distribution for the stochasticity terms describes better the perceived value from the decision makers for the available alternatives.

In the single choice framework, the Exponomial choice has been proved to offer better behavioral and data fitness properties compared to a regular MNL. This work presents the development and properties of the Multiple Discrete-Continuous Exponomial Choice (MDCEC) that holds an elegant closed form for the likelihood function that, unlike the MDCEV, offers easiness of implementation for heteroscedasticity across alternatives.

The ability from MDCEC to retrieve the true value of the parameters is demonstrated using simulated data under a variety of conditions and later, the MDCEC is compared to the MDCEV in an empirical case of activity time use for activity-based travel demand applications, where the

MDCEC approach provides a significant better fit to the empirical data.

TABLE OF CONTENTS

LIST OF TABLES………………………………………………………………………………………………….. v

ACKNOWLEDGEMENTS……………………………………………………………………………………… vi

Chapter 1  Introduction……………………………………………………………………………………………. 1

Chapter 2  Literature Review…………………………………………………………………………………….. 5

Activity based travel demand………………………………………………………………………………. 5

Multiple discrete-continuous modeling………………………………………………………………….. 7

Chapter 3  Methodology…………………………………………………………………………………………. 11

Chapter 4  Simulation analysis…………………………………………………………………………………. 19

Chapter 5  Empirical application………………………………………………………………………………. 22

Chapter 6  Concluding remarks………………………………………………………………………………… 32

References………………………………………………………………………………………………………….. 34

Chapter 1 Introduction

 

Discrete choice modeling serves as a powerful tool to analyze events where the decision makers are offered a specific set of alternatives for consumption. In single choice, the alternatives are considered as perfect substitutes, because they offer a very similar or identical use, for instance, from a set of soft drinks, all of them satisfy the consumer needs to hydrate, refresh, and enjoy a tasty drink according to the unique preferences of each individual, but no drink  has significant differences compared to the rest.

Recently, the literature has presented more interest into discrete analyses beyond traditional multiple-choice models, such as multinomial logit (MNL) or multinomial probit. One particular area of development arises when the decision makers can spend from a continuous budget (e.g., time, money, or mileage) into a set of imperfect substitutes, for instance, a regular soft drink, an energy drink, orange juice, and water, in the context of soft drinks. These are imperfect substitutes because each product satisfies different needs of the consumer, unlike the example where all the alternatives were soft drinks. The consumption of these products is typically constrained to a budget, in this case how much money to allocate on each type of drink; this is known in the literature as multiple discrete-continuous (MDC) models.

Because of the generality of MDC modeling, it has multiple applications: from marketing, production and consumption of goods and services (like the drinks example above), to allocation of investments and diversification of a portfolio in specific financial instruments (e.g., stocks, bonds, commodities, real estate, etc.).

In the transportation field, MDC models can be applied to estimate the household usage from a set of available vehicles (e.g., sedan, SUV, convertible, truck, motorcycle), where each vehicle serves better for different trip purposes. More recently, it can be used to analyze the ownership and usage of electric, hybrid or other alternative-fuel vehicles compared to more standard types of vehicles in the household, and in the future, usage of autonomous vehicles in the household. The usage can be estimated as the time (from all the time spent traveling or commuting) or mileage allocated into each type of vehicle. On a broader sense of commuting, it can also be applied to estimate the allocation of weekly or monthly travel into multiple modes (e.g., private vehicle, bus, train, walking, cycling, taxi, ride-hailing, etc.).

From a business perspective, the vehicle fleet from a delivery company, transit agency, airlines, cruise ships, cargo ships, freight or passenger trains, or in general, any business that operates with a fleet can be modeled for different types of ground vehicles, aircrafts or ships and the miles or time that is allocated for each type of vehicle. For instance, a transit agency might use small of buses for long distance routes with low ridership and articulated buses with more capacity for urban routes with high rush hour demand. A delivery company might use big trucks for long distance between cities and small vehicles for final delivery.

From a city planning perspective, the types of land use and how much to build for each land use can also be modeled for land development decisions, whether for development companies or in a macro level of consumption of the city land resources.

For activity demand, MDC models can be used to estimate how much time do individuals spend in a set of discrete activities (e.g., staying at home, working, shopping, visiting, eating out) in a regular day. In long-distance leisure travel, it can be used to analyze where the individuals go, how many days, or how much money to spend in different activities. This application in activity demand is particularly relevant for its applications for activity-based travel demand to generate more accurate and realistic predictions for travel demand based on activities and time use.

Traditionally, travel demand has been modeled using the “four-step travel model” (trip generation, trip distribution, mode choice, and route assignment), but uses aggregated data that 3

does not reflect the behavioral nature of the decision makers (Bradley, M., Bowman, J., & Lawton, 1999) and therefore, more detailed methods are needed to address these limitations from the traditional models (Ben-Akiva & Bowman, 1998; Bhat & Koppelman, 1999; Pinjari & Bhat, 2011). Instead of modeling the travel demand itself and given that the travel demand is a consequence of a broader activity demand (Ben-Akiva & Bowman, 1998; Bowman, J. L., & Ben-Akiva, 2000; Jones, P., Koppelman F., 1990), an alternative approach focuses of activity-based travel demand, in which the time and features of the activities from each individual are estimated and later incorporated into the travel demand modeling (Castiglione, Bradley, & Gliebe, 2015).

When modeling the activity demand, it is assumed that the individuals can choose from a set of discrete activities and they allocate as much time as they want on each alternative, constrained to the available total time for all activities.

Most of the MDC development has focused around models based on Gumbel distributed errors, i.e., extreme value type I distribution, which yields the name MDCEV and can be seen as a generalization of the MNL for MDC modeling. Although the MDCEV performs well, it ignores some important behavioral aspects of the decision makers regarding the amount of consumption, given the willingness to pay or perceived value of each alternative. The exponomial choice approach for MDC (MDCEC) considers these behavioral attributes by using negative exponential distributed error terms. We present an empirical application of the proposed MDCEC model for time allocation of individuals in the context of activity-based travel demand. The proposed MDCEC model is also compared to the standard MDCEV approach, resulting in more adequate behavioral properties and better data fit to the empirical data.

The objectives of this study include to 1) present in detail the fundamentals and development of the MDCEC model, 2) implement MDCEC for convenient use under different scenarios, 3) evaluate the appropriateness of the model to retrieve the true value of the parameters using synthetic datasets, and 4) compare the performance of MDCEC and MDCEV under identical homoscedastic conditions with an empirical application to predict the time allocation in different activities.

The rest of the thesis is organized as follows: Chapter 2 presents a summary of the previous studies both in travel demand and in discrete-continuous modeling. Chapter 3 describes the methodological and theoretical development of the proposed MDCEC. Synthetic datasets are used in Chapter 4 to demonstrate the appropriateness of the MDCEC to retrieve the true parameter values under different conditions. In Chapter 5, we compare the proposed model to the standard state-ofthe-art MDCEV using empirical data for time-use in a context of activity-based travel demand. The concluding remarks presented in Chapter 6 summarize the results and delineate the future work needed.

EXPONOMIAL MODEL FOR MULTIPLE DISCRETE-CONTINUOUS CHOICES: ANALYSIS OF ACTIVITY TIME-USE PATTERNS IN DUAL EARNER HOUSEHOLDS

Sharing is caring!