An Empirical Investigation of Household Vehicle Type Choice Decisions

Abolfazl (Kouros) Mohammadian Assistant Professor Department of Civil and Materials Engineering University of Illinois at Chicago 842 W. Taylor Street Chicago, IL 60607-7023 Tel: (312) 996-9840 Fax: (312) 996-2426 Email: [email protected]

Eric J. Miller Professor Department of Civil Engineering University of Toronto 35 St. George Street Toronto, ON, Canada M5S 1A4 Phone: 416-978-4076 Fax: 416-978-5054 Email: [email protected]

Paper submitted for publication in the Journal of Transportation Research Record 2003

Word Count: 5095 + (9*250) = 7345

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ABSTRACT Automobile ownership models are an integral part of comprehensive transportation modeling systems. Recent works and on- going advances in the area of activity-based travel demand modeling have recognized the need for increased experimentation with automobile choice models. On the other hand, while automobiles are very important in our everyday lives, they also have a serious impact on the environment. This impact occurs at the micro- level (pollution) as well as the macro- level (emission of greenhouse gases and global warming). Such impacts have led to increased interest to reduce motor vehicle emissions. The primary objective of this study was to develop a household automobile type choice model at a disaggregate level that can provide a direct forecast of consumer demand for personal- use vehicles given the available choices. In this paper, a well-developed form of discrete choice modeling techniques, nested logit model, was used to investigate the process of household automobile type choice decisions given that a transaction has occurred. Key Words: Nested Logit Model, Automobile Ownership, Vehicle Choice, Vehicle Class and Vintage

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1. INTRODUCTION Governments around the world seek strategies to reduce greenhouse gas emissions. International agreements such as Kyoto Protocol intensify the need for more research in this area for a comprehensive solution that can help governments to meet their commitment to reduce greenhouse gas emissions and at the same time sustain economic and job growth, and increase competitiveness in the global market. The promotion of technologies including fuel cells and the use of new fuels such as ethanol, as well as understanding and shifting of consumer behavior seem to be among possible solutions. On the other hand, automobiles play a pivotal role in our daily life which makes them a subject of interest in many academic fields. Transportation planners are interested to know how many and what type of automobiles are owned by households, how people adjust their fleet and utilize their vehicles. Therefore, understanding the behavioral responses of consumers to the actions of business and government should be of interest to a wide spectrum of society. Within this context, models can be useful for understanding individuals’ responses as well as studying relationships and for prediction and forecasting. Model development deals with the discovery of hidden knowledge, unexpected patterns and new rules from observations of real life behavior. Models may be very simple (e.g. simple linear regression) or extremely complex. Over the past few years, increasing attention is being paid to the use of microsimulation modeling approaches to activity-based travel forecasting. Some of the earliest applications of microsimulation in the transportation field involved dynamic modeling of auto ownership and a strong case exists for including explicit models of household automobile choice within the overall travel demand modeling process (1). The Integrated Land-Use, Transportation, and Environment model (ILUTE) is currently being developed at the University of Toronto to address the need for a comprehensive modeling system in a dynamic microsimulation framework for policy analysis in the Greater Toronto Area (2). The primary objective of this study was to develop a comprehensive model of household automobile class and vintage choice at a disaggregate level to be used in ILUTE framework that can provide a direct forecast of consumer demand for personal- use vehicles given the available choices. There has been a large effort to study automobile ownership and many different types of models have been developed in the literature to address various combinations of this issue. The majority of these models are developed in a discrete choice framework. As in most other research works studying discrete choice behavior, automobile ownership studies have typically been modeled using multinomial logit model. These models identify two major components of automobile ownership, the number of vehicles owned and vehicle type. Several studies have been conducted in this area. One of the first disaggregate studies used a multinomial logit model structure was Lave and Train’s work (3) on vehicle type choice. Their model includes several explanatory variables including household attributes, vehicle characteristics, as well as gasoline price. In another study Manski and Sherman (4) developed multinomial logit models for the number of vehicles owned and vehicle type choice. Separate models for automobile type choice were developed for households with one or two vehicles in their fleet. In terms of choice set, they used a sampling procedure suggested by McFadden (5) to randomly generate choice sets consisting of 25 alternatives including the observed choice from a total of 600

