Trip generation modeling using data collected in single and repeated cross-sectional surveys

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1 JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2014; 48: Published online 20 February 2012 in Wiley Online Library (wileyonlinelibrary.com)..217 Trip generation modeling using data collected in single and repeated cross-sectional surveys Judith L. Mwakalonge* and Daniel A. Badoe Department of Civil and Environmental Engineering, Tennessee Technological University, Cookeville, TN 38505, U.S.A. SUMMARY The majority of US metropolitan regions still use the four-step urban transportation modeling system to develop their travel forecasts. Trip generation, the first step of this system, has as objective of predicting the expected total travel demand in a region. The commonly used methods in planning practice for predicting this expected total travel demand typically use only the most recent cross-sectional data available from a study region for model development, which ties the resulting travel-forecast model to the economic environment prevailing at the time of data collection. Applying such models to generate forecasts of travel in economic environments significantly different from those embodied in the estimated model parameters could result in greater errors than would otherwise be the case. To address the aforementioned problem, this paper proposes the development of trip generation models estimated on multiple independent cross-sectional datasets collected in the same urban region but at different times representing different economic environments. Data used in the research were collected in crosssectional household travel behavior surveys undertaken in the Greater Toronto Area, Canada in 1986, 1996, 2001, and The results lead to the conclusion that well-specified models, estimated on pooled multiple crosssectional datasets, yield travel predictions in the base and horizon years, respectively, that have smaller error compared with corresponding travel predictions generated with single cross-sectional models. Copyright 2012 John Wiley & Sons, Ltd. KEY WORDS: trip generation modeling; trip rates; cross-sectional data; data pooling 1. INTRODUCTION The commonly used procedure for developing travel forecasts for metropolitan regions is still embodied in the four-step Urban Transportation Modeling System [1]. Trip generation, the first step of this modeling system, determines the overall scale and pattern of trip making within a study region and is the focus of this paper. A number of methods are documented in the travel demand modeling literature for accomplishing trip generation. One of the more widely used of these methods makes use of multiple linear regression analysis [1,2]. The typical data used in the development of a trip generation model estimated by linear regression analysis is collected in a single cross-sectional travel survey. The use of a single cross-sectional dataset for model development requires the assumptions, first, that the surveyed households are at the demand supply equilibrium point at the time that the survey is undertaken and, second, that the travel behavior relationship established at this equilibrium point remains stable over time. Forecasting with such models means that variations in travel behavior observed across households in a cross section can be extrapolated longitudinally to predict the travel behavior of households in response to changes in demographic characteristics that they experience over time. These assumptions are quite strong because in reality, at the time a *Correspondence to: Judith L. Mwakalonge, Civil and Mechanical Engineering Technology, South Carolina State University, Orangeburg, SC U.S.A. jmwakalo@scsu.edu Copyright 2012 John Wiley & Sons, Ltd.

2 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA 319 survey is conducted, whereas some respondents would have fully adjusted their travel patterns to the prevailing cost of travel, others could be in the process of adjusting their patterns to a more stable configuration consistent with the resources that they have and with the costs that they face. Very importantly, if a travel survey were to be conducted when the economy was at a high or low point, the coefficients of variables specified in a travel demand model would reflect the characteristics of the high or low point. As an example, a household of specific composition could in economically good times participate in several non-home activities resulting in several trips being made. However, during an economic recession, the general lack of positive news could lead them to reduce their participation in non-home activities even though no change would have occurred in their demographic characteristics. Thus, the assumption of temporal stability has been suggested to be too strong indeed, empirical studies point to the travel behavior of households of similar composition not necessarily remaining stable over time [3]. The aforementioned implication is twofold. If the prevailing economic environment at the time of survey influences travel behavior negatively, then a trip generation model developed on cross-sectional data collected during this period would have variable coefficients that are relatively smaller in magnitude. Long-range forecasting with such a model would lead to a lower-than-expected travel demand and possibly result in under-provision in transportation infrastructure and services. On the other hand, if the economy is at the high point of a business cycle, then the general economic environment would influence travel positively. A trip generation model developed on cross-sectional travel data collected during this period would have variable coefficients that are relatively higher in