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Improving ADA Paratransit Demand Estimation: Regional Modeling (2012)

Chapter: Chapter 3 - The ADA Paratransit Demand Models

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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
×
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
×
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Suggested Citation:"Chapter 3 - The ADA Paratransit Demand Models." National Academies of Sciences, Engineering, and Medicine. 2012. Improving ADA Paratransit Demand Estimation: Regional Modeling. Washington, DC: The National Academies Press. doi: 10.17226/22720.
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26 C h a p t e r 3 This chapter describes the component models that make up the full modeling systems, how these components are related to each other, the results of the model estimation process, how the models were calibrated, and the results of sensitivity tests. Overview of the Model Components The model system is made up of aggregate components and disaggregate components: • The aggregate components include a model that predicts the number of registered users of the ADA paratransit system living in each census tract and traffic analysis zone (TAZ) within the region. Further steps transform the output of this model into a “synthesized population” in each TAZ needed to run the disaggregate components. In addition there is an aggregate calculation of the ADA paratransit service level (expressed as “generalized travel time” compared to driving a private car) that applies to the entire region. • The disaggregate components are a series of models that can be applied to the detailed survey data (or a synthesized population) to predict the number, purpose, mode, and destination of trips made during a representative weekday for a registered user of the ADA paratransit system. The model system can be run in two modes, a “regional mode” and a “sketch mode.” • The regional mode can use detailed demographic data (e.g., at the census tract level) from a region other than the Dallas-Fort Worth region that was treated in the research. • The sketch mode uses demographic data from the Dallas-Fort Worth region, but allows a user to assume changes in region-wide demographic statistics and ADA paratransit service characteristics and see how these changes affect predicted travel. Most of the aggregate model components are only run in the regional mode. The disaggregate components can be used to predict the characteristics of all trips made on a typical weekday by the given sample of ADA-eligible users and are the components used in the “sketch mode” of running the model. However, those results are specific to the particular ADA-eligible population in the Dallas-Fort Worth region and to the specific residence locations of our survey sample within that region. Further models and analysis were required to transform the model system into a model of ADA paratransit demand that can be applied to other regions. Two main approaches could have been followed: 1. Synthesize a population of ADA-registered persons within each TAZ of a region. 2. Use our survey sample of ADA-registered persons, and re-expand it for each TAZ of a region to represent an ADA-eligible population within each TAZ The ADA Paratransit Demand Models

the aDa paratransit Demand Models 27 Although the first approach is more typical in applied travel demand modeling, the second approach seems more accurate for this study context. There are at least two important reasons for this. First, there are no available data sources, such as the census, that can tell us what the detailed characteristics of the ADA-registered population are. Our own survey sample is likely the best source of detailed data that exists for this purpose, so we should try to use that informa- tion to the greatest extent possible. Second, our models contain a few variables, such as disability type, that are not available from standard data sources. (The census definitions of disability are unlikely to be useful for this purpose.) Therefore the second approach has been used. The “aggregate model components” are shown in Table 3-1 and introduced briefly below. Following that, the disaggregate components are introduced before discussing the detailed results for each model. Aggregate Components The ADA paratransit registration rate model: This model predicts the percentage of the adult (age 18+) population within a census tract who are registered as eligible to use ADA paratransit service and have either made an ADA paratransit trip or else registered within the Aggregate components (run for each census tract or TAZ) Model Choice level Predicts Key input variables ADA paratransit registration rate model Census tract (could also be applied at other spatial levels) Percent of people that register to use ADA paratransit Tract age distribution Tract income distribution Tract household size and type distribution ADA-ADA paratransit registered population synthesis Census tract (could also be applied at other spatial levels) Expansion factors for the survey sample specific for each census tract Tract income distribution Tract age distribution Tract household size and type distribution Corresponding regional distributions Allocation of ADA- registered population to zones TAZ Residence TAZ for each survey record within each tract Zonal population Tract population More detailed inputs Generalized ADA paratransit service levels All zone-to-zone pairs Generalized travel time by ADA paratransit (based on Stated Preference data) ADA paratransit travel time (relative to driving own car) ADA paratransit fare ADA paratransit punctuality (at pick-up or drop-off point) Disaggregate components (run for each person in synthesized population) Model Choice level Predicts Key input variables Tour generation model Person-day Number and main purpose of home- based tours made in the day Household characteristics Person characteristics Residence zone accessibility measures Tour main mode choice model Tour Main mode used for the tour Household characteristics Person characteristics Residence zone accessibility Tour main purpose Intermediate stop generation model Tour Number and purpose of intermediate stops made during tour Tour main purpose Tour main mode Number of tours made in day Trip mode choice model Trip Mode used for each trip in a tour Tour main mode Position of trip in the tour Trip destination choice model Trip Destination zone for each trip in a tour Trip purpose Trip mode and tour mode Trip origin zone Automobile travel time and distance between all zone pairs Zonal attraction variables Table 3-1. Model system components.

28 Improving aDa paratransit Demand estimation: regional Modeling previous 12 months. (Those characteristics describe the sampling universe for our survey sam- ple.) It was estimated by tabulating the number of actual registered users in the Dallas (DART) and Fort Worth (MITS) databases to the census-tract level and regressing that against tract-level data from the 2000 census, using data on the age, income, household size, and household type distributions within each tract. The output of this model is used in the ADA paratransit regis- tered population synthesis procedure described below, giving the size of the population to be synthesized within each census tract. ADA paratransit registered population synthesis: This procedure re-expands the survey sample, which was originally expanded to represent the entire region, but is now expanded to represent each census tract separately. With this procedure, a new sample expansion factor is generated for each sample member for each census tract, so that the sample is now representative of each tract. This is done using iterative proportional fitting (IPF) based on the characteristics of each sample member and on the population distribution of each tract relative to the region as a whole. The ADA paratransit registration rate model determines how many registered users there are in each census tract—thus the total size of the registered population that is synthesized in each tract. Allocation of ADA-registered population to zones: Using the best available estimate of the fraction of the population within each census tract living in each TAZ within the tract, synthetic households in each tract are randomly allocated to specific TAZs, assuming that the spatial distribution of the ADA-eligible population across zones in the tract is the same as the spatial distribution of the general population. Generalized ADA paratransit service levels: The user of the model system can set assump- tions regarding the travel time via ADA paratransit relative to driving one’s own car, the fare for ADA paratransit trips, and the punctuality of ADA paratransit in terms of the frequency of delays at the pick-up or drop-off point. Using tradeoff analysis from the Stated Preference data collected as part of our survey, these inputs are translated into a “generalized travel time” via ADA paratransit for each origin-destination zone pair in the region, and that generalized time is used as input to the disaggregate model components described below. Disaggregate Components The tour generation model: This model predicts the number of home-based tours that a particular person makes during the day, and, for each purpose, predicts the main purpose for making the tour. A small percentage of tours have multiple out-of-home stops with different activity purposes, so a “tour main purpose” is designated, as described in more detail below. The likelihood of making tours for various purposes is modeled as a function of household charac- teristics (e.g., size, income, and number of vehicles), person characteristics (e.g., age, gender, and type of disability), as well as measures of residence zone accessibility. In total, there were roughly 1,030 home-based tours recorded by the survey respondents during approximately 1,600 travel diary person-days, or an average of 0.63 tours per person-day. The tour main mode choice model: For each tour generated by the generation model, the main mode choice model predicts the primary mode used to make that tour as a choice of the following alternatives: car drive-alone, car shared-ride, ADA paratransit, scheduled public transit, other special transit, and walk/wheelchair. A small percentage of tours use more than one mode (e.g., ADA paratransit in one direction and car passenger in the other direction), so a “tour main mode” is designated as described in more detail below. The likelihood of choosing each mode is modeled as a function of the household, person, and residence zone characteristics modeled above for tour generation; of mode “accessibility” (a measure of overall ability to reach activities by each mode); and of the tour main purpose.