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vehicle make, model, and vintage combinations. In addition to potentially being an IIA violation, Manski and Sherman's assumption that households simultaneously evaluate a large number of alternatives at once is unlikely to be an accurate representation of the actual decision- making procedure. It seems more likely that the choice set is first reduced to some manageable set of feasible alternatives through the use of simple rules or a more thorough weighting of "class" attributes, and then the best alternative is chosen from the reduced choice set. Mannering and Mahmassani (6) also used the same random sampling procedure to gene rate choice sets of 10 alternatives from 93 in the full set. They also tested for choice sets of 20 and 30 to show that they found no changes in parameter estimates. The objective of their study was to explicitly test the hypothesis that vehicle attributes are valued differently between foreign and domestic vehicles. The study is restricted to new car purchases. In another study Mannering and Winston (7) attempted to model number of vehicles, vehicle type, and vehicle usage in an interrelated framework. The number of vehicles and vehicle type are modeled using the nested logit model. The second level vehicle choice model includes continuous vehicle usage variables from earlier time periods. They estimated separate models for single and 2 vehicle households. Hensher and Plastrier (8) used a nested logit structure to model a household’s automobile holdings and composition choice. Their holdings model includes an inclusive value for expected maximum utility of vehicle type choice. Brownstone et al (9) used stated preference data. In their study six hypothetical alternatives are presented to respondents with a number of randomly distributed attributes within certain ranges, however these alternatives are in car/van or car/truck pairs with otherwise similar attributes. The model is multinomial logit, which means that the assumption is made that there is no correlation between alternatives. An IIA test was performed to make sure that the MNL model is valid. Separate models are estimated for 1 vehicle and 2 vehicle households. There are no model estimated for zero, three, or more vehicle households. This paper is structured in six sections. Section 2 briefly explains modeling approach employed in this study. Section 3 describes the data set used and the process of generating composite factors. Sections 4 presents the process of development of nested logit model including the definition of the choice set, decision tree structure, utility function specifications and estimation results. Section 5 describes the analysis of the results obtained from maximum likelihood estimation of nested logit model. Finally, Section 6 will present the conclusion and discussion. 2. MODELING APPROACH Modeling consumers’ behavior is a key aspect of demand analysis. Researchers have employed discrete choice methodology to analyze and predict consumers’ choice decision. Most models used for travel behavior applications are based on utility theory, which assumes that the decision maker’s preference for an alternative is captured by a value, called utility, and the decision maker selects the alternative in the choice set with the highest utility. Random utility models assume that the decision maker has a perfect discrimination capability. However, the analyst is assumed to have incomplete information and, therefore, uncertainty must be taken into account (10). Among random utility models, Multinomial Logit (MNL) models have been the most widely used

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structure for modeling discrete choice problems. For a complete discussion and derivation of MNL model see Ben-Akiva and Lerman (11). An important property of the multinomial logit model is “Independence from Irrelevant Alternatives (IIA)”. This implies that the ratio of the probabilities of any two alternatives is independent of the choice set and the systematic utilities of any other alternatives. The IIA property of the multinomial logit models is a limitation for some practical applications. This property makes the model fail in the presence of correlated alternatives. In this case and when the choice set is complex or multidimensional, modeling approach can be in a nested structure. Nested Logit (NL) model permits covariance in random components among subsets (or nests) of alternatives. The Nested Logit (NL) model, first proposed by Ben-Akiva (12), is based on the partitioning the choice set into several nests. As presented in Figure 1, a nested logit model with two levels has been developed in this study. The Automobile Ownership module of the ILUTE project is a dynamic marketbased decision making model that is suitable for modeling household automobile transaction and holding choices within a microsimulation framework. It assumes that decision makers evaluate their vehicle fleet yearly. This was felt to be a reasonable time aggregation for the purpose of this study with acceptable potential error. The modeling framework is a two-stage modeling system, the first stage is a "Dynamic Automobile Transaction model" which simulates the vehicle acquisition process, including decisions to purchase, dispose, or replace a vehicle (13). The second stage is an "Automobile Choice model" which simulates the decision to buy a specific vehicle type and vintage. The model uses input data on household structure and life cycle, fleet attributes and prices, and socioeconomic characteristics to generate the number and type of vehicles available to a household. Expected price of the fleet in different stages of the simulation process can be estimated using a hedonic price model developed for this project (14). This paper focuses on the development of automobile class and vintage choice model given that a transaction has occurred. Understanding and predicting individuals’ behavior to become active in market and modeling the dynamics of vehicle transaction behavior is the focus of another study which can be found elsewhere (13). 3. THE DATA The data set used in this study was obtained through the Toronto Area Car Ownership Study (TACOS) which was a retrospective survey conducted at the University of Toronto, Canada (15 and 16). The results of this survey contain information on household vehicle transactions for up to 9 years from 1990 to 1998 in the Greater Toronto Area (GTA), including information on automobile transactions of more than 900 households. Vehicle characteristics for each vehicle in the sample were obtained from the Canadian Vehicle Specifications System, which contains information for 1971 to 1999 model year vehicles (17). The Fuel Economy Guide Database (18) provided fuel consumption information, and vehicle market values at time of purchase were gathered from the Canadian Red Book (19 and 20). Thus, the prices which enter the models are not the individual sales prices of the specific vehicles in the sample (which would be subject to reporting errors and potential self-selection biases), but rather average market values for each given make/model/vintage of vehicle in the sample.