magnitude. Long-range forecasts of travel with such a model would lead to relatively higher expected travel demand and, therefore, the possibility of over-provision of transportation infrastructure and/or services. The latter was experienced by the UK and other industrialized countries in the late 1980s [4]. From the foregoing, the theoretically preferable data for modeling travel demand is panel data, which has the ability to capture peoples responses to changes in values of transportation-influencing variables over time [5 7]. However, the use of panel data by planning agencies has been rather limited because of the challenges associated with their collection and use [8]. These challenges include sample attrition and the proneness to bias of subsequent panel survey results due to decline in reporting accuracy caused by panel fatigue of respondents to the repeated survey questions [3]. As a result of these and other reasons, cross-sectional data and cross-sectional travel demand models continue to be extensively used. Usually, planning agencies undertake cross-sectional surveys at specific time intervals or whenever resources become available. Over time, an agency would have multiple cross sections of data available for modeling purposes. As an example, at the present time, the Twin Cities (Minneapolis St. Paul) Metropolitan Council in Minnesota has four cross-sectional datasets, whereas the San Francisco Metropolitan Transportation Commission in California has five cross-sectional datasets. Despite the availability of multiple independent cross-sectional datasets to transportation planning agencies, the practice has been to develop travel demand models using only the most recent dataset available to the agency. The thought behind this practice is that the most recent cross-sectional dataset captures the prevailing relationship between travel and the factors on which it is conditioned and thus would be more appropriate for forecasting purposes. But, as has been discussed earlier, reliance on a single cross section of data has its risks as well. Consequently, the availability of multiple cross sections of data motivates an investigation into whether older travel datasets, collected at considerable cost to a region, can be combined (pooled) with the most recent dataset available on a region for development of travel forecasting models. Wooldridge [9], Lee et al. [10], and Mark and Swait [11] in the econometrics literature all discuss advantages of pooling data from multiple sources for model development. Prime among these is the increase in statistical efficiency and precision of estimators on account of the increase in overall sample size. Furthermore, several studies that have investigated the use of multiple datasets in model estimation have presented positive results. Badoe and Wadhawan [12] investigated the performance of pooled disaggregate logit mode choice models estimated on two cross-sectional datasets. The study investigated five model specifications ranging from simple to complex. In this study, naive pooling and single cross-sectional models did not replicate the observed travel choices as well as other models. Models with period-specific modal constant terms had better predictive performance, indicating that the impact of unexplained contextual

3 320 J. L. MWAKALONGE AND D. A. BADOE factors change in significant ways from one temporal period to another and their impact supersedes that of changes in variances of the random modal utilities in the different periods. Badoe and Miller [13] compared the performance of several model-updating methods using data from two surveys conducted in the Toronto region in 1964 and The results of the study indicated that the combined transfer estimator did not perform well because of the large transfer bias. The joint context estimator yielded results that were superior to the other model-updating methods investigated in the study and also had the advantage of having a significantly more parsimonious parameter structure. The potential of multiple cross-sectional datasets serving as a surrogate to panel data and the potential for reduced costs in data collection and, therefore, in transportation decision-making motivate the investigation into pooling multiple cross-sectional datasets collected in the same urban region for developing travel demand models. Specific objectives of this research are as follows: (1) To investigate alternative methods for developing a trip generation model (pooled model) with data from multiple independent cross-sectional datasets collected in the same urban region or from a combination of previously estimated cross-sectional trip generation models on data from the same urban region. (2) To compare the performance of these alternative pooled models to that of the single cross-sectional model in prediction of travel on the estimation dataset. (3) To compare the performance of these alternatively specified pooled models to that of the single cross-sectional model both in short-range and long-range forecasting. The rest of the paper is organized as follows. The following section presents the statistical theory to the methods proposed for developing travel demand models using multiple independent crosssectional datasets. The sections on data and model specification present the sources of data used in this study and a description of variables specified in the model, respectively. The results section discusses the empirical results of modeling trip generation with data from multiple independent cross-sectional surveys. Finally, the paper presents the conclusions and recommendations for future research. 