the aDa paratransit Demand Models 29 The intermediate stop generation model: As part of the 1,030 home-based tours in the data, there were approximately 300 “extra” stops made in addition to the stop at the primary tour destination. This small number of stops was deemed important enough to include in the model system, but not large enough to estimate a detailed model with all household and person charac- teristics. Therefore, a relatively simple model was estimated to predict the number and purpose of any extra stops made during each tour as a function of only the tour main purpose, the tour main mode, and the number of tours predicted to be made during the day. The tour mode is important because some modes, particularly the private automobile, can be used more flexibly than others, and therefore are more amenable to making multiple stops during a single tour. The trip mode choice model: Out of roughly 2,400 person-trips that are part of the survey data, there are only about 200 trips where the trip mode is not the same as the main tour mode. Again, this is important enough to represent in the model system, but there were not enough cases to estimate a detailed model. A simple classification model was created to predict the mode for each trip as a function of the tour main mode and the position of the trip in the tour (from home, back to home, or non-home-based). Trip destination choice model: Knowing the number and purposes of all stops made on a tour, and the mode used to reach each stop, the final model predicts the destination zone for each trip. This is modeled primarily as a function of the time to reach each possible destination zone via the trip mode, as well as the attractions (jobs of various types and households) within each zone. The trip destination model is applied beginning at home (the origin of the first trip in the tour) and predicting the destination of each trip from the current destination. The destination of the last trip does not need to be predicted, because the tour returns to the home zone by definition. The placement of trip destination choice at the “bottom” of the decision hierarchy is some- what different than the approach used in traditional four-step models and tour-based models. However, it is an approach often adopted in the United Kingdom and some other countries. In this study, the decision was made because of the distinct characteristics of the ADA-eligible population. Relative to the general population, this population tends to have less of a choice among competing modes of transportation, so that the choice of where to go is constrained by the availability of a mode to get there more often than the choice of travel mode is constrained by where one wants to go. Clearly, across any group of people, there will be instances of both types of constraints, and the choices of mode and destination are highly interdependent. On balance, however, conditioning the choice of destination on which mode is used was judged to be more behaviorally representative for this population context. Details of the Aggregate Models The ADA Paratransit Registration Rate Model This model predicts the percentage of the adult (age 18+) population within a census tract who are registered as eligible to use ADA paratransit service and have either made an ADA para- transit trip or else registered within the previous 12 months. (Those characteristics describe the sampling universe for our survey sample.) The dependent variable for the model was determined by first geocoding the addresses of all the DART and MITS clients who were in the sampling universe for the travel diary survey (including those who had made one or more trips in the preceding 12 months or had become eligible and registered within the preceding 12-month period but had made no trips in that time) and locating them by census tract. In total, this included 14,929 ADA-registered people spread across 746 different tracts in the Dallas-Fort Worth area. That is an average of 20 persons

30 Improving aDa paratransit Demand estimation: regional Modeling per census tract, with about 90 of those tracts having only one registered person, and 9 tracts having over 100 registered persons. One extreme case is a tract in the Fort Worth area that has 555 registered persons, almost 30% of the adults in that census tract. This is likely to be a tract that contains a number of assisted living or other type of senior residential facilities. Using 2000 census-tract-level data for the population by age group, the fraction of adults regis- tered to use ADA paratransit in each tract was calculated as the total number of registered people in our database divided by the census value for population age 18 or older in the tract. This value was regressed against various census-tract characteristics. Models were tested using the fraction and the log of the fraction as the dependent variable, with the log-linear models giving the best fit and most reasonable results. Also, models were estimated using all 936 census tracts in the region, using only the tracts with at least one person registered (723 tracts), and using only the tracts with at least two persons registered (642 tracts). The models using all tracts were rejected because: (1) most of these tracts are completely outside the DART and FWTA scheduled transit service areas, and thus not strictly eligible for ADA paratransit service; and (2) to implement a log-linear model, one must assign an arbitrarily low value to use as a substitute for the log of 0, and the model results can be sensitive to that assumption. The model based only on the 642 tracts with at least two persons registered was selected as the best model, and the results are shown in Table 9. It is most important to have a model that predicts well for tracts that have many registered users, because the tracts with very few users will not contribute much to the overall forecast model system results. The model in Table 3-2 is a simple least-squares linear regression model (with a logged depen- dent variable). The R-squared for the model, adjusted for degrees of freedom, is 0.723, which is quite high for a regression model with over 642 observations and only 14 parameters. Each variable in the model is discussed below. Most of the variables are based on 2000 census data for the distribution of population and households in each tract. Age group: In general, an older population will mean more likely ADA paratransit users. This was found for the age groups 40–59 and 60–74 relative to younger age groups. However, we could not find any effect for the fraction of the population age 75+. Dependent variable LN(Fraction of adult population registered) Tract observations used* 642 R-squared (adjusted) .723 Variable Coeff. T-stat Residual constant -6.611 -12.2 Fraction of population age 40-59 1.400 2.2 Fraction of population age 60-74 2.054 2.5 Fraction of population below poverty level 1.898 4.8 Median income in tract in 1999 ($K) -0.0059 -3.1 Fraction of HH 1 person single females 1.907 2.3 Fraction of HH 2+ person single female head 2.907 5.5 Fraction of HH non-family -5.430 -4.4 Average household size -0.099 -1.0 Fraction of HH within DART service area 1.618 15.9 Fraction of HH within FWTA service area 2.138 13.3 Tract is in MITS service area 0.378 2.2 Average walk mode accessibility measure -0.117 -3.3 Outlier tract with very high registration rate 2.855 4.8 * Tracts with 2+ people registered Table 3-2. Census tract ADA paratransit registration rate model.

the aDa paratransit Demand Models 31 Income: Two income variables were found to be significant. The first is that the registration rate increases with the fraction of the population with incomes below the poverty level. It also decreases with the median income in the tract, which captures much of the variation above the poverty level. Household size and composition: Two types of households in particular are associated with higher registration rates in tracts where these types of households are most prevalent. The first is females living alone in one-person households. The second is households of two or more people where the head of household is a single female. (This could be a single mother with children, or a single woman living with other adults.) On the other hand, for reasons not obvious, a higher fraction of non-family households is associated with lower registration rates. (These may be student areas and other areas with a high proportion of young adults sharing rental housing, which tend to attract younger, mobile residents.) In addition to these variables, the registration rate decreases slightly as the average household size increases, perhaps indicating more neigh- borhoods where many households have children present. Scheduled transit service areas: Two variables were used, representing the fraction of house- holds in each census tract within the DART and FWTA service areas. There are an average of 6 TAZs in each census tract, and each zone has been designated by NCTCOG as being in the DART or FWTA service area if the zone centroid is within 20 minutes walking time (1 mile) of a transit stop. If a TAZ is designated to be in the service area, then all people living in that zone are designated to be in the service area for the purposes of this calculation. The results show that these two variables are very highly significant. These variables do much of the job in explaining which tracts have very low registration rates (because much of the tract is not near any scheduled transit stops). DART versus MITS area: After all other variables are accounted for, it appears that the MITS area has a slightly higher registration rate than the DART ADA paratransit service area, but the difference is not large compared to other variables in the model. Walk mode accessibility: Using the TAZ-specific accessibility measures described above and in Table 3-1 (Model System Components), population-weighted accessibility measures were computed for each tract as a weighted average across all TAZs in the tract. One would expect the need for ADA paratransit service to be somewhat lower in an area with high walking accessibil- ity to retail and service establishments. The results in Table 3-2 show the expected result, with somewhat lower registration rates where walk accessibility is highest. Sensitivity to outliers: As mentioned above, there is one tract with very high ADA paratransit registration—over 30% of adults. To give some idea of the model’s sensitivity to outlier cases, the model was estimated, isolating the effect of this one tract (as in Table 3-2), or else not isolat- ing it so that it would contribute to all other estimates. It was found that the other estimates do not change very substantially when the “outlier” dummy variable is dropped, so the model even manages to explain the very high registration rate in that tract reasonably well. Results of the ADA registration rate model: The actual total number of in-scope registered persons is 7,134 in tracts in the DART service area and 4,426 in tracts in the MITS service area. Applying the regression model to the same data from which it was estimated gives predicted values of 7,193 registered persons in all DART tracts and 4,465 registered persons in all MITS tracts, both within 1% of the actual figures. The ADA registration rate model was run a number of times, each time increasing one of the input variables by 10% for every census tract in the region. This shows the sensitivity of the predicted registration rate to region-wide demographic shifts. The sensitivity test results shown in Table 3-3 are very similar for the DART and MITS regions. The elasticity (percent change in

