This research investigates the transferability of person-level disaggregate trip generation models (TGMs) in time and space using two model specifications: multinomial linear regression and Tobit. The models are estimated for the Tel Aviv and Haifa metropolitan areas based on data from the 1984 and 1996/97 Israeli National Travel Habits Surveys. The paper emphasizes that Tobit models perform better than regression or discrete choice models in estimating nontravelers. Furthermore, the paper notes that variables and file structures in household surveys need to be consistent. Results of the study show that the estimated regression and Tobit disaggregate person-level TGMs are statistically different in space and in time. In spite of the transferred forecasts, the aggregate forecasts were also similar.
KEYWORDS: Trip generation, transferability, multinomial linear regression, Tobit model.
Trip generation models (TGMs) are used as a first step in classical four-step travel demand modeling and, therefore, any over- or underprediction of trip generation rates can cause errors throughout the entire transportation planning process. Inappropriate decisionmaking due to these types of errors can account for premature investments in infrastructure in the case of overprediction and loss of labor hours, pollution, and low levels of service in the case of underprediction.
TGMs are usually estimated based on periodic surveys of the travel habits of individuals or households. They are expensive and difficult to perform and are not conducted often. For our research, we used the last Israeli National Travel Habits Surveys collected in 1984 and 1996/97. Transportation planners use models previously estimated and sometimes in different contexts. The planners can perform forecasts for the same areas and, if justifiable, transfer the models to other areas. Hence, it is important to know whether these models can be transferred in time and in space.
Recently, researchers and planning agencies began to implement tour-based activity modeling systems rather than trip-based modeling systems.1 The advantage in using an activity modeling approach is the ability to model each individual's tours. However, in this paper, we were only able to investigate the stability of individual predictions of trips. This research presents the characteristics of trip generation in Israel and tries to answer the question of whether linear regression and Tobit TGMs can be transferred in time and space, given the dynamic changes in metropolitan areas and socioeconomic characteristics. The TGMs estimated and analyzed in this research include only vehicular trips.
We estimated the models for the geographically diverse metropolitan areas of Haifa and Tel Aviv in Israel and tested them for transferability in space and in time. The topography of Haifa is hilly, with the core of the city poorly connected to the rest of the metropolitan area. Tel Aviv lies on level topography, with a well connected road network. The metropolitan areas also differ structurally: Tel Aviv is interconnected like a spider web, including several minor cores with high-density population and employment concentrations. On the other hand, Haifa's less connected road network and rolling terrain give it a lower level of accessibility. When comparing the areas by land use, the Tel Aviv metropolitan area consists of neighborhoods that combine residential shopping and personal business areas. Haifa, on the other hand, contains highly separated areas with each area consisting of a uniform land use.
Given the difference in accessibility and land use, the calibrated models were restricted to demographic and socioeconomic variables. The average number of daily trips per person was higher in the Haifa metropolitan area (2.14 in 1984, and 2.03 in 1996/97) than in the Tel Aviv metropolitan area (1.83 in 1984, and 1.91 in 1996/97). The difference in the average trip rates may be explained based on the variation in land uses. The lack of mixed land uses in Haifa may encourage the generation of more trips. Furthermore, Haifa's hilly topography may encourage more vehicular trips than in Tel Aviv, where shorter trips are probably done on foot. The comparison between these metropolitan areas and the calibrated models is possible due to the similarity of the distribution of most demographic and socioeconomic variables. (See table 1 for a partial presentation of the comparison.) A more detailed comparison of Haifa and Tel Aviv characteristics is presented in Cotrus (2001).
Over the last few decades, several papers have discussed the transferability of trip generation models. The debate among researchers, in general, focused not only on the transferability of models in space and time but also on the model specification and level of aggregation. The aggregation levels are usually defined as area (zonal), household, and person. Estimating the models (see, e.g., Ortuzar and Willumsen 1994) at more disaggregate levels improves the transferability of TGM.