2. METHODOLOGY The methods for estimating a travel forecasting model using multiple independent cross-sectional datasets are grouped into two categories. The first category has methods that combine directly the vectors of model coefficients/parameters from two or more periods. The methods in this first category are the weighted (based on sample sizes) mean of the vector of parameters for the different periods and weighted (based on parameter covariance matrices) mean of the vector of parameters of the different periods. The second category has methods that develop a travel forecasting model using the combination of data from multiple periods. More specifically, here, alternative model specifications for estimation with pooled data are formulated for testing Cross-sectional models Given the availability of travel and demographic data from T independent cross sections/periods, each period has n t observations, t =1,..., T; the linear model of trip generation for each period t may be formulated as follows: y it ¼ a t þ XK k¼1 x itk θ tk þ e it t ¼ 1;...; T (1) where i indexes household observations in period t, k indexes the household characteristics, y it is the number of trips made by household i in period t, x itk is the kth household characteristic of household i in period t, a t is the constant term for period t, θ tk is the kth coefficient of the kth explanatory variable in period t, and e it is the random term for household i in period t. Equation (1) can be expressed in vector notation as follows:

4 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA 321 y t ¼ X t b t þ «t ; t ¼ 1;...; T Assuming that Gauss Markov conditions apply (i.e., E(«t ) = 0 and varðe t Þ ¼ s 2 t I n t ¼ P t; t ¼ 1;...; T), then the least squares estimator of the vector of model parameters for each period/cross section t is given by b t ¼ X tx t 1 X t Y t ; t ¼ 1;...; T 2.2. Category 1: Combining vector of model parameter estimates Here, the alternative methods for formulating a single trip generation model from combining trip generation models for multiple periods are presented. Methods in this category are suited to situations in which the cross-sectional trip generation models for earlier periods are available but the actual crosssectional datasets used in model estimation are unavailable. The assumption to the methods here is that model specification has not changed over time. The combined estimator is obtained by taking a weighted average of the vector of model parameters for the different periods. The weight selected for each vector of model parameters is proportional to their importance as captured by an appropriate measure such as sample size, variance, or time. The alternative model specifications in this category and the motivation to them are as follows: Model 1 The reliability of model parameter estimates is affected by the size of sample from which they are developed. Therefore, to account for sample size differences among surveys, a weighted model with sample size used as a measure of the importance of the parameter vector was estimated. By this, models estimated on larger sample sizes would receive greater weight in the combined estimator, b combined, than models estimated on smaller sample sizes. In mathematical terms, the model is expressed as follows [10]: b combined ¼ XT t¼1 n t! 1 X T t¼1 n t b t (2) where n t is the size of sample in period t and b t is the model for period t, t =1,..., T. Model 2 The weight associated with the vector of model parameters for each cross section is determined based on the parameter covariance matrices. The method assumes that the vector of model parameters for each period/cross section is an unbiased estimator of the true vector of model parameters. The weights are defined such that the resultant combined estimator has minimum variance. Mathematically, the minimum variance of the unbiased combined estimator is defined as follows. Let b 1, b 2,..., b T be the unbiased estimators of the underlying true vector of model parameters b combined and A 1, A 2,..., A T be the corresponding weights associated with the parameter vector for each cross section. Then, the weighted linear combination of the T independent estimators is [13] b combined ¼ XT t¼1 A t b t (3) where A t ¼ X 1 1 þ þ X 1 T 1X 1 t P 1 t is the inverse of the parameter covariance matrix for period t.

5 322 J. L. MWAKALONGE AND D. A. BADOE 2.3. Category 2: Modeling with pooled data In this category, models are specified to be estimated on a pooled dataset. This pooled dataset is obtained from combining the data collected in multiple independent cross-sectional surveys. Four alternative models are specified to capture travel behavior across periods and their parameters jointly estimated. The theory to each of these models is presented as follows. Model 3 This model assumes the homogeneity hypothesis is accepted; that is, the true model parameters governing household trip generation and the error variance have remained unchanged over time. More explicitly, it assumes that neither the observed factors known to influence travel behavior that are specified in the model nor the unobserved factors have changed over time. All T cross-sectional datasets are combined and treated as a single cross-sectional dataset for model estimation. The aforementioned assumptions can be expressed mathematically by imposing the following constraints on Equation (1): a 1 ¼ a 2 ;...; a T ¼ a θ 1 ¼ θ 2 ;...; θ T ¼ θ 2 e 1 e cov ¼ s2 I n1 þn 2 þ þn T e T 3 The least squares estimator bof Β the true vector of model parameters is given by where b ¼ ½a; θš ; Y; and X are as defined earlier. Model 4 1X b ¼ X X Y (4) This model assumes the vector of the coefficients of the specified explanatory variables to be temporally invariant but allows the constant term to vary across periods. From a travel behavior viewpoint, the interpretation to these assumptions is that the impact of the observed household characteristics, such as household size, on trip making are constrained to be identical across periods. However, the impacts of unspecified factors such as travel cost, change in technology, and change in transportation system that affect travel behavior are allowed to vary across periods. From the notation adopted earlier, the following constraints are imposed on Equation (1): a 1 6¼ a 2 ;...; 6¼ a T θ 1 ¼ θ 2 ;...; θ T ¼ θ 2 e 1 e cov ¼ s2 I n1 þn 2 þ þn T e T 3