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The next step was to determine the possible characteristics and attributes of vehicles which consumers value, and to identify variables which represent those attributes in explaining variations in vehicle utility. A wide variety of variables are used in the literature to explain the difference in utility between different models. These include: turning circle, breaking distance, axle ratio, rpm, horsepower, luggage space, headroom, legroom, length, width, fuel efficiency, engine size, weight, etc. In order to keep the model as simple as possible, only those characteristics were chosen that are judged to be the most important ones in representing variation in the utility, and which are also relatively easy to generate within the simulation process. In addition to class and vintage as vehicle characteristics, other variables such as weight, engine displacement, fuel intensity, luggage capacity, luxury, and origin of vehicles were chosen. Table 1 shows the list of vehicle characteristics that are employed. The vehicle characteristics shown in Table 1 present a special difficulty when estimating a model. Due to technological reasons, many of these variables are highly correlated. For example, a correlation of 0.84 was found between fuel intensity and engine displacement and a correlation of 0.82 between car weight and engine displacement. This high multi-colinearity between variables might create problems of identification of the influence of car characteristics on vehicle utility. Factor analysis and, more particularly principal components analysis, provides a means to solve this problem. In very broad terms, factor analysis is a method for reformulating a set of natural or observed independent variables into a new set (usually fewer in number, but necessarily not more in number) of independent variables, such that the latter set has certain desired properties specified by the analyst. Principal component analysis is the search through data to try to find the factors or components that may reduce the dimensions of variations and may be given a possible meaning (21). In order to identify the various correlations between vehicle characteristics, principal component analysis was used. Five variables were chosen to be included in the principal component analysis. These are weight, engine displacement, fuel intensity, size, and space. The latter is a composite variable, which represents the available space for non-cargo vehicles. The results of the principal component analysis using the Varimax rotation method (with Kaiser normalization) are presented in Table 2. Two factors were identified, explaining 89% of the total variance in the sample. The two factors can be identified as follows: 1. Vehicle performance factor: this factor consists of three variables that define fuel consumption, which are vehicle weight, engine displacement, and fuel intensity. This is mainly because of technological dependencies between these variables. 2. Space factor: this factor consists of two variables of size (sedan vs. wagon, van, and SUV) and space (which represents luggage capacity and wheelbase). The results of the principal component analysis, which are two composite factors, were used as two new variables (vehicle performance factor and space factor) in the utility functions of the model.

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4. AUTOMOBILE TYPE CHOICE MODEL This section describes the process of development of an automobile class/vintage choice model for ILUTE project. A nested logit model was employed for this problem and this section presents the empirical results of the static vehicle choice model. 4.1.

Choice Set Specification

The choice set from which individuals make their choices is defined by the ava ilable alternatives in the dataset. The dataset used for this model is derived from the TACOS database as described in Section 3. It contains useable records of information on all vehicles bought from 1990 to 1998 by households in the sample. These are vehicles at the time of purchase. Therefore, other vehicles in the households’ vehicle fleet were not entered into this dataset. Initially, there are 14 different vehicle classes in the database. These are: two seater, mini compact, sub compact, compact, mid-size, large, small station wagon, mid-size station wagon, large station wagon, small pickup, standard pickup, van, and special purpose vehicles (SUV and mini vans), and motorcycles. It is evident from the descriptive analysis that some classes are by far the least common types of vehicles owned. Therefore, after eliminating motorcycles, the remaining 13 classes were aggregated into the 7 most common classes which are: sub-compact, compact, mid-size, large, station wagon, special purpose vehicles (SUV and pickup), and van (van and minivan). Later during model development, it became clear that there are not enough number of significant observations (without missing values) with the class choice of station wagon in the dataset. As a result, the station wagon class was eliminated from the choice set. Although, station wagon seems to be an important type of vehicle class, it felt necessary to proceed without this class in order to develop a statistically significant model. Table 3 summarizes the assumed equivalent classes of vehicles. The ages of vehicles were calculated for the time of purchase varying from brand new to more than 25 years old. Vehicle price index books consider any vehicle with the age of 8 years or more, as an old vehicle and any vehicle between 1 to 7 years old is considered as a used car (19 and 20). Considering these assumptions as well as the distribution of age at the time of purchase in the dataset, and heuristic assumptions such as the date of contract expiration for leased vehicles, vintages of vehicles were categorized in four categories as shown in Table 4. The dataset extracted to develop this model contains 597 observations of vehicle type choices. Based on available choices defined in Tables 3 and 4, a decision maker faces 24 different combinations of choices available to choose from. It is assumed that all choices are available for all individuals. 4.2. Decision Tree Structure Different decision structures were tested. These include: nested logit model, joint model, and sequential model. A nested decision structure was chosen based on the result of these evaluations. Two different decision sequences within a nested structure were tested to better understand which decision is made first. It was originally hypothesized that individuals