32 Improving aDa paratransit Demand estimation: regional Modeling the prediction divided by the percent change in the input variable) is in the range of 0.2 to 0.4 for most of the variables tested. The walk mode accessibility variable has the largest elasticity, although it is not intuitively clear what changes in land use or pedestrian infrastructure would be needed to cause a 10% shift in that accessibility measure. ADA Paratransit Registered Population Synthesis The disaggregate models are designed to use as input a sample of individual households and people within each TAZ. A common practice in travel demand modeling is to use the Public Use Microsamples (PUMS) available from the census. In order to apply the ADA paratransit demand models, a similar sample of households with ADA-ADA paratransit-eligible individu- als is needed. Given that no such sample is actually available, a “synthetic population” is created within each census tract and TAZ using the following procedure. 1. For each tract, using census data, compare the regional population distribution to the tract- specific population distribution along three dimensions: • Age group: e.g., 18–39, 40–54, 55–64, 65–74 and 75+ • Income group: e.g., $0–15,000, $15–30,000, $30–60,000, and $60,000+ • Household type: e.g., 1 person male, 1 person female, 2+ person single female, 2+ person non-family, 2+ person family with children, 2+ person other 2. Using the full weighted representative survey sample, estimate the marginal and joint distri- butions across the three dimensions above for the 15,000 or so registered ADA users in the region. 3. For each tract in the region, estimate new marginal distributions for the ADA-registered population in that tract using a pivot-type procedure based on the total adult population characteristics in the specific tract relative to the entire region: Marginal fraction for ADA-eligible in total region Marginal fraction for Marginal f ( ) × = raction for full adult population in tract( ) ADA-eligible in tract Marginal fraction for full adult population in region( ) 4. For each tract in the region, using the joint distribution for the weighted survey sample from Step 2 as a starting point, apply iterative proportional fitting (IPF) to the expansion factors in the survey sample to calculate new, tract-specific expansion factors for each observation so that the distributions for the weighted sample in the tract match the adjusted marginal fractions from Step 3. 5. Using the best available estimate of the fraction of the population within each census tract living in each TAZ in the tract, randomly allocate each synthetic household in each tract to a Variable (Based On Model Application) Elasticity DART MITS Fraction of population age 40-59 0.34 0.32 Fraction of population age 60-74 0.18 0.18 Fraction below poverty level 0.36 0.41 Median income level -0.23 -0.21 Fraction single female 1 person HH 0.28 0.28 Fraction single female 2+ person HH 0.60 0.58 Fraction non-family HH -0.31 -0.29 Average household size -0.28 -0.28 Average walk mode accessibility -0.94 -0.90 Table 3-3. Elasticities for ADA registration rate.

the aDa paratransit Demand Models 33 specific TAZ. This assumes that the spatial distribution of the ADA-eligible population across zones in the tract is the same as the spatial distribution of the general population. This may not always be correct, but, unless there is more accurate local data available about the spatial distribution of the ADA-registered population, this is the best that can be done. (Such data is available in Dallas/Fort Worth, but the objective is to create a method that can be applied even in regions with less detailed data.) In theory, if the data were available, the process described above could be applied at a level smaller than a census tract, such as a block group or even a single census block or TAZ. For future applications it may be worth investigating if this same method could be applied using block group data, perhaps from the most recent years of the ACS survey. Note that if it were possible to apply Steps 1 through 4 above at a TAZ level instead of a tract level, then Step 5 would not be necessary. It is also worth mentioning that the above procedure will generally produce a synthetic sample that has more persons than the actual ADA-eligible population, with average expansion factors less than 1.0. As an alternative, it would be possible to sample just the estimated number of ADA-registered people within each tract, so that every case has an expansion factor of exactly 1.0, following the sampling procedure typically used for activity-based models. However, such a sampling method introduces extra stochastic simulation error that is not introduced with the re-expansion procedure above. Also, it would be difficult to incorporate the information pro- vided by the current sample expansion factors. In the re-expansion procedure outlined above, the information from the original expansion factors that adjust for survey oversampling is main- tained throughout the process. Generalized ADA Paratransit Service Levels The model incorporates sensitivity to ADA paratransit service variables, such as fare and punctuality, by means of factors that translate changes in the level of service variables into equiv- alent changes in travel time. Because travel time is a variable already included in the demand models, this method allows the model system to be sensitive to ADA paratransit fare and reli- ability as well. The resulting modified travel time is referred to as “generalized ADA paratransit travel time.” The procedure is necessary because all of the surveyed ADA paratransit users in the Dallas- Fort Worth area are offered virtually the same ADA paratransit service in terms of fares, reliabil- ity, reservation system, and so on, so it is not possible to impute the influence of those variables on demand from the travel diary data alone. The factors for converting level of service variables into equivalent travel are derived from a separate Stated Preference (SP) experiment that was included in the travel survey. Each respon- dent was given five tradeoff questions requiring a choice between various scenarios, each involv- ing randomized combinations of fare, travel time, late pick-up or drop-off, reservations policy, and time on hold to make a reservation. Further detail is provided in the survey report. Analysis of the respondents’ choices yields the coefficients shown in Table 3-4. Fare: The effect of fare was estimated separately for the lowest income group (<$15,000/year) and all others. Each group was about 50% of the sample. For both groups, fare has a significant coefficient with the expected negative sign, meaning that a higher fare reduced the probability of choosing the associated scenario. Also, as expected, the coefficient is larger (more negative) for the lower income group than the higher income group. In the “Equivalent Fare” column of Table 3-9, the equivalent of a dollar fare for the lower income group is set at $1.00. For the higher income group, a dollar of fare only has an equivalent utility value of about $.58 cents, which is