6 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA 323 Equation (4) gives the least squares estimator b of Β the true vector of model parameters, where b ¼½a 1 ; a 2 ;...; a T ; θš ; Y; and X are as defined earlier. Model 5 In the models discussed earlier, it was assumed that the variance of the unobservable error term, var (e it ), conditional on the observed household characteristics, is constant across periods. In this model, this assumption is relaxed. However, the vector of model parameters and the constant term are assumed to be temporally invariant. The period-specific variance of the error term, varðe it Þ ¼ s 2 t, violates the homoscedasticity requirement of the Gauss Markov conditions for use of ordinary least squares, which would lead to a biased estimator of b should ordinary least squares be used. This can be addressed by rewriting Equation (1) as y it = st ¼ a t = st þ XK k¼1 x itk = st θ tk þ e it = st (5) From the notation adopted earlier, the model assumptions translate into the following constraints imposed on Equation (1): a 1 ¼ a 2 ;...; a T ¼ a θ 1 ¼ θ 2 ;...; θ T ¼ θ varðe it Þ ¼ s 2 t where t =1,..., T; and i =1,..., n t. The least squares estimator b of Β true vector parameters is given by X b ¼ X 1 1 X X 1 1 þ X 1 2 X X 2 2 þ þ X 1 1 T X X T T X 1 1 Y 1 1 þ X 2 X 1 2 Y 2 þ þ X T X 1 Y T T where b ¼ ½a; θš, Y t = vector of trips made households in period t, X t = design matrix for period t, and the variance of the vector of error terms e t is given by varðe t Þ ¼ s 2 t Ι n t ¼ P t : Model 6 This model allows for both the constant term and the variance to vary across periods but constrains the rest of the vector of model parameters to be equal across periods. If ordinary least squares were to be applied for model estimation under this condition; that is, with the variance of the error terms being free to vary across periods varðe it Þ ¼ s 2 t also referred to as heteroscedasticity, the resulting estimator would be biased. The heteroscedasticity issue can be addressed by imposing the following constraints on Equation (1) as in Equation (5). From the notation adopted earlier the model assumptions translate into the following constraints imposed on Equation (1): (6) a 1 6¼ a 2 ;...; 6¼ a T θ 1 ¼ θ 2 ;...; θ T ¼ θ varðe it Þ ¼ s 2 t

7 324 J. L. MWAKALONGE AND D. A. BADOE where t =1,..., T; and i =1,..., n t. Equation (6) gives the least squares estimator b of Β the true vector parameters, where b ¼½a 1 ; a 2 ;...; a T ; θš ; Y t is the vector of trips made households in period t, X t is the design matrix for period t, and the variance of the vector of error terms e t is given by varðe t Þ ¼ s 2 t Ι n t ¼ P t : 2.4. Data The data used in the empirical test were collected in travel surveys called Transportation Tomorrow Surveys (TTS) conducted in years 1986, 1996, 2001, and The telephone interview was used as the survey instrument in the four surveys. The 1986 travel survey was a 1-day survey of 4% of the households within the Greater Toronto Area (GTA), consisting of approximately households in total. The 1996 travel survey expanded the survey area to include the GTA and selected surrounding counties. A total of households were successfully interviewed, representing 5% of all households in the survey area. This study though uses travel information from households drawn from the GTA only for geographical area consistency across years. The 2001 TTS covered the same area as the 1996 survey excluding the Regional Municipality of Waterloo while expanding into other counties outside of the GTA. Altogether, approximately households were interviewed. Again, for consistency purposes, this study uses the travel data from the households that were sampled from the GTA. The 2006 TTS covered all of the area involved in the 2001 survey plus the Regional Municipality of Waterloo, which had previously been surveyed in 1996 but not 2001; the City of Branford; and the County of Dufferin, which had not been surveyed in previous TTS data collection efforts. Approximately households were successfully interviewed, but only the households that were sampled from the GTA were used in this study for the reason of consistency. In addition, it is worth noting that the data expansion factors provided in each dataset was used in the analysis. The Data Management Group [14] documents the details of the aforesaid travel surveys in a report Household trip and person trip rates by analysis year Figure 1 shows both the person trip and household trip rates for each of the analysis years. With the exception of 1996, Figure 1 shows that the person trip rate in the GTA remained relatively stable over the analysis years. The plot of household trip rate in Figure 1 shows that household trip rate was highest in 1986 and lowest in The 2001 and 2006 trip rates fall between the 1986 and 1996 values. The changes in travel behavior during the period may have been influenced by the impact of the economic recession that occurred in on the GTA s economic base. With respect to travel demand modeling, forecasting travel in 2001 using the 1986 cross-sectional model would have led to the over prediction of travel, 6.5 Trip rate distribution trip rate household level person level year Figure 1. Household trip and person trip rates by analysis year.