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first decide on the vintage of their vehicles and later on classes available in that group. The reason behind this assumption was the fact that when an individual has a fixed budget to invest on an automobile, while comparing the price of different vehicles to choose from, vintage plays more important role than class of the vehicle. However, this assumption was rejected since this model generated negative coefficients for inclusive value and as per NL model properties, coefficients of inclusive value should only take values between 0 and 1. When the value is 0, the model is in fact a sequential model and when it takes the value of 1, the model is in fact a joint model. Subsequently, a nested logit model structure was introduced using the six different vehicle class choices described in Table 3 as the upper level in the choice hierarchy. This identifies the marginal probability that a given household chooses to hold a Sub-Compact, Compact, Mid-Size, Large, Special Purpose Vehicle, or Van. The class choice set is assumed to be available to all households. The vintage choice model then defines the probability of a household choosing a particular vintage conditional on chosen class. Each lower level subset or nest contains four vintage choices as introduced in Table 4. In order to define and estimate the best NLM, it is suggested to estimate a MNL model first for each level (22). Then the MNL and NLM estimation results should be compared and the best model adopted. In adopting this approach, one must keep in mind the logit model’s IIA property, which can be violated for multiple-choice decisions where some alternatives are expected to be correlated. Moreover, it is often true that the satisfactory utility specification in the context of one structure specification may be unsatisfactory in another specification and vice versa. It is also possible that there is more than one acceptable combination of utility and structure specification. Keeping all these issues in mind, both MNL and NLM frameworks were explored in order to obtain the best utility and structure specification. Final Class-Vintage choice estimation results were arrived at after empirical assessment of alternative choice model strategies and extensive screening of MNL models of class choice and vintage choice. 4.3. Utility Function Specification More than 190 variables were imported into the Limdep Econometric Software (23) environment which was used for parameter estimation. In order to specify the utility function, decisions have been made concerning which variables to include and in what form in the model. Variables entered the utility functions include: alternative specific constants, vehicle attributes, decision maker attributes and socioeconomic characteristics, and combinations of these variables. These variables entered the utility functions as generic, alternative specific, and logarithmic functional forms. Ultimately, twenty- nine variables (X s) were used to specify the utility of each alternative in the choice set. These variables are described in Table 5. In addition, an alternative specific constant is included for some alternatives in each level of choice structure. They represent the systematic impact of omitted variables in the utility function. Some variables are introduced to the utility function in logarithmic form. Using a logarithmic form of variables versus linear form implies differences in individual’s perception of an increase or percentage increase in the value of a variable. Size variables should generally enter logarithmically.