Atherton and Ben-Akiva (1976) emphasized that disaggregated models tend to maintain the variance and behavioral context of the response variable and, therefore, are expected to give better estimates when transferred. Downes and Gyenes (1976) pointed out that when the explanatory power of the model is of interest rather than the aggregate forecasts, the disaggregate level should be selected. Wilmot (1995) indicated that disaggregate models are preferred because of their independence from zonal definitions. In Supernak et al. (1983) and Supernak (1987), the person level was preferred for TGM because of the identity of the response factor (trip) and the generative (the person). One advantage of disaggregate person-level models is the reduced amount of data required for model estimation. (For more details, see Fleet and Robertson 1968; and Ortuzar and Willumsen 1994.) Other types of model specification techniques include cross-classification, regression, logit-based models, artificial neural networks, fuzzy logic, and simulations.
A number of studies found spatial transferability of models satisfactory (Wilmot 1995; Atherton and Ben-Akiva 1976; Supernak 1982, 1984; Duah and Hall 1997; Walker and Olanipekun 1989; Rose and Koppelman 1984; Caldwell and Demetsky 1980; and Kannel and Heathington 1973). On the other hand, Smith and Cleveland (1976) and Daor (1981) found spatial transferability unsatisfactory. We should emphasize that Smith and Cleveland pointed out that although the explanatory variables are distinctive, their effects vary in space. A number of researchers found the transferability of models in time (i.e., their temporal stability) satisfactory (Downes and Gyenes 1976; Yunker 1976; Walker and Peng 1991; Kannel and Heathington 1973; and Karasmaa and Pursula 1997). Unsatisfactory results, however, were obtained in other studies (Doubleday 1977; Smith and Cleveland 1976; and Copley and Lowe 1981).
While several international studies explored model transferability in time and space, in Israel the transferability of discrete mode choice models has been the main focus (Prashker 1982; Silman 1981). This study deals with the investigation of trip generation characteristics but also provides local estimates of TGMs and their validation for transferability in time and space. The study also explores the implementation of Tobit models in TGM.
We often approach trip generation from an economic viewpoint, where trips are defined as the product and the person/household as the customer. The strongest argument to model trips on a disaggregate level is that any zonal outcome is based on the aggregation of several customers, ignoring the heterogeneity among them. The explanatory variables for the power of consumption of each person/household can be found in several categories including demographic, geographic, and economic.
As discussed above, several approaches exist to model trip generation, including regression-based models such as multiple linear regression (Wilmot 1995) and cross-classification (Walker and Olanipekun 1989); discrete choice models such as probit, logit, and ordered probit (Zhao 2000); simulations such as Smash, Amos, and the Starchild System; fuzzy logic models; and artificial neural networks (Huisken 2000). Clearly, the issue of trip generation can be approached from several directions and tested for transferability in time and space. Therefore, researchers will choose the modeling approach based on the size of the database at hand, the nature and structure of the variables, the aggregation level desired, as well as other considerations. The main problem with using a regression model is the treatment of trip rates as continuous rather than discrete variables. Discrete choice models and spatially ordered response models may better account for the behavioral process of trip generation. However, due to practical reasons, in most models to date, the dependent variable is treated as a continuous variable. For this reason, we perform our analysis on such models.
In this research, we first estimated regression models for each metropolitan area for each year, taking into account the inconsistency of the household surveys (table 2). We then estimated Tobit TGMs based on the same variables and tested whether these models are suitable for trip generation estimation and for transferability. The regression model form is presented in equation 1.
y i = α + β 1x 1, i + β 2x 2, i + β k x k, i + ξ i
∀ i = 1, , n
∀ k = 1, 2, k (1)
yi = trip rate generated by individual i,
xk,i= explanatory variable k for individual i,
n = the number of observations,
k = number of explanatory variables, and
ξi = error term of the ith observation.
Hald (1949) first presented the model that, in its final form, is called the Tobit model (1958). Tobit models differentiate from regression models by the incorporation of truncated or censored dependent variables. Tobit analysis assumes that the dependent variable has a number of its values clustered at a limiting value, usually zero. The Tobit model can be presented as a discrete/continuous model that first makes a discrete choice of passing the threshold and second, if passed, a continuous choice regarding the value above the threshold. This approach is appropriate for trip generation, as an individual must decide whether to make any trips and, if so, how many trips to make.