34 Improving aDa paratransit Demand estimation: regional Modeling calculated by dividing the fare coefficient of –0.168 for this group by the fare coefficient of -0.288 for the lower income group. The result is shown in the Equivalent Fare column. Another way to say this is that the higher income group values a dollar difference in fare 42% less than the lower income group. Travel time: The travel time coefficient is very significant. Each multiple of car time has a value of about $1.73 for the lower income group (the time coefficient divided by the low-income fare coefficient). In other words, if the travel time for a trip that takes 3 times as long as by car were reduced to a time only 2 times as long as by car, these respondents would be willing to pay an extra $1.73 in fare. If the average car travel time were, say, 30 minutes, then this would imply a value of time (VOT) of about $3.50 per hour, which seems reasonable for this low-income population. For the higher income group (which is still mostly in an income range less than $35,000 per year), the VOT would be about $5.50 per hour. In the Equivalent % Travel Time column of Table 3-4, the value for travel time is set arbitrarily as 100%. Then the coefficients for other variables are used to calculate equivalent percentages of travel time. For example, for the higher income group, the fare coefficient of -0.168 is 34% of the travel time coefficient of -0.497. This is interpreted as meaning that $1.00 of fare has an equivalent utility value of a change in travel time of 34% of the travel time by car for the same trip. For example, a $1.00 fare increase would be equivalent to increasing ADA paratransit travel time from twice the travel time by car to 2.34 times as long as the travel time by car. Note that actual ADA paratransit travel times relative to private car travel times in Dallas-Fort Worth are not known, so this result is used only to represent the effect of other variables in terms of equivalent changes in travel time. Reliability: Late pick-up and drop-off times: This variable also has the expected nega- tive sign and is very significant. To reduce the chance of a very late pick-up by 5% (1 in 20 trips), the person would be willing to pay about $1.06 more in fare. The variable was even more important when presented in terms of drop-off time at the destination instead of pick- up time at the origin. In that case, reducing the chance of a late drop-off by 5% is valued at $1.73 in fare. Each of these is also shown in terms of equivalent change in travel time. For example, to reduce the chance of a late drop-off by 5%, respondents would be willing to have an increase in travel time from twice as long as the same trip by car to 2.82 times as long as the same trip by car. Days in advance reservations are allowed: This variable also has a negative and significant effect. In this case, however, we had expected a positive effect from being able to reserve earlier. A possible explanation is that people interpreted this variable as the number of days in advance required to reserve a trip, instead of the number of days allowed. If people suspect that trips will fill up ahead of time, then they may interpret those two concepts to mean more or less the same thing. Given that requiring a reservation more than 1 day in advance is not permitted under ADA regulations, this result has no application in the model. Variable Coefficient T-statistic Equivalent Fare Equivalent % Travel Time Fare($) - lowest income segment -0.288 -4.5 $ 1.00 58 % Fare($) - higher income segment -0.168 -2.2 $ 0.58 34 % Travel time- multiple of car time -0.497 -8.0 $ 1.73 100 % Late pick-up- times out of 20 trips -0.305 -6.5 $ 1.06 61 % Late drop-off- times out of 20 trips -0.406 -9.7 $ 1.41 82 % Days in advance reservations are allowed -0.0599 -6.8 Not used Not used Time may wait on hold (min) 0.0258 1.0 Not used Not used Table 3-4. Stated preference estimation results.

the aDa paratransit Demand Models 35 Time may have to wait on hold on the telephone: This variable also has an unexpected sign, with a slight positive coefficient for more minutes spent waiting on hold. In this case, however, the result is not significantly different from zero, so we can assume that the effect of this variable is negligible compared to the other ones, and omit this variable from model application. This does not mean that hold time is actually unimportant, but the Stated Preference procedure was not able to gauge its importance. Predicted sensitivity to service variables: To see how fares, travel time, and on-time service affect travel demand in the model, the model system was run to test the sensitivity to ADA paratransit travel time, which is a variable already included in the choice models (described in the next section). The resulting elasticities with respect to changes in ADA paratransit travel time are The number of ADA paratransit passenger trips = -0.5 The number of ADA paratransit passenger-miles = -1.1 The total number of trips made by ADA-eligible persons = -0.1 This means that if ADA paratransit travel time increased by 10%, the number of passen- ger trips would decrease by 5%, and the ADA paratransit trips would become shorter, on average, so the number of passenger-miles would decrease by 11%. Most of the decrease in ADA paratransit trips would be made up by a corresponding increase in trips by other modes (mode shift), but not all of them—there would be a 1% decrease in total trips made by ADA-eligible persons (trip frequency shift). This elasticity for total trip-making is quite small, but still quite a bit higher than trip “suppression” elasticities estimated for the general population, which are typically much smaller than -0.1. Conversely, the mode- specific elasticity of –0.5 is toward the low end (in absolute value) of the range of values typically estimated for the general population, based on the experience of the research team. On average, the ADA-eligible population tends to have fewer mode options than the general population, which would explain the results of relatively less mode switching and more trip suppression. In the model, the effects of changes in ADA paratransit fare and ADA paratransit reliability are incorporated by making the equivalent percentage change in ADA paratransit travel time, as taken from the right-hand column of Table 3-4 above. The results of changing these variables in the model system base scenario are shown in Table 3-5. The first row shows the same sensitivity to travel time change as described above. The next two rows show the predicted effects of a $1.00 fare change for the income segments above and below $15,000 per year. At the existing fare level in Dallas and Fort Worth of $2.75, this would be a fare elasticity of –0.41 for the lowest income group and –0.23 for the higher income groups. These are in the same general range as fare elasticities typically estimated for scheduled transit riders. The model is quite sensitive to punctuality, where, following the Stated Preference results, a change in punctuality of 5% (1 in 20 trips) has more effect on demand than a $1.00 change in fare. Change in Variable Change in ADA Paratransit Trips Change in Trips by All Modes 10% increase in travel time 5% decrease 1% decrease $1 fare increase: lowest income segment 12% decrease 2% decrease $1 fare increase: higher income segment 7% decrease 1% decrease 5% (1 in 20) more trips are late 14% decrease 2% decrease Table 3-5. Predicted trip changes for service variables.

36 Improving aDa paratransit Demand estimation: regional Modeling Details of the Disaggregate Models Disaggregate Model Input Data Three main types of data were used to estimate the disaggregate models: 1. Travel survey data: Full trip diary data for 2 days for each of 800 respondents 2. Zonal attraction data: For each of 5,386 designated TAZs in the NCTCOG region, the fol- lowing variables were used: • The number of resident households • The number of resident people • The number of service jobs • The number of retail jobs • The number of other jobs (called “basic” employment) • The number of hospital/medical center jobs (an important subset of service jobs) 3. Zone-to-zone travel time and cost matrix data: For each origin-destination zone pair, NCTCOG provided network matrices of the best path values of • AM peak period automobile travel times • PM peak period automobile travel times • Off-peak period automobile travel times • AM peak period transit variables (fare, in-vehicle time, wait time, walk time) • Off-peak period transit variables (fare, in-vehicle time, wait time, walk time) The times are from network “skim” matrices based on the shortest path through a congested network loaded with a number of trips appropriate to the specific time period. The automobile skims used are for single-occupant vehicles, not including use of any carpool-only lanes. Using this data, we also created composite accessibility variables for travel from each TAZ. These variables give a measure of ability to reach activities of interest by each mode. The acces- sibility variables are specified as Accessibility LN sum across destinations Att= raction variable EXP impedance variable( )[ ]( ) This is essentially the expected value (logsum) from a simple destination choice model, which is a formulation often used in travel demand modeling and is consistent with discrete choice theory. The specific attraction and impedance variables are different for each mode. Table 3-6 shows the measures created for this study and the corresponding definition of the attraction and impedance variables. ADA paratransit accessibility (not shown in the figure) is calculated using the same equations as the automobile accessibility variable, but substituting ADA paratransit “generalized time” for the automobile travel time. ADA paratransit generalized time is initial- ized to be the same as automobile time, but then adjusted according to the user input changes for ADA paratransit travel time, ADA paratransit fare level, and ADA paratransit fare, using the Stated Preference analysis results. ADA paratransit accessibility is used in the tour generation Accessibility measure Attraction variable Impedance variable Off-peak automobile Service + retail jobs (Off-peak outbound automobile time + off- peak return automobile time) / 40 minutes Peak auto Total jobs (AM peak outbound automobile time + PM peak return automobile time) / 40 minutes Walk Service + retail jobs (Off-peak outbound automobile distance + off-peak return automobile distance) / 2 miles Off-peak transit Service + retail jobs (Off-peak transit in-vehicle time + 2.0* Off-peak out-of-vehicle time) / 80 minutes Peak transit Total jobs (AM peak transit in-vehicle time + 2.0* AM peak out-of-vehicle time) / 80 minutes Table 3-6. Zone accessibility measures.