8 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA 325 whereas using the 1996 cross-sectional model would have led to the under-prediction of travel. As shown by the arrow in Figure 1, an average model that combines travel information from the 1986 and 1996 datasets would under predict travel in 2001 with a lower error magnitude compared with the prediction that would be yielded by a model estimated on the 1996 data only Model specification The first task in modeling with data from multiple cross sections is to come up with an appropriate model specification for the trip generation model. Various techniques of model search were employed namely stepwise regression, analysis of variance, and likelihood ratio tests. The details of the aforementioned analysis are documented elsewhere [15]. Table 1 presents the household socio-economic and demographic variables specified in all the models developed in this research. These variables include the logarithm of the number of persons in the household, number of household members that work full time, the number of household members that are students, the number of household members that possess a driver s license, and two dummy variables that capture the impact the number of vehicles available to a household has on trip making. The models were estimated using STATA 9.0 (StataCorp, College Station, TX, USA) data analysis and statistical software. 3. RESULTS 3.1. Discussion of estimated model parameters The output from estimating a cross-sectional model on each of the respective cross-sectional travel data are presented in Table 2. The results from estimating models on pooled data are presented in Table 3. Models estimated on data pooled from three cross-sectional surveys conducted in 1986, 1996, and 2001 are abbreviated as pooled in the table, whereas models estimated on data pooled from two cross-sectional surveys conducted in 1986 and 1996 are abbreviated as pooled Table I. List of household characteristics considered for model development. Variable code Loghhsize Nveh1 Nveh2 Nlicense Nworkers Nstudent Description Logarithm of the number of persons in a household Household vehicle ownership dummy variable 1. For households with one vehicle, Nveh1 = 1; otherwise, Nveh1 = 0 Household vehicle ownership dummy variable 2. For households with two or more vehicles, Nveh2 = 1; otherwise, Nveh2 = 0 Number of persons in a household possessing a driver s license Number of full-time workers in a household Number of students in a household. A student is any person enrolled as either full time or part time at an academic institution. Table II. Cross-sectional models estimation output. Variable Year Loghhsize Nveh Nveh Nworkers Nlicence Nstudent Constant Sample size

9 326 J. L. MWAKALONGE AND D. A. BADOE Table III. Pooled models estimation results. Models estimated on data pooled from three cross-sectional surveys conducted in 1986, 1996, and 2001 Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Loghhsize Nveh Nveh Nworkers Nlicence Nstudent Constant constant constant constant Pooled Sample size Models estimated on data pooled from two cross-sectional surveys conducted in 1986 and 1996 Loghhsize Nveh Nveh Nworkers Nlicence Nstudent Constant constant constant Pooled Sample size The coefficients of all the variables have the expected sign; that is, households with more members, more workers, more people licensed to drive, and more students on average are expected to make more trips; hence, a positive sign is expected for their respective coefficients. Further, households with two or more vehicles are on average expected to make more trips compared with households with one vehicle only. Similarly, households with one vehicle are expected to, on average, make more trips than households with no vehicle. On the basis of this, first, the expectation is for the sign of the coefficients of both household vehicle ownership dummies to be the positive sign. Second, the expectation is for the magnitude of the coefficient of household vehicle ownership dummy variable 2 (Nveh2) to be larger than the coefficient of household vehicle ownership dummy variable 1 (Nveh1). These latter two expectations are met in the four cross-sectional models presented in Table 2. Additionally, the pooled models estimated from two cross-sectional datasets (1986 and 1996) have coefficients that lie between the 1986 and 1996 model coefficients, thus confirming the discussion on trip rates associated with Figure 1. With the use of a 5% significance level criterion, all the estimated model parameters presented in Tables 2 and 3 are found to be statistically significantly different from zero the p-values of the coefficients are not included in Tables 2 and 3 for space purposes. The estimated vectors of cross-sectional model parameters for the different periods were used to formulate pooled models in Category 1, which has two models namely Models 1 and 2. It is worth noting here that the results of the statistical test of stability of the vector of model coefficients for 1986, 1996, and 2001 relative to the vector of model coefficients for 2006 indicated no stability. The details of model-coefficients stability are presented elsewhere [15] Prediction of household travel in 1986, 1996, 2001, and on the pooled datasets The results of predicting travel in the GTA with the use of single cross-sectional models and pooled models formulated from multiple independent datasets are presented later. At the time of model estimation, the analyst has no knowledge of exactly how these models will perform in the future. Therefore, the analyst selects a forecasting model from a set of candidate models on the basis of how well each model is able to replicate travel behavior in the estimation context. Given this, both cross-sectional models and pooled models were used to predict travel in the estimation-data context.