Tobit analysis uses all observations when estimating the regression line, including those at the limit (no trips) and those above the limit (those who chose to travel). As shown by McDonald and Moffitt (1980), Tobit analysis can be used to determine the changes in the value of the dependent variable if it is above the limit, as well as changes in the probability of being above the limit. Since the surveys include observations at the limit (i.e., persons that are not traveling), it was also interesting to find out how well the Tobit model can predict persons doing no travel at all. The Tobit model form is presented in equation 2:
y i = X i β + ξ i if X i β + ξ i > 0
y i = 0 if X i β + ξ i ≤ 0
∀ i = 1, 2, 3, , (N - 1), N (2)
N = number of observations,
yi= trip rate generated by observation i,
Xi = vector of independent variables,
β = vector of coefficients, and
ξ = independently distributed error term ~ (0, σ2).
Because Tobit models have not been used previously in the context of trip generation, this research investigates their suitability for that purpose. We also compared the predictions obtained using regression models with those produced using the analogous Tobit model. The best specification of the regression model is not necessarily the best specification of the Tobit model. However, in order to allow for basic comparisons of the model parameters, we estimated the regression models first; then, after the determination of the final variables in the model, we estimated Tobit models with the same variables.
All models were estimated at the disaggregate person level. At the person level of modeling, we maintained the heterogeneity among observations and kept a good identity between the consumer of the product (the person) and the outcome (number of daily trips taken by the person). As discussed above, disaggregate models tend to show better transfer results than aggregate models and also incorporate the power to understand and control the production of trips. The models were estimated for a 24-hour period2 and tested for transferability in space and in time. Figure 1 presents the sequence of the analysis.
Statistical tests were conducted to determine the spatial and temporal stability of the estimated models by assessing the transferability of the coefficients from one area to another, and for each metropolitan area between the two survey years. Transferability was also tested by comparing the overall aggregate prediction obtained by the transferred model with the local model. Furthermore, we analyzed the ability of Tobit models to represent and evaluate nontravelers, that is, people who do not generate trips based on the given survey data.
The Israeli Central Bureau of Statistics (CBS) conducted some limited scope3 Traveling Habits Surveys in the 1960s. Comprehensive National Traveling Habits Surveys have been conducted by CBS every 12 years since 1972. Because the 1972 survey is not available on magnetic media, it was not possible to do a computer-based statistical analysis. Therefore, we based this research on the 1984 and 1996/97 household surveys.
The main problems we encountered in doing this research were related to the inconsistency in the investigated variables, the structure of the surveys, the definition of variables, the period of investigation, the geographic deployment, and the database structure (see table 2 again). The 1984 and 1996/97 household surveys differ in several ways: the geographic deployment (number and size of jurisdictions in the survey), the size of the survey (number of households), the definitions of the investigation period, and the variables that were excluded from the surveys. For example, income is included in the 1984 survey but is omitted from the 1996/97 survey.
Despite definition and database differences in the two surveys (1984 was an activity survey and 1996/97 was a trip survey), we were able to bring the variables in the models to a common basis. In particular, the 1984 survey included bicycle and walking trips among the means to accomplish the activities, while the later survey excluded them. To resolve this difference, we excluded walking and biking trips from the 1984 database; only motorized trips were considered for each person.
The 1984 survey files included data for 5,420 persons in the Tel Aviv metropolitan area and 4,056 persons in the Haifa metropolitan area. The final files used for model calibration after sieving incomplete and anomalous observations totaled 4,385 and 3,258 persons, respectively. The 1996/97 files included data for 20,436 persons in the Tel Aviv metropolitan area and 6,417 persons in the Haifa metropolitan area. The final files used for model calibration totaled 15,729 and 5,041 persons, respectively.