the aDa paratransit Demand Models 37 and tour mode choice models, while the generalized ADA paratransit time is used in the model of destination choice for ADA paratransit trips. Many regions have attraction employment variables split into more categories than the list above, including government employment, office employment, food service employment, and entertainment employment. An advantage of using the few categories available from NCTCOG, however, is that the model will be applicable in most other regions, because almost all regions have a split of jobs into at least the three categories of service, retail, and other. Many regions may not have hospitals and medical centers coded as a separate employment category, but could generate such data from available data sources if needed for this model. Scheduled Transit Service Data Ideally, the model would use transit times and fares for transit trips. As mentioned above, NCTCOG did provide origin-destination (O-D) matrices for scheduled transit times and fares, for both peak and off-peak periods. However, when using this data together with the survey records, it was found that the NCTCOG matrices only have transit connections for 4 of the 57 O-D zone pairs for which transit trips were actually reported in the survey data. We checked carefully for possible problems in our geocoding of the trip-ends to the NCTCOG zone system and did not find errors. We also input various reported transit trip origin and destination addresses into the Dallas and Fort Worth online transit route information systems and found that there are actually valid transit connections for those address pairs. So, the problem in this case appears to be incomplete coverage of transit connections in the NCTCOG transit matrices. This is a typical occurrence in travel modeling, where some transit trip observations need to be rejected from the models because there are no network time and cost data for the O-D zone pair of the observed trip. In this case, however, the problem affects most of the scheduled transit trip observations, for which we have very few to begin with. As a result, we have estimated the models described below without making extensive use of the NCTCOG transit time and cost matrices, but in a way that still allows us to keep the scheduled transit mode alternative in the models. In terms of applicability of the model, there is some attraction to this approach, because it will make the resulting model system much easier to use, especially for smaller regions and ADA paratransit agencies that do not have access to scheduled transit network matrix data. Because the 29 scheduled transit tours in the survey are only 2.9% of all tours reported and there are over 22 times as many ADA paratransit tours as scheduled transit tours, the inability to use detailed scheduled transit travel time and cost data has little effect on the overall results. The Tour Generation Model This model predicts how many home-based tours (a chain of two or more trips starting and ending at home) a person will make during a day, as well as the main purpose of each of those tours (the activity purpose at the main tour destination). The following purposes were distin- guished in the data: • Dialysis • Other medical purpose • Work/work-related • School/school-related • Adult daycare • Shopping • Other errands • Personal business • Eat a meal

38 Improving aDa paratransit Demand estimation: regional Modeling • Civic/religious • Recreation • Social visit In cases where more than one destination was visited during a tour, the primary destination and purpose was defined as the one with the highest priority activity purpose, with the assumed priority order as above—medical the highest and social visit the lowest. In cases where the same activity purpose was carried out at two different destinations within a tour, the primary tour destination was selected as the one with the longest duration of stay at that location. A “nested logit discrete choice model” was used to represent the choice to make a tour during the travel day for any of the different purposes or else stay at home. (Saying the model is “nested” is a technical matter not always clearly related to behavioral issues. Nesting is a way of represent- ing that certain alternatives are more closely related than others in statistical terms.) If the person makes one tour, then there is a choice to make another tour during the day or to stay at home and not make any more tours and so on. In cases where a person makes another tour, the model also predicts the primary purpose of the tour. It is specified as a nested model across nine different alternatives, as shown below: Level 1: Alternative 1: Make another tour Alternative 2: Stay home for the rest of the day Level 2: Eight alternatives nested under Alternative 1 above: 1A. Dialysis/other medical tour 1B. Work tour 1C. School tour 1D. Adult daycare tour 1E. Shopping/restaurant tour 1F. Recreation tour 1G. Social visit tour 1H. Personal business/other errand/civic/religious tour Each of the nine alternatives (1A-1G and 2) has explanatory variables related to the likeli- hood of choosing that alternative. The “base” alternative was specified as 1H, personal business/ errands/civic and religious, so the variables for the other tour purposes represent the likelihood of making a tour for that purpose relative to personal business. The model results are shown in Table 3-7. A wide variety of different variables was tested, and, after discussion of initial results, a selection was made based on statistical and behavioral considerations of which variables to keep in the model. In Table 3-7, for each purpose and each explanatory variable, two numbers are shown: 1. A coefficient, which represents the strength of the relationship; the higher the coefficient, the more the variable increases the likelihood of making a tour for this purpose. A negative coefficient means that the variable makes it less likely that a person will make a tour for this purpose. 2. A T-statistic, which is related to the statistical probability that the estimated relationship is real, i.e., that the coefficient is actually different from zero. T-statistics of 1.8 or greater are generally interpreted as meaning that a coefficient is significantly different from 0, although the significance is related to sample size as well, and it is sometimes valid to maintain variables that are somewhat less significant but have a reasonable outcome based on experience with other travel behavior models.

the aDa paratransit Demand Models 39 Model name Tgen2bw # Observations 2612 Final log-likelihood -2664.0 Rho squared w.r.t. 0 0.536 Rho squared w.r.t. constants only 0.229 Nesting of tour purposes under stay-at-home alternative Coeff= 0.727 t-stat= 5.2 Choice medical tour work tour school tour adult daycare tour shopping / meal tour recreation tour social visit tour personal business tour stay at home Chosen unweighted 340 159 44 68 204 69 20 125 1583 Chosen weighted 331 97 31 49 221 88 28 128 1640 Unweighted Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Variable % of observ. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. Age 16 to 39 20.4% -0.701 1.179 1.012 -1.232 -2.9 4.2 1.9 -3.4 Age 65 to 74 24.2% 0.346 1.172 1.5 3.9 Age 75 and up 13.7% 0.564 0.963 0.528 1.124 1.187 0.937 1.9 1.5 1.8 2.9 2.4 3.2 Female 66.0% -0.748 0.486 1.396 -2.2 2.7 2.5 Sensory impairment 23.7% 0.966 2.4 Physical impairment 72.3% 0.980 0.331 0.348 4.8 1.0 1.7 Mental impairment 22.7% 2.068 -1.476 5.3 -1.7 Income under $15,000 59.6% -0.426 1.669 -0.503 -2.8 4.3 -1.1 Single-person HH 38.2% -0.760 -2.722 0.696 -4.5 -2.3 3.5 No cars in HH 53.5% -2.994 -0.469 -0.331 -4.0 -2.7 -1.3 Full-time worker 10.3% 0.819 7.568 1.819 1.9 8.0 4.6 Part-time worker 8.0% 6.715 7.4 Full-time student 5.6% 4.107 7.5 Part-time student 4.1% 4.160 7.5 Proxy answers 8.1% 0.511 1.7 Second diary day 48.7% 0.360 2.5 Already made 1 tour 36.0% 3.781 4.3 Already made 2 tours 3.2% 4.323 4.6 Already made 3 tours 0.2% 6.212 2.8 Home zone accessibility 100.0% 0.569 0.569 0.569 0.569 0.569 2.6 2.6 2.6 2.6 2.6 DART area 51.3% 1.145 -0.652 2.0 -1.8 Residual constant 100.0 7.609 2.669 3.503 -1.435 -0.207 -0.934 -2.885 8.836 2.6 0.9 1.2 -2.7 -0.9 -3.8 -5.1 3.1 Table 3-7. Tour generation model results.