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4.4. Estimation Results The results of full information maximum likelihood estimation of the model are summarized in Table 6. It required 75 iterations to reach a solution. 5. ANALYSIS OF THE RESULTS Almost all attributes have t- statistics greater than 1.64 (95 percent confidence level) except for two class-specific constants. The chi-squared statistic, which tests for the significance of the model over the equally- likely model (with no variables), is 996.843, significant at a 0.005 level of confidence, so the hypothesis that the coefficients for all variables are zero can be safely rejected. The likelihood ratio test (ρ2 statistic) is the most commonly used statistic to measure the information explained by the model. Overall the model has a ρ2 of 0.263 when comparing the log likelihood at zero and log likelihood at convergence. It is considered to be indicative of a good model fit. Although several other models were also developed with much higher ρ2 values, the model presented here was selected to be used in ILUTE microsimulation model. These other models are considered as descriptive models due to the fact that not all parameters introduced into these models are feasible to be generated within the microsimulation process with the current available data. For instance, it was difficult to predict whether a household decides to purchase a car or lease one. This is mainly due to the fact that the buy/lease decision is more affected by economy situation and cash flow of the household rather than socioeconomic characteristics of the households which were available in the database. The constants alone contribute 0.057 of the 0.263, suggesting the attributes in the utility expressions do have an important role to play in explaining class and vintage choices. The signs of all utility parameters are correct and unambiguous. Analyst would expect that a negative sign would be associated with cost or other attributes that may cause negative utility. It is obvious that an individual’s relative utility would increase when cost decreases. This should justify negative signs for "Natural logarithm of market price", and “Class-Vintage average ownership cost” which indicate negative utility for expensive cars and vehicles with higher ownership and operating costs. The model indicates that where the average market price of the fleet is higher the chance of buying a brand new or 1-2 years old car is higher. But if the average age of the fleet is higher, the household is less likely to buy a brand new vehicle. People with higher degree of education are more likely to buy brand new vehicles and less likely to buy old vehicles. It has been also shown that if the transaction choice is trade (rather than buy), the purchased vehicle is most likely to be a brand new one. The average length of ownership in fleet parameters for used and old vintages are almost identical, suggesting that one degree of freedom could be saved by imposing an equality restriction on these two utility parameters, treating them as generic to these two vintages. It indicates that if the average length of ownership in fleet increases, the newly purchased vehicle is less likely to be an old or used vehicle. The performance factor is a generic parameter with a positive sign for all alternatives. However the space factor was found to be important only for Special Purpose Vehicles (SPV) and Vans with positive sign, showing the increase in utility

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where the factor increases. Managers are more likely to buy mid-size, large, or SPV, while professionals are more likely to buy sub-compact vehicles. Heavier average weight in the fleet will result in a lower probability of buying a sub-compact or a compact car. Drivers with higher level of education and households with higher average age of people in the household are less likely to buy a SPV. The probability of buying a van increases when the proportion of number of children with respect to the number of people in the household increases. Male drivers are more likely to buy bigger cars (large, SPV, and van). And finally, availability of a particular vehicle class in the vehicle fleet has a positive impact on the choice of that particular class. This might imply that people’s behavior is state dependent and their previous choices can affect their current behavior. All inclusive value parameters are statistically significant at 99% confidence level. Inclusive value parameters should only take values between 0 and 1. The IV parameter for special purpose vehicle was slightly more than 1. Therefore, it was fixed to take the value of 1. This implies that the special purpose vehicle nest in model in fact works as a joint model rather than a hierarchical model. All other IV parameters are in the acceptable range. Overall, the percentage predicted correct for this model is 49.2%. Tables 7 and 8 compare observed and predicted choices for both individuals and market shares. 6. CONCLUSIONS In this paper, the use of a well-developed form of discrete choice modeling techniques, nested logit, was used to study household vehicle choice behavior. The model presented in this paper is developed at a disaggregate level and is a part of an integrated land-use, transportation, and environment modeling system. It intends to provide a direct forecast of consumer demand for personal-use vehicles given the available choices. The model has well reproduced the aggregate market shares, even though the overall percentage predicted correct for this model was 49.2% implying the predicted choice for an individual is unlikely to exactly match the actual choice. Although it might slightly be a point of concern for predicting the choice of a specific individual, the model is statistically valid and also has external validity at the aggregate market share level. It is important to keep in mind that thousands of different class-vintage combinations were aggregated into 24 alternatives categories and modeling a choice problem with such diversity in the choice set is a difficult task to accomplish, given the limited number of observations. The results obtained here seem to be the best achievable outputs for a complex behavioral problem with thousands of available alternatives and an unknown decision hierarchy. At the very least, these are good improvements on the 4% (1/24) rate one could expect from a random prediction which, after all, is the reason we continue to build such models. Acknowledgements The research reported in this paper is supported by the Natural Science and Engineering Research Council of Canada (NSERC) as well as by a major collaborative research initiative grant from Social Science and Humanities Research Council of Canada (SSHRC). REFERNCES