The selected trip generation models included six categorical variables: age, car availability, possession of a driver's license, employment, education, and status in the household. Data fell into five age categories: 8-13, 14-17, 18-29, 30-64, and 65 and over. Ortuzar and Willumsen (1994) found that life cycle variables were an important factor for explaining trip generation. Different trip rates can be expected for households and people at various stages of life. Furthermore, age should correlate with employment, having a driver's license, and marital status. Car availability included three categories: 0, 1, and ≥ 2 cars in the household. Clearly, households with more cars available will generate more trips. The driver's license category has only one variable: whether the person has a license (including motorcycle) or not.
The employment variable indicates whether the person was employed or not. Employed persons were expected to generate more trips, because they usually make at least two trips: to and from work.
Household status refers to whether the person defines himself or herself as the head of the household. This variable indicates the responsibility and availability of household resources as an incentive for consumption of trips.
Finally, four education categories were defined based on the number of years of study (0, 1-8, 9-12, and 13 or more). The literature shows good correlation between education and income. In the absence of a pure economic indicator, education is used also as a proxy for income. Respondents with higher education (hence higher income) were expected to generate more trips. All variables were found significant and the coefficients corresponded with our expectations.
Table 3 shows the estimation results for the regression models for 1984 for both metropolitan areas. As can be seen from the table, all coefficients were found to be significant at the 95% level. The number of observations remaining in the estimation process resulted from the limited scope of this survey and the elimination of incomplete observations in the original database.
Estimation results for these models show that all variables affected trip generation as expected. The education coefficients show that people with higher education generated more trips. This can be explained not only by the assumption of the relationship between education and income but also by assuming that a person with higher education is more likely to pursue culture and perhaps leisure activities. Also, as expected, persons with driver's licenses and employed persons tended to generate more trips than the equivalent nonworking and/or nondriving persons. Heads of household tended to generate more trips, as assumed, because of the responsibility and availability of resources. The coefficients of the age categories indicate that persons aged 14 to 17 travel more than people with similar characteristics of other age groups, probably because they are young and active and have less household or work responsibilities.
The overall R2 of the 1984 models was 0.33 for the Tel Aviv model and 0.34 for the equivalent Haifa model. These R2 values are modest but not anomalous for trip generation modeling. They indicate that a substantial portion of trip generation can be explained by nonhousehold factors, such as relative location of residence, employment, and other parameters. Statistical Z tests (assuming known variances, normal distributions, and independence of populations) for the transferability of the coefficients (without updating) show that, at a 95% level of confidence, the coefficients differ, except for the coefficient defining the head of household. To verify the results we also conducted Chow tests for the transferability of the models. The calculated statistic was 7.86 in comparison with the critical 1.72 F-value (at a 95% level of confidence), and yield the same conclusion that the 1984 models are not transferable in space.
Table 4 shows the results of transferring the models in space by showing the predictions from the estimated models and the 1984 database, each applied for both metropolitan areas. The table shows that the Haifa model overpredicts the actual trip rate when applied to the Tel Aviv database, in comparison with the Tel Aviv model applied to the Haifa database. This was expected, as the Haifa trip rate is higher than that for Tel Aviv.
Table 5 presents the estimation results for the 1984 Tobit models using the 1984 household survey data. When we transferred the estimated Tobit models in space and used them to predict the average trip rate in the other city, we found that the Haifa Tobit model overestimated the trips in Tel Aviv by 21.9% (table 6). When we used the estimated Tel Aviv Tobit model to predict the average trip rate for Haifa, we found that it underestimated the total trips by 27.5%. However, transferability t-tests at a 95% level of confidence showed that most of the coefficients are not significantly different in space, except for the license variable and the 8-13 and 30-64 age category variables. On the other hand, χ2 tests at the 95% level of confidence strengthen the alternative hypothesis, that the models vary in space (x 213, 0.95 = 22.36 < 91.198) .