10 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA 327 The mean absolute error (MAE) measure is used to assess the performance of the models in prediction of travel. This measure has been used in other studies including those by Hadayeghi et al. [16], Badoe [17], and Koppelman and Wilmot [18]. It measures the average magnitude of misprediction by a model. A value close to zero suggests that the model, on average, predicts the observed travel behavior well. MAE is mathematically defined as MAE ¼ P N i¼1 jy i ^y i jw i P N i¼1 w i (10) where y i is the observed number of trips produced by household i, ^y i is the predicted number of trips produced by household i, w i is the expansion factor, and N is the sample size. The results shown in Table 4 indicate that the pooled models, estimated with two datasets, 1986 and 1996 (pooled ), perform equally as well as the 1986 cross-sectional model, whereas the pooled models estimated with three datasets, 1986, 1996, and 2001 (pooled ), perform marginally lower in terms of explaining the variation in household trips in the 1986 dataset. Further, the results indicate that the component of each of the pooled models that is applicable to 1996 performs equally as well as the 1996 cross-sectional model in terms of explaining the variation in household trips on the 1996 dataset. All models explain approximately 43% of the variation in trips made by households in the 1996 dataset. From Table 4, it is apparent that all pooled models with a 2001 component explain more than 45% of the variation in trips made by households in the 2001 dataset, which is equivalent to the one yielded by the 2001 cross-sectional model. The values of MAE yielded by the pooled models with a 1986 component are all lower than that yielded by the 1986 cross-sectional model. Specifically, of the pooled models, Models 5 and 6 yield the lowest MAE values. For pooled models with a 1996 component, Models 5 and 6 yield an MAE value of 2.33, which is lower than the MAE value of 2.35 yielded by the 1996 cross-sectional model. Models 1 to 4 yield MAE values that are higher than the MAE value yielded by the 1996 cross-sectional model. Further, it is observed that all pooled models with a component that is applicable to 2001 perform equally as well as the 2001 cross-sectional model in terms of the MAE measure. Generally, it is evident from the MAE values in Table 4 that on average, all the models under-predict or over-predict daily household trips by 2.4 trips, which is lower than half the typical household daily trip rate for all the periods analyzed. Additionally, of the pooled models, Models 5 and 6 yield a marginally lower MAE value than the cross-sectional models in all applications analyzed Prediction of household travel in the GTA in 2006 using cross-sectional models and pooled models One of the objectives of this study was to compare the forecast performance of the trip generation model estimated on the year 2001 cross-sectional data only with that of the pooled models estimated on a multiperiod dataset obtained from pooling cross-sectional data from 1986, 1996, and To further investigate the performance of cross-sectional models in predicting future trips as compared with pooled models, the 1986 and 1996 cross-sectional models, respectively, were also used to predict travel in 2006 the 2006 dataset served as an independent dataset for assessing the forecast performance of these models. Table 5 shows the values of MAE evaluated using the predictions of household travel in 2006 by the cross-sectional and pooled models. They show that of the three cross-sectional models, the 1986 model yields the highest forecast error. It is followed by the 2001 model and then the 1996 model. With respect to pooled models, Model 6 consistently yields the lowest MAE value followed by Model 5. In predictions on the estimation dataset, both Models 5 and 6 had similar predictive performance. Therefore, for forecast purposes, Models 5 and 6 are expected to yield more accurate forecasts compared with Models 1 to 4. Furthermore, by comparing the predictive performance of the pooled models with the 2001 cross-sectional model, it is observed that with the exception of Model 3, all the pooled models yield marginally lower values of the error measure compared with the value yielded by the 2001