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Miller, E.J., “Microsimulation and Activity- Based Forecasting”, in Texas Transportation Institute (eds.) Activity- Based Travel Forecasting Conference, June 2-5, 1996 Summary, Recommendations, and Compendium of Papers, Washington, D.C.: Travel Model Improvement Program, U.S. Department of Transportation and U.S. Environmental Protection Agency, 1996, pp. 151-172. Miller, E.J., Hunt, J.D., Abraham, J.E., and Salvini, P.A., “Microsimulation Modeling Research in Canada”, presented at the 7th ASCE Applications of Advanced Technology in Transportation Conference, Boston, August 5-7, 2002. Lave, C.A., and K. Train, “A Disaggregate Model of Auto-Type Choice”, in Transportation Research A., Vol. 13A, 1979, pp. 1-9. Manski, C.F., and L. Sherman, “An Empirical Analysis of Household Choice Among Motor Vehicles”, in Transportation Research A, Vol. 14A (5,6), 1980, pp. 349-366. McFadden, D., “Modelling the Choice of Residential Location”, in Special Interaction Theory and Planning Models, A., Karlqvist, L. Lundqvist, F. Snikers, and J.W. Weibull, eds., Amsterdam, North Holland, 1978, pp. 75-96. Mannering, F., and H. Mahmassani, “Consumer Valuation of Foreign and Domestic Vehicle Attributes: Econometric Analysis and Implications for Auto Demand”, in Transportation Research A, Vol. 19(3), 1985, pp. 243-251. Mannering, F. and C. Wilson, “A Dynamic Empirical Analysis of Household Vehicle Ownership and Utilization”, in Rand Journal of Economics, 16(2), 1985, pp. 215-236. Hensher, David A., and Vicki Le Plastrier, “Towards a Dynamic Discrete-Choice Model of Household Automobile Fleet Size and Composition”, in Transportation Research B, Vol. 19(6), 1985, pp. 481-495. Brownstone, D., D.S. Bunch, T.F. Golob, and W. Ren, “A Transactions Choice Model for Forecasting Demand for Alternative-Fuel Vehicles”, Working Paper UCIITS-WP-96-4, University of California at Irvine, Institute of Transportation Studies, 1996. Ben-Akiva, Moshe and Michel Bierlaire, “Discrete Choice Methods and Their Applications to Short Term Travel Decisions”, in Handbook of Transportation Science, edited by Randolph W. Hall, Kluwer Academic Publishers, USA, 1999. Ben-Akiva, Moshe and S. Lerman, “Discrete Choice Analysis: Theory and Application to Travel Demand”, Cambridge, The MIT Press, USA, 1985. Ben-Akiva, Moshe, “Structure of Passenger Travel Demand Models”, Transportation Research Record, 1974. No. 526. Mohammadian, A., and E. J. Miller, “Dynamic Modeling of Household Automobile Transactions”, forthcoming in the Journal of the Transportation Research Record 2003. Mohammadian, A., and E. J. Miller, "Estimating the expected price of vehicles in a transportation microsimulation modeling system", Journal of Transportation Engineering, ASCE, Vol. 128, No. 6, Nov. 2002, pp. 537-541. Roorda, M.J., A. Mohammadian, and E.J. Miller, “Toronto Area Car Ownership Study: A Retrospective Interview and Its Applications”, Journal of the Transportation Research Record, 2000, No. 1719, pp. 69-76.

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16. Roorda, M.J., “Toronto Area Car Ownership Study: A longitudinal Survey and A Preliminary Analysis of Results”, M.A.Sc thesis, University of Toronto, 1998. 17. Canadian Association of Technical Accident Investigators and Reconstructionists (CATAIR), Canadian Vehicle Specifications System: Version 1999.2, “http://www.catair.net/”, Accessed August 1, 2002. 18. U.S. Environmental Protection Agency, Office of Mobile Sources, National Vehicle and Fuel Emissions Laboratory (various years) Fuel Economy Guide Database files, Ann Arbor, MI, USA, “http://www.fueleconomy.gov/feg/download.shtml”, Accessed August 1, 2002. 19. Canadian Red Book, Inc., “Canadian Red Book, Official Used Car Valuations”, Toronto, Canada, 1990-1998. 20. Canadian Red Book, Inc., “Canadian Older Car / Truck Red Book”, Toronto, Canada, 1990-1998. 21. Stopher, P.R., and A.H. Meyburg, “Survey Sampling and Multivariate Analysis for Social Scientists and Engineers”, Lexington Books, USA, 1979. 22. Koppelman F.S., and C.V. Forinash, “Application and Interpretation of Nested Logit Models of Intercity Mode Choice”, Transportation research Record, 1993, No. 1413, pp. 98-106. 23. Greene H. William, “LIMDEP Version 7.0 User’s Manual”, Econometric Software Inc., Bellport, NY, USA, 1995. 24. Domencich, Thomas and Daniel McFadden, “Urban Travel Demand: A Behavioural Analysis”, A Charles River Associates research study, Amsterdam, North-Holland, 1975.