An important issue was to find out whether the Tobit model could explain and capture the nontravelers in the population. As can be seen in table 7, the results are not consistent for the two models. The Haifa 1984 model correctly estimated only 13.5% of the observed nontravelers in the Haifa data and 18.5% in the Tel Aviv data. The Tel Aviv model obtained better results estimating correctly 41.9% of the observed nontravelers in the Tel Aviv data and 34.7% in the Haifa data. These results encourage further research.
Table 8 presents the estimation results of the 1996/97 regression models. As can be seen, the 1996/97 coefficients differ substantially from those of 1984, and most of the coefficients are significant at the 95% confidence level. The best model specification for 1984 was found to be also the best specification for the 1996/97 model, indicating that the most important variables affecting trip generation are similar in both models. The main problem raised during the basic comparison was the difference in the geographic scope (definition of the metropolitan survey area) for the two.
The overall R2 of the 1996/97 models, 0.21 for the Tel Aviv model and 0.23 for the equivalent Haifa model, are even smaller than the values achieved for the 1984 models. But they are still not anomalous in the field of trip generation modeling. Statistical Z-tests conducted at the 95% level of confidence show that none of the coefficients are the same for the two metropolitan areas; that is, the coefficients differ in space. To verify the results, we conducted Chow tests for the transferability of the models. The calculated statistic was 6.91 in comparison with the 1.72 tabular F-value (at a 95% level of confidence), thus yielding the same conclusion, that the 1996/97 models are not transferable in space.
Table 9 presents the predicted average daily trips using the 1996/97 data for each model and each metropolitan area. As in 1984, the 1996/97 Haifa model overpredicts trips compared with the Tel Aviv model, however, the differences are smaller. One should remember that in regression models, the regression line always passes through the average (center of gravity of the observations). Since the observed average number of trips (in Tel Aviv and Haifa) was equal in the 1996/97 metropolitan files, the estimation difference was expected to be smaller.
However, the similar predicted aggregate trip rates indicate overrepresentation of particular sections of the population. For example, the calculated average car availability per household in metropolitan Tel Aviv was higher in the 1996/97 surveys than in metropolitan Haifa (0.60 > 0.55), but in 1984 the average car availability per household was almost the same (0.489 ≈ 0.484). Statistically, different definitions of the sampling areas could affect the transferability of the estimated models
Table 10 shows the Tobit model results for 1996/97. A comparison with table 8 shows the resemblance in the effect of the explanatory variables and the difference in the magnitude of the coefficients between the Tobit and the regression models. Transferring the models in space and evaluating the estimated average trip rate from the models, for 1996/97, we found that the Haifa Tobit model overestimated the trips in the Tel Aviv file by 7.2% and the Tel Aviv Tobit model underestimated the trips in the Haifa file by 7.1% (table 6). These values are quite similar to the over- and underprediction of the equivalent regression models shown in table 9. Spatial transferability t-tests held at the 95% level of confidence show that most of the coefficients are not significantly different between the metropolitan areas, except age categories and the education "non-educated" category. χ2 tests for the spatial transferability of the models at the same level of confidence reach the same conclusion (x 213, 0.95 = 22.36 << 82.01).
In table 11, the 1996/97 Tobit model prediction of nontravelers is even worse than in the analogous 1984 models. When trying to represent nontravelers, the Haifa 1996/97 Tobit model captured only 6.8% of the observed nontravelers in the Tel Aviv file and 11.8% in the Haifa file. The Tel Aviv 1996/97 Tobit model captured only 3.8% of the nontravelers in the Haifa file and 9.8% in the Tel Aviv file. A point worth mentioning is the resemblance in the proportion of nontravelers in the two surveys (about 35% of the persons represented in the sample files did not generate trips). Finally, about 70% to 75% of the estimated nontravelers are observed nontravelers.
Table 12 shows the estimation results for temporal transferability of the regression and Tobit models. When we tested for temporal transferability using the 1984 models to predict 1996/97 trip rates, we observed that the 1984 Tel Aviv regression model underestimated the observed total number of trips in Tel Aviv in 1996/97 by 7%. The Haifa 1984 regression model overestimated the observed total number of trips in 1996/97 Haifa data by only 2.8%. Taking into account that the average number of daily trips in the Haifa 1984 survey was 2.17 and in the 1996/97 survey it was 2.07, the difference is not surprising. However, it may also be affected by the different definition of the geographic scope of the two household surveys.