40 Improving aDa paratransit Demand estimation: regional Modeling Weighting of observations: In order to gain efficiency in data collection and heterogeneity in the sample, the survey sample was drawn using a stratified approach, oversampling frequent ADA paratransit users and younger age groups. In a tour frequency model, the choice probabil- ity of making a tour is not independent of the probability of being in the sample, particularly given that we oversampled more frequent travelers. To adjust for this, we used weighted logit estimation, weighting each observation using the expansion factors described earlier, so that the overall weighted sample is representative of the full ADA-eligible population. The weighting fac- tors were also normalized to have an average value of 1.0 in the estimation data so that the total weighted number of observations is the same as the unweighted total (2,612 observations). The top rows of Table 3-7 show both the unweighted and weighted frequency with which each choice alternative is observed in the estimation data. The use of weighting reduces the choice frequency for the types of tours made most regularly (e.g., work, school, and adult daycare) and increases the frequency for the types of discretionary tours made on a less regular basis (e.g., shopping, recreation, and social visits). As one would expect, the weighting also increases the frequency of the stay-at-home alternative. Age group: Dummy variables were included for the age groups 16–39, 55–64, 65–74 and 75+. A dummy variable is 1 if the person is in the category (i.e., in a certain age group) and 0 other- wise. The model results show the impact of being in each category (age group). The column to the left shows, for instance, that the 16–39 age categories comprises 20.4% of the unweighted sample. Persons age 40–54 were designated as the “base” age group, and all other age group effects are interpreted relative to that base category. For people in the base age group, all of the dummy variables are zero. (In a logit model, the effects of variables must all be relative to the effects of some other category, so a “base” category always needs to be specified where the effect is constrained to 0.) The base age group is not shown in Table 3-7 (nor is the 55–64 age group, because no significant effects were found for that age category relative to the base group). The results show that, all else being equal, those in the youngest age group are less likely to remain at home, less likely to make medical tours, and more likely to make recreation and social visit tours. (Positive coefficients indicate that a variable is associated with an increase in the probability of an alternative being chosen, and negative coefficients just the opposite.) Relative to the other age groups, those in the oldest two age groups are more likely to stay at home instead of traveling, as one might expect. They are also more likely to make tours for medical purposes. Those in the oldest age group are also somewhat more likely to travel for medical purposes, adult daycare, and various discretionary purposes. Gender: After other variables are accounted for, there are few differences related to gender. The base case (dummy variable = 0) is male and is not shown. Females make somewhat fewer tours than males for the adult daycare, but somewhat more tours for shopping and social visits. Type of impairment: Respondents were asked if they were subject to sensory/visual impair- ment, physical/motor impairment, or mental/cognitive impairment, or any combination of those. A respondent could have any number of impairments, so for each impairment the base case is not having that impairment. These variables are self-reported and not objective catego- rizations and may not be useful in a forecasting model for the general population. However, they may be useful for research purposes for explaining behavior. The results show that those with physical impairments are more likely to travel for medical, work, and shopping purposes, while those with sensory/visual impairment are more likely to go to adult daycare. Those with mental impairments are most likely to attend adult daycare and somewhat less likely to make social visit tours. Income level: Only one income group was tested, under $15,000/year, the lowest survey category, which includes a full 60% of the sample. The base case is income over $15,000 per year, including 40% of the sample. None of the higher income groups have large enough samples to

the aDa paratransit Demand Models 41 estimate income effects reliably. Compared to those with higher incomes, those with the low- est incomes are more likely to attend adult daycare, but less likely to travel for social visits and medical purposes. Household size: It was hypothesized that those living alone may have different behavior from those living with others, who make up the base case. The results show that those in single-person households are somewhat less likely to travel for medical and adult daycare tours, but somewhat more likely to travel for shopping (perhaps because they do not have others to do the shopping for them). Car ownership: Those in households with no cars are somewhat less likely to make adult day- care tours, shopping/meal tours, and recreation tours. Another variable specified as the number of cars per licensed driver in the household was also tested, but did not show any significant effects. Overall, car ownership has less influence in the trip generation model than it does in the mode choice model (reported below). Employment status: Not surprisingly, full-time workers and part-time workers are much more likely to make work tours than non-employed people (the base case) are. Full-time work- ers are also more likely to make medical and recreation tours. Student status: As one would expect, full-time and part-time students are the most likely to make school tours. No other significant result was found related to student status. Proxy responses: Those whose diary information was reported by proxy (another person) have a positive coefficient for staying at home. This suggests that there is some under-reporting bias of travel related to proxy responses. It is also possible that proxy answers occurred most often for those with severe mental incapacity, and these individuals do actually travel less than others. In any event, the effect is fairly small, only applies to 8% of the survey sample, and can be adjusted for in model application. Second diary day: Relative to the first diary day (the base case), respondents were more likely to choose the “stay-at-home” alternative for the second diary day data. As the diary days were selected randomly, this indicates an effect of respondent fatigue where people were less likely to record or report their travel on the second day relative to the first. In any case, we can estimate this effect and adjust for it when applying the models. Numbers of tours already made: As one would expect, the more tours that somebody has already made in the day, the more likely they are to stay at home for the rest of the day. Note that only a very small percentage of the sample made more than one tour in a day. Residence zone accessibility level: The intent of this variable is to test whether having more places available to go to increases trip-making for some purposes. An average of the off-peak automobile accessibility measure described in Table 3-6 and the weighted ADA paratransit-specific accessibility was used to represent this effect, given that most trips by registered users are made either as private automobile passengers or ADA paratransit pas- sengers. The number of service and retail jobs is used to represent the level of attraction; for example, retail jobs indicate the presence of retail activities that would attract shopping trips. (“Accessibility” here refers not to accommodation for people with disabilities but to the ability of travelers in one zone to reach potential destinations in other zones.) In the model results, a significant positive effect of this accessibility was found on the likelihood of mak- ing tours for discretionary purposes (all purposes except medical, school, and work). When estimated separately for each purpose, the effects were similar, but not significant, so the variable was estimated jointly across the purposes. No effect was found for medical, school, or work purposes. These tours tend to be non-discretionary, so their frequency will not be greatly influenced by accessibility.

42 Improving aDa paratransit Demand estimation: regional Modeling Service area: About 51% of the observations are from those living in the DART (Dallas) ser- vice area and the other 49% are from the MITS (Fort Worth) service area. After accounting for all other variables, there are only minor differences between the residents of the two areas, with those in the DART area somewhat more likely to make school tours and somewhat less likely to make adult daycare tours than those in the Fort Worth area (the base case). Residual constants: The alternative-specific constants are residual to the other variables and have no behavioral interpretation in themselves—their values depend on what other variables are included in the model specification. Nesting parameter: The nesting of the eight tour purpose alternatives versus the stay-at-home alternative has a logsum coefficient of 0.727 and is significantly different from both 0 and 1, indi- cating that this is a statistically correct nesting structure. In summary, this model suggests which variables contribute most to the level of mobility of the ADA-eligible population. It appears, as might be expected, that the frequency of travel decreases somewhat with age and increases somewhat with automobile ownership, but that different types of people are likely to travel for different purposes. The Tour Mode Choice Model The tour mode choice model is the choice among six main modes: • ADA paratransit • Other specialized transit/shuttles • Regular scheduled transit • Car shared-ride • Car drive-alone • Walk/wheelchair/scooter In cases where more than one of these modes was used on a tour (a small minority of the observed tours), the main tour mode was specified as the highest priority mode in the above hierarchy, where ADA paratransit is the highest and walk is the lowest. The mode choice results reported in Table 3-8 are generally what one would expect, with very significant car ownership effects and some differentiation by tour purpose (included as dummy variables). Weighting of observations: As in the trip generation model, our sample was non-representative because we had oversampled on frequent ADA paratransit users, so weighted estimation was used to adjust for that fact. Looking at the unweighted versus weighted mode shares at the top of the table, we see the main difference in the ADA paratransit choices (666 unweighted versus 510 weighted) and private car choices (251 unweighted versus 403 weighted), while the weighted choices for the other mode alternatives increase only slightly. Mode availability: All modes were set available for all tours, with one exception: automobile drive-alone is only available if the respondent has a license and the household owns one or more cars. This was the case for only 178 of the 1,022 observed tours. Mode nesting structure: We tested various mode nesting structures, which indicate how certain choices are more closely related than others. A structure that proved reasonable and statistically significant was to group the modes into three nests as follows: 1. Road-based, flexible route and schedule: (1a) Car shared-ride, (1b) Car drive-alone, (1c) ADA paratransit, (1d) other specialized transit