Mohammadian and Miller LIST of TABLES and FIGURES TABLE 1 Characteristics of Vehicles Used in the Model TABLE 2 Principal Component Analyses of Characteristics of Vehicles TABLE 3 Equivalent Classes of Vehicles Used in the Model TABLE 4 Equivalent Vintages of Vehicles Used in the Model TABLE 5 Variables Introduced to the Utility Functions TABLE 6 Parameter Estimates for Class/Vintage Choice Model TABLE 7 Comparison of Observed and Predicted Choices of Individuals TABLE 8 Comparison of Observed and Predicted Market Shares FIGURE 1 Nested logit model tree.

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TABLE 1 Characteristics of Vehicles Used in the Model Characteristics Unit Engine displacement Liter Weight Metric ton Fuel intensity Liter/100 Km Luggage capacity M3 Wheelbase Meter Origin Domestic, Japanese, or European New If the vehicle is a new vehicle at the time of purchase Luxury If the vehicle is a luxury vehicles Size If the vehicle is a wagon, van, or sport utility vehicle Cargo If the vehicle is a cargo-van or a pickup Space (1-Cargo) × Luggage capacity ÷ Wheelbase

13

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TABLE 2 Principal Component Analysis of Characteristics of Vehicles Variable

Weight Engine displacement Fuel intensity Size Space % Variance explained

Factor Loading Factor 1 Factor 2 (Veh. Performance) (Space Factor) 0.339 0.000 0.413 -0.166 0.357 -0.035 -0.049 0.515 -0.157 0.596 53

36

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TABLE 3 Equivalent Classes of Vehicles Used in the Model Alternative Code 1

Equivalent Class Used in the Model Sub-Compact

2 3

Compact Mid-Size

4 5

Large Special Purpose Vehicle (SPV) Van

6

Classes of vehicles in the original dataset Two Seater, Mini-Compact, SubCompact Compact, Small Station Wagon Mid-Size, Mid-Size Station Wagon Large, Large Station Wagon Sport Utility Vehicle, Small and Standard Pickups Van, Mini- Van

Percentage of observations 19.3% 21.9% 20.4% 10.7% 17.3% 10.4%

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TABLE 4 Equivalent Vintages of Vehicles Used in the Model Alternative Code I II III IV

Equivalent Vintage Used in the Model Brand New Second-Hand Used Old

Age of vehicles (year) in the original dataset -1 and 0 1 and 2 3,4,5,6, and 7 8+

Percentage of observations 47.2% 17.6% 21.4% 13.7%

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TABLE 5 Variables Introduced to the Utility Functions Explanatory Variable Natural logarithm of (market price divided by (income – ownership & operating cost of current household fleet)) Class-Vintage average ownership cost Average market price of household fleet Natural logarithm of average age of people in household Average age of household fleet Average length of ownership in household fleet Natural logarithm of driver's age No. of age code III (used) vehicles in household fleet No. of age code IV (old) vehicles in household fleet No. of people with elementary level of education in household No. of people with B.Sc. degree in household No. of people with graduate degree in household Trade transaction dummy No. of employment type 3 (health and medicine) in household Owner's highest completed level of education Market price divided by natural logarithm of income Vehicle performance factor Vehicle space factor Driver has skill level 1 (manager) Driver has skill level 2 (professional) No. of class1 (sub-compact) vehicles in household fleet No. of class3 (mid size) vehicles in household fleet No. of class4 (large) vehicles in household fleet No. of class5 (special purpose) vehicles in household fleet Driver is male Average weight in fleet (metric ton) Driver's highest completed level of education Natural logarithm of average age of people in household No. of children divided by no. of people in household

Model used in Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Vintage Class Class Class Class Class Class Class Class Class Class Class Class Class Class

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TABLE 6 Parameter Estimates for Class/Vintage Choice Model Explanatory Variable Alternatives Coefficient Characteristics of Household Natural logarithm of average age of people in household Natural logarithm of driver's age No. of people with elementary level of education in household No. of people with B.Sc. degree in household No. of people with graduate degree in household No. of employment type 3 (health and medicine) in household Owner's highest completed level of education Driver has skill level 1 (manager) Driver has skill level 2 (professional) Driver is male Driver's highest completed level of education Natural logarithm of average age of people in household No. of children divided by no. of people in household