Chow tests of the temporal stability of the 1984 models compared with the 1996/97 show that the statistic for the 1984 Tel Aviv model was 4.53, bigger than the 1.72 tabular F-statistic at the 95% level of confidence, meaning that the 1984 coefficients differ from the 1996/97 coefficients. The statistic for the temporal stability of the 1984 Haifa model was 8.39 compared with the 1.72 tabular F, reaching the same conclusion. Transferability χ2 tests of the Tobit models in time show that, at the 95% level of confidence, we can reject the null hypothesis; that is, the models for the two time points are different (x 213, 0.95 = 22.36 < 128.72).
In our research, statistical tests indicated that the regression and Tobit models estimated for two metropolitan areas and two time periods differ statistically in time and in space. One exception was the Tobit transferability in space, where the coefficients from the two models for the same year were not significantly different. The distinction cannot be well explained, but it might be due partially to geographic, demographic, socioeconomic, and spatial structure differences between the two metropolitan areas. The smaller sample size and scope of the 1984 household survey compared with the 1996/97 household survey (as shown in table 2) did not allow us to represent the ethnicity of the survey participants, a variable believed to be related to trip generation. Also, the incorporation in the models of a pure economic variable such as income was not possible, because it was not included in the 1996/97 survey.
We ascribed the temporal instability of the estimated models to changes in the structure and development of the metropolitan areas of Tel Aviv and Haifa, changes in lifestyle and socioeconomic variables that are not all accounted for in the model, as well as the inconsistency of the two surveys. A partial explanation may be that 1984 was an economically unstable year, featuring high inflation rates and uncertainty, while 1996/97 was considered to be economically stable.
An important conclusion based on our results is that in order for trip generation models to be transferable they need to account for variables not included in the current models: income, land use and spatial structure, the economy, the transportation system and accessibility, and more detailed socioeconomic and life style variables. If we could estimate a perfect disaggregate model accounting for all factors that affect trip generation and with appropriate segmentation, it would likely be transferable. With this data lacking, models are not transferable, because unobserved variables affect coefficients of observed variables with which they are correlated.
Another conclusion is that household surveys conducted on a regular basis will be more useful if the design stays constant. Differences in the structure, variables, range, investigation period, definition of the variables, and database structure affect the transferability of the estimated models.
We also would emphasize the need for further research on the implementation of Tobit models in the context of trip generation. Tobit models tend to represent the mechanism of trip generation more realistically, capturing and estimating (partially) nontravelers. As a combination of regression and discrete choice models, the Tobit model may be more suitable for implementation in TGM than discrete choice or regression models, particularly because Tobit is better formulated to differentiate nontravelers from travelers. The underestimation of nontravelers may be partly due to the fact that we did not necessarily estimate the best Tobit model.
For the linear regression models, almost all variables were significant at the 95% confidence level, but the coefficients were shown to vary in time and space. For the Tobit model, while almost all variables were significant at the 95% confidence level, the coefficients of the models of the two metropolitan areas were statistically similar but they differed in time for each city.
The nature of the local household surveys raises a need to validate the results of this study in future research. In particular, further research can identify what makes two study areas "similar enough" to justify transferring a model from one to the other. We also suggest further research incorporating Tobit models in TGM and for investigating the characteristics of nontravelers.
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1 A. Cotrus, Department of Civil Engineering, Technion, Israel Institute of Technology, Haifa 32000, Israel. E-mail: firstname.lastname@example.org
2 J. Prashker, Transportation Research Institute,Technion, Israel Institute of Technology, Haifa 32000, Israel. E-mail: email@example.com
3 Corresponding Author: Y. Shiftan, Transportation Research Institute,Technion, Israel Institute of Technology, Haifa 32000, Israel. E-mail: firstname.lastname@example.org