the aDa paratransit Demand Models 43 Social tour 2.0 -1.008 -2.1 DART area 52.3 0.268 1.7 Residual constant 100.0 -6.534 -0.277 -4.327 -8.444 -1.519 -8.1 -1.0 --4.9 -2.6 -1.0 Model name mode2bw # Observations 1022 Final log- likelihood -971.1 Rho squared w.r.t. 0 0.429 Rho squared w.r.t. constants only 0.179 Nesting of scheduled transit and walk in separate nests Coeff. = 0.646 T-stat = 3.5 Choice ADA paratransit Other special transit Car shared- ride Car drive- alone Scheduled transit Walk/ wheelchair # chosen- unweighted 666 16 226 25 29 60 # chosen- weighted 510 18 334 69 32 63 unweighted Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Variable % of sample T-stat. T-stat. T-stat. T- stat. T-stat. T-stat. Mode accessibility 100.0 0.877 0.877 0.877 0.877 0.877 0.877 logsum 2.3 2.3 2.3 2.3 2.3 2.3 Age 16-39 22.1 1.780 1.9 Age 40-54 20.8 1.468 1.5 Age 55-64 25.1 2.794 2.6 Female 64.0 -1.674 -2.8 Sensory impairment 26.1 -1.115 -0.860 -6.0 -1.7 Income under $15,000 51.7 -1.558 -1.303 - 1.263 -2.9 -2.4 -2.0 No cars in HH 49.3 -1.561 4.999 -8.4 1.9 Cars per driver in HH 50.7 4.245 4.8 Work tour 15.4 1.960 2.654 5.5 2.3 School tour 4.3 1.559 3.439 2.9 2.9 Medical/dialysis tour 23.2 0.162 2.588 0.7 3.8 Adult daycare tour 6.7 1.348 3.6 Shopping/meal tour 19.7 -1.494 -5.7 -0.7 Recreation tour 6.9 -0.229 Table 3-8. Tour mode choice model results.

44 Improving aDa paratransit Demand estimation: regional Modeling 2. Road-based, fixed route and schedule: (2a) Regular scheduled transit 3. Non-road-based: (3a) Walk/wheelchair The estimated nesting logsum coefficient of 0.646 is significantly different from both 0 and 1, indicating closer substitution between the four flexible road-based modes than across the three groups. Several other nesting structures were tested during model estimation—for instance nesting ADA paratransit with regular scheduled transit—but none gave statistically acceptable results with logsum coefficients between 0 and 1. Different types of variables were tested, most of them defined in the same way as for the tour generation model above. The effects of each variable are described below. Mode-specific accessibility logsum: Because the tour mode choice model is applied before destination choice, we do not know exactly where each tour goes when we predict mode choice. For that reason, we use the accessibility measures defined in Table 3-6 to help explain the choice of mode as a function of overall accessibility by each mode from the resi- dence zone to all possible destinations. The off-peak automobile accessibility logsum was used for all alternatives except for scheduled transit and walk/wheelchair, which used the off-peak transit accessibility and walk accessibility measures, respectively. The resulting coef- ficient of 0.877 is significantly different from 0, which shows that differences in accessibility between ADA paratransit, walk, transit, and automobile across all destinations influence the choice of tour mode somewhat. Age group: The only age effects found are that the walk/wheelchair mode is most likely to be chosen in the younger age groups under age 65. Gender: Females are less likely to choose the slowest mode, walk/wheelchair. Similar trends for gender and age are typically found for the walk mode in regional travel models. Impairment type: Although variables were tested for all three impairment types, significant effects were found for only one of them—those with sensory/visual impairments are somewhat less likely to choose ADA paratransit or walk/wheelchair (so, by inference, somewhat more likely to travel as car passengers). Income level: Those in the lowest income category are less likely to travel by ADA paratransit or by private auto. This means that they travel by walk/wheelchair, scheduled transit, or spe- cialized transit/shuttles instead; however, the sample was too limited to estimate coefficients for these modes. Household size: This variable was tested on various modes, but no significant results were obtained. Car ownership: Those with no cars in the household (about 50% of the cases) are more likely to choose scheduled transit and less likely to choose car shared-ride. (Also, car drive-alone is not available for those households.) For households that do own cars, a variable was included as the number of cars per licensed driver in the household, capped at a maximum value of 1.0. Those in households with more cars per driver were more likely to choose the car drive-alone mode. Although the model shows no direct effect of car ownership on the likelihood of choosing ADA paratransit, there is a strong indirect effect, because travel by car is the main alternative among the respondents to traveling by ADA paratransit. Tour primary purpose: Because of the limited number of tours in the data, we did not esti- mate separate mode choice models for each tour purpose. Instead, we tested dummy variables to look for cases where certain modes are more likely to be used for certain types of tours. The results show that ADA paratransit is more likely to be used for the most regular tour types, including work, school, and adult daycare tours, and less likely to be used for several of the

the aDa paratransit Demand Models 45 discretionary purposes—shopping, meals, recreation, and social visits. Other specialized transit services are most likely to be chosen for work, school, and medical purposes, corresponding to the types of institutions/facilities most likely to offer those services. Service area: About 52% of the observations are from those living in the DART (Dallas) service area. After accounting for all other variables, those in the DART service area are slightly more likely to choose ADA paratransit than those living in the MITS service area, but the effect is small. Residual constants: The alternative-specific constants are residual to the other variables and have no behavioral interpretation in themselves—their values depend on what other variables are included in the model specification. The Intermediate Stop Generation Model The intermediate stop model is specified in a similar way as the tour generation model. For each half of a tour (the first half from home to the main tour destination and then the second half from the main tour destination back to home), this model predicts how many intermedi- ate stops are made (if any) and what the purpose of each stop is. The top rows in Table 3-9 show that out of 2,342 choice observations in this model, 2,062 of the choices (unweighted) are to make no intermediate stops, meaning that there are only 280 such stops observed in the survey data. Most of those stops are for shopping/meals (121) or personal business/errands (78). The weighted data shows an even higher percentage of stops for those discretionary purpose stops. Apart from the constants, all of the variables in this model are for the “No (more) stops” alter- native, with a positive coefficient meaning fewer extra stops per tour and a negative coefficient meaning more extra stops per tour. Only the residual constants are used to determine which purpose each stop is for. The model is specified this way (1) because there are very few observa- tions for most stop purposes, and (2) because of the hierarchical way that the main tour purpose is determined, the tour purpose can limit the possible stop purposes on any tour. For example, medical stops can only be on medical tours—if they were on any other tour, then medical would have been designated as that tour’s main purpose. Similarly, work stops can only be found on work tours and medical tours, and so on. So, the tour purpose already goes a long way toward determining the stop purpose. The explanatory variables in the model shown in Table 3-9 are described below. Tour main mode: Three tour main modes are used as explanatory variables. As expected, the tour main mode is very important in explaining the number of extra stops on a tour. ADA para- transit tours tend to have fewer extra stops, while private car tours tend to have more. The effect is particularly strong for car drive-alone tours, which are the most flexible in terms of making multiple stops along the tour. These mode-specific differences are why we chose to model extra stop generation after modeling the main tour mode. Tour main purpose: Five tour main purposes are used as explanatory variables. Because of the time schedules and constraints particular to specific types of tours, tours for some purposes may tend to include more extra stops. The results show that the less discretionary tour purposes (work, school, medical, adult daycare) all tend to include fewer extra stops, while shopping/meal tours include somewhat more stops, on average. These differences, however, are not as large as the mode-specific differences described above.