t-stat

II I II

0.510 1.409 0.369

2.027 4.324 2.305

I IV II

0.411 -0.841 0.882

3.339 -1.765 3.271

III 3,4,5 1 4,5,6 5 5 6

-0.246 0.670 0.546 0.820 -0.263 -1.226 1.780

-2.411 2.499 2.459 4.071 -2.375 -4.020 2.625

I, II I IV III, IV IV III 1 3,4 4 5 1,2

0.101 -0.102 0.067 -0.148 -1.058 0.383 0.490 0.690 1.417 0.699 -0.519

4.183 -3.483 1.625 -3.475 -2.605 2.047 2.667 3.683 4.709 2.957 -2.986

I, II, III, IV

-0.975

-1.931

I, II, III 1,2,3,4,6 1,2,3,4,5,6 5 6 I

-1.251 -0.112 0.603 2.221 7.583 0.473

-12.127 -1.864 4.530 4.784 7.813 2.041

Constant Terms Brand New vehicle (vintage I) constant Second hand vehicle (vintage II) constant Used vehicle (vintage III) constant Sub-compact (class 1) constant Compact (class 2) constant Mid-size (class 3) constant Large (class 4) constant Special-purpose (class 5) constant

I II III 1 2 3 4 5

7.347 10.424 11.601 1.785 2.113 0.682 -0.236 3.825

4.184 6.492 10.296 2.414 2.983 1.002 -0.339 2.875

Inclusive Value Parameters for Sub-compact Compact

1 2

0.657 0.621

7.359 7.902

Characteristics of Household Vehicle Fleet Average market price of household fleet Average age of household fleet Average age of household fleet Average length of ownership in household fleet No. of age code III (used) vehicles in household fleet No. of age code IV (old) vehicles in household fleet No. of class1 (sub-compact) vehicles in household fleet No. of class3 (mid size) vehicles in household fleet No. of class4 (large) vehicles in household fleet No. of class5 (special purpose) vehicles in household fleet Average weight in fleet (metric ton) Characteristics of Vehicle Natural logarithm of (market price divided by (income – ownership & operating cost of current household fleet)) Class-Vintage average ownership cost Market price divided by natural logarithm of income Vehicle performance factor Vehicle space factor Vehicle space factor Trade transaction dummy

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Mid-size Large Special-purpose vehicle Van

3 4 5 6

Log likelihood at zero Log likelihood at constants Log likelihood at convergence Chi-squared Log likelihood ratio (ρ 2 )

-1897.298 -1789.717 -1398.877 996.843 0.263

0.832 0.587 1.000 0.813

9.149 6.093 Fixed 8.765

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TABLE 7 Comparison of Observed and Predicted Choices of Individuals Class/Vintage Sub-Compact – Brand New Sub-Compact – Second Hand Sub-Compact – Used Sub-Compact – Old Compact – Brand New Compact – Second Hand Compact – Used Compact – Old Mid-Size – Brand New Mid-Size – Second Hand Mid-Size – Used Mid-Size – Old Large – Brand New Large – Second Hand Large – Used Large – Old Special Purpose – Brand New Special Purpose – Second Hand Special Purpose – Used Special Purpose – Old Van – Brand New Van – Second Hand Van – Used Van – Old Total

Observed 50 16 29 20 62 20 27 22 45 29 30 18 31 11 13 9 58 20 18 7 36 9 11 6

Predicted 27 4 9 7 29 7 12 9 38 8 16 12 17 4 4 4 27 7 10 3 29 3 4 4

% Right 54% 25% 31% 35% 47% 35% 44% 41% 84% 28% 53% 67% 55% 36% 31% 44% 47% 35% 56% 43% 81% 33% 36% 67%

597

294

49.2%

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TABLE 8 Comparison of Observed and Predicted Market Shares Class/Vintage Observed Predicted |Difference| Sub-Compact – Brand New 50 65 15 Sub-Compact – Second Hand 16 9 7 Sub-Compact – Used 29 27 2 Sub-Compact – Old 20 16 4 Compact – Brand New 62 65 3 Compact – Second Hand 20 18 2 Compact – Used 27 25 2 Compact – Old 22 18 4 Mid-Size – Brand New 45 83 38 Mid-Size – Second Hand 29 11 18 Mid-Size – Used 30 19 11 Mid-Size – Old 18 22 4 Large – Brand New 31 32 1 Large – Second Hand 11 5 6 Large – Used 13 8 5 Large – Old 9 10 1 Special Purpose – Brand New 58 43 15 Special Purpose – Second Hand 20 11 9 Special Purpose – Used 18 18 0 Special Purpose – Old 7 5 2 Van – Brand New 36 58 22 Van – Second Hand 9 15 6 Van – Used 11 5 6 Van – Old 6 9 3 Total

597

597

186

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Upper Level Choice Class1

Class2

Class3

… ClassN

Lower Level Choice

… Vintage 1 … VintageM

Vintage1

...

VintageM

FIGURE 1 Nested logit model tree.