11 328 J. L. MWAKALONGE AND D. A. BADOE Table IV. Models prediction performance in the estimation data. Model type Model Application data R 2 MAE Cross-sectional models pooled Model pooled Model pooled Model pooled Model pooled Model pooled Model pooled pooled Model pooled Model pooled Model pooled Model pooled Model pooled Model pooled model. The nature of the forecast performance exhibited by these three cross-sectional models in comparison with the pooled models provides impetus to the idea of developing models with multi-period data rather than with a single cross-sectional dataset. With respect to the degree to which the variation in household trips in 2006 is explained, all the pooled models explain more than 45% of the variation in household trips. The value of transfer R- squared yielded by pooled models in pooled are marginally higher compared with that yielded by the 2001 cross-sectional model Prediction of travel in the Greater Toronto Area in 2001 and 2006 using pooled models Another objective of this study was to compare the predictive performance of the pooled models and cross-sectional models both in short-term and long-term forecasting. Therefore, the pooled models

12 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA 329 Table V. Models prediction performance in Category Model Transfer R 2 MAE Cross-sectional models pooled Model Model Model Model Model Model Table VI. Prediction performance of pooled models in predicting travel in 2001 and Application year Model R 2 MAE Model Model Model Model Model Model Model Model Model Model Model Model Model Model were used to forecast travel both in the short-term 2001 and long-term Table 6 show the results of the models performance in predicting travel at the disaggregated household level in 2001 and All the six pooled models are able to explain approximately 45% of the variation in trips at the household level in the observed 2001 sample, which is marginally lower than the explanatory power yielded by 1996 cross-sectional model. With respect to long-range forecast, all the pooled models explain the variation in trips in 2006 marginally better than the 1996 cross-sectional model. The MAE values computed at the disaggregate household level show that Model 5, which allows for the constant term to change over time, and Model 6, which allows both the constant term and the error variance to vary over time while constraining the vector of model coefficients to be equal, yield the lowest MAE values both in short-term and long-term forecasting. Thus, in these application contexts, Models 5 and 6 marginally outperform the 1996 cross-sectional model, whereas the 1996 crosssectional model outperforms Models 1 to CONCLUSIONS This study investigated six alternative methods for formulating trip generation models using multiple independent cross-sectional data. The performance of these pooled models in their prediction of travel on the estimation datasets and on an independent dataset was compared with that yielded by conventional cross-sectional models. The following conclusions are reached based on the results of this study: (1) The estimated pooled models had a performance in prediction of travel on the independent crosssectional datasets that was very comparable with that yielded by the single cross-sectional models. Further, of the different pooled models, Models 5 and 6 yielded values of the MAE measure, which were smaller than those yielded by the single cross-sectional models. These findings lead to the

13 330 J. L. MWAKALONGE AND D. A. BADOE conclusion that pooled models, in their prediction of travel on the estimation datasets, perform as well if not better than single cross-sectional models. (2) Two methods (Models 1 and 2) that combine directly the vectors of model parameters from two or more periods were investigated. Of the two, the model that computes the weighted mean of model parameters using as weights functions of the parameter covariance matrices had a marginally better performance in forecasting travel. The higher magnitude of MAE value for Model 1 may be attributed to it not accounting for differences in parameter covariance matrices across the different survey years. (3) With respect to the methods that develop a travel forecasting model using the combination of cross-sectional data from multiple periods, Model 6 which allows for period-specific constant terms and period-specific error variances while constraining the vector of model parameters to be equal across periods yielded the best forecast performance. It was followed by Model 5, which constrained the constant term to be identical across periods but allowed for period-specific error variances. It is concluded from this finding that model specification is important to development of a good forecasting model with data from multiple cross-sectional surveys. This conclusion is consistent with econometric theory on the modeling of travel with single cross-sectional data. (4) Despite not finding universal parameter stability over time, Models 5 and 6 estimated on data pooled from years 1986, 1996, and 2001 performed better than the cross-sectional model estimated on only year-2001 data by yielding the lowest error values in predicting household travel in year Under current modeling practice, only the 2001 cross-sectional model would have been used for travel forecasting purposes. As evidenced by the modeling results, the older cross-sectional data had useful information that would have been ignored in model development had current practice been followed. These findings lead to the conclusion that pooling data and models results in a travel forecasting model that is superior to a single cross-sectional model. (5) In the short-term forecast application (forecast of travel in 2001) using the pooled models estimated on two cross-sectional datasets (1986/1996), Models 5 and 6 yielded error values that were lower than that given by the 1996 cross-sectional model. Additionally, the 1996 cross-sectional model yielded a lower value of the MAE measure compared with Models 1 to 3. In the long-term forecast application (forecast of travel in 2006), out of the six pooled models, Models 5 and 6 again yielded values of the error measure that were lower than that yielded by the 1996 crosssectional model, whereas Models 1 to 3 were outperformed by the 1996 model. Again, these findings lead to the conclusion that pooling data and models results in a travel forecasting model that is superior to a single cross-sectional model. Generally, with regard to modeling with multiple cross sections of data, this study managed to show that there is potential to develop better models using multiple datasets. However, there are still some issues that need to be addressed in future research, which include the following: (1) Conducting a study similar to that reported in this paper but using datasets from other metropolitan regions. This will allow the reaching of more general conclusions. (2) The other approach to modeling with multiple independent cross sections of data is the use of pseudo panel data. This study recommends a comparison of the predictive performance of pooled models investigated in this study with that of pseudo panel models. REFERENCES 1. TRB. Metropolitan travel forecasting: current practice and future direction. Transportation Research Board Special Report 288, Washington, DC, Horowitz AJ. Statewide travel forecasting models. NCHRP Synthesis 358, Transportation Research Board, Kitamura R. The development of a household panel survey plan. Report Prepared for Puget Sound Council of Governments, Davis, California, Ortuzar JD, Willumsen LG. Modeling Transport, 3rd edn, John Wiley and Sons, Inc.: Chichester, England, Kitamura R. Panel analysis in transportation planning: an overview. Transportation Research, Part A 1990; 24A(6): Meurs H. Dynamic analysis of trip generation. Transportation Research Part A 1990; 24A(6): Goodwin PB, Dix MC, Layzell AD. The case of heterodoxy in longitudinal analysis. Transportation Research, Part A 1987; 21A(4/5):

14 MODELING TRIP GENERATION WITH MULTI-CONTEXT DATA Bonsall PW. Issues in survey planning and design. Transport Planning and Traffic Engineering, C. A. O Flaherty, ed., Arnold, Great Britain, 1997, Wooldridge JM. Introductory Econometrics: a Modern Approach. The Thomson South-Western: Kentucky, Lee S, Davis WW, Nguyen HA, McNeel TS, Brick JM, Flores-Cervantes I. Examining trends and averages using combined cross-sectional survey data from multiple years. California Health Interview Survey Methodology Paper, California, Mark TL, Swait J. Methodology using stated preference and revealed preference modeling to evaluate prescribing decisions. Health Economics 2004; 13(6): Badoe DA, Wadhawan B. Jointly estimated cross-sectional mode choice models: specification and forecast performance. ASCE Journal of Transportation Engineering 2002; 128(3): Badoe DA, Miller EJ. Comparison of Alternative Methods for Updating Disaggregate Logit Mode Choice Models. Transportation Research Record 1493, Transportation Research Board: Washington, D.C, 1995, Data Management Group. 2006, 2001, 1996, 1991 and 1986 travel survey summaries for the Greater Toronto Area. Report Prepared for the Toronto Area Transportation Planning Data Collection Steering Committee, Mwakalonge JL. Econometric modeling of total urban travel demand using data collected in single and repeated cross-sectional surveys. PhD Dissertation. Department of Civil and Environmental Engineering, Tennessee Technological University, Cookeville, Tennessee, Hadayeghi A, Shalaby AS, Persaud BN, Cheung C. Temporal transferability and updating of zonal level accident prediction models. Accident; Analysis and Prevention 2006; 38: Badoe DA. an investigation into the long range transferability of work-trip discrete mode choice models. PhD Dissertation. Department of Civil Engineering, University of Toronto, Ont., Canada, Koppelman FS, Wilmot CG. Transferability analysis of disaggregate choice models. Transportation Research Record 295, Transportation Research Board, Washington, DC, 1982,