46 Improving aDa paratransit Demand estimation: regional Modeling Age 40-54 22.5% -0.323 -2.2 Physical impairment 70.2% 0.707 3.9 Sensory impairment 24.8% 0.543 3.0 Proxy data 6.2% 0.458 1.6 Number of tours in day 100.0% 1.066 5.1 1st half tour 46.7% 1.297 5.4 2nd half tour- No. of trips in 1st half tour 53.3% 0.254 1.6 Already made 1 stop 11.2% -0.394 in half tour -2.3 Already made 2 stops 3.6% 0.184 in half tour 0.7 Already made 3 stops 1.2% 1.224 in half tour 2.3 Residual constant 100.0 -1.606 -2.748 -0.923 -2.342 0.675 -1.632 -1.016 0.557 -3.5 -3.7 -2.9 -4.1 5.2 -6.6 -5.2 1.2 Model name sgen2bw # Observations 2342 Final log- likelihood -1239.2 Rho squared w.r.t. 0 0.707 Rho squared w.r.t. constants only 0.123 Choice medical stop work stop school stop adult daycare stop shopping / meal stop recreation stop social visit stop personal business stop No (more) stops # chosen unweighted 8 4 11 2 121 21 35 78 2062 # chosen weighted 5 2 12 3 179 20 38 91 1991 weighted Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Variable % of sample T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. ADA paratransit tour 44.9% 0.439 1.7 Car drive-alone tour 9.3% -1.627 -5.8 Car shared-ride tour 35.0% -0.755 -3.0 Medical/dialysis tour 33.7% 0.496 2.5 Work tour 9.2% 0.667 2.1 School tour 2.7% 5.0 Const Adult daycare tour 4.8% 0.419 1.2 Shopping/meal tour 25.3% -0.275 -1.4 Income under $15,000 60.6% 0.333 2.4 Table 3-9. Intermediate stop generation model results.

the aDa paratransit Demand Models 47 Household income: Those in lower income households tend to make fewer extra stops per tour, on average. It is a typical result in travel studies that the number of activities outside the home tends to increase with income. Age group: Those in the 40–54 age group tend to make more stops per tour than others—this tends to be one of the busiest age groups in general. Type of impairment: Those with physical and sensory impairments make the fewest extra stops per tour. Complex, multi-stop tours may be more difficult physically for those people to manage. Proxy data: People whose travel diary data was reported by proxy tend to have fewer extra stops per tour. The person reporting the travel may not know all of the details of the person’s tour, or people who need to use proxy reporting may actually make fewer stops. In either case, the effect is moderate and only applies to 6% of respondents. Number of tours in the day: In activity-based models, it is a common finding that people who make more tours during a day tend to make fewer stops per tour—instead of chaining trips together into a single tour, they tend to split them across multiple tours. The result here shows the same—the more tours generated in the day, the more likely to choose the “no stops” alternative. Outbound or return tour half: There tend to be fewer extra stops made on the first (out- bound) tour half than on the second (return) half. This is also a typical result, as people often go to the main/most important activity of their tour first upon leaving home and then make extra stops on the way home, particularly for longer, scheduled activities such as work and school. Number of trips made in the first half tour: In general, the more extra stops that some- body has made on the first half tour, the fewer stops they will need to make on the return half. This coefficient is not very large, however, implying that some people make stops on both halves. Number of extra stops already made in the current half tour: If somebody has already made one extra stop in the current half tour, they are actually more likely to make another stop than somebody who has not made any extra stops yet. This result implies that extra stops can often occur in pairs. However, the coefficients for people who have already made two or three stops in the tour go in the other direction, meaning that it is very rare to make more than two extra stops in a half tour. Residual constants: In this model, the residual constants partly determine the purpose of any intermediate stops. The constants for all purposes other than shopping/meal and personal business/errand are significantly negative, because those other types of intermediate stops are much less common. The Trip Mode Choice Model The trip mode choice model is actually just a simple table that gives the probability of each possible trip mode as a function of (1) the main tour mode and (2) the position of the trip in the tour—from home, back to home, or non-home-based (NHB). The survey observations that this model is based on are shown in Table 3-10. In total, there are 1,021 trips from home, 1,021 trips returning back to home, and 315 NHB trips, indicating that most tours are simply one trip out and another trip back with no extra stops. Also note that the large majority of the trips are on the diagonals, with the trip mode the same as the tour mode. The function of the trip mode choice model is to predict those few cases where the trip

48 Improving aDa paratransit Demand estimation: regional Modeling mode is different from the tour mode. Most of those cases are car passenger trips as part of ADA paratransit tours (97 cases) and walk/wheelchair trips that are part of ADA paratransit or scheduled transit tours (70 cases). There are only 34 other cases across all cells. Choice distribution fractions based on the data in Table 3-10 are shown in Table 3-11. The diagonal nature of the tables (highlighted with bold font) is based on the hierarchy used to define the main tour mode, where ADA paratransit tours can include any other modes, but ADA para- transit trips can only be part of ADA paratransit tours. At the other end of the hierarchy, walk/ wheelchair tours can only include walk/wheelchair trips, but walk/wheelchair trips can be part of any tour. Notice that almost all private car tours (as a driver or passenger) include only private car trips and no trips by other modes. In model application, these fractions will be applied “as is,” conditional on tour mode and trip position within the tour. The Trip Destination Choice Model Finally, once we have predicted how many trips are made as part of a tour and what mode is used for each trip, we predict the exact destination zone location for each trip. This model is specified to work somewhat differently depending on whether a tour has a single out-of-home destination or multiple destinations. Single-destination tours: This is the majority of all tours, particularly for ADA paratransit tours. For these tours, the destination choice model is applied just once to predict the location zone of the single out-of-home destination. The model has two main parts: Trip mode Trip type Tour mode ADA paratransit Special transit Scheduled transit Car passenger Car driver Walk/ wheelchair Total From home ADA paratransit 630 1 3 24 1 2 661 From home Special transit 16 16 From home Scheduled transit 25 1 5 31 From home Car passenger 219 6 225 From home Car driver 28 28 From home Walk/wheelchair 60 60 From home Total 630 17 28 244 29 73 1021 NHB ADA paratransit 71 1 1 25 31 129 NHB Special transit 0 1 7 8 NHB Scheduled transit 6 1 4 11 NHB Car passenger 123 1 124 NHB Car driver 27 27 NHB Walk/wheelchair 16 16 NHB Total 71 1 8 149 27 59 315 To home ADA paratransit 596 5 48 12 661 To home Special transit 13 1 2 16 To home Scheduled transit 15 16 31 To home Car passenger 223 2 225 To home Car driver 28 28 To home Walk/wheelchair 60 60 To home Total 596 13 21 271 28 92 1021 Table 3-10. Trip mode choice model: survey data trip observations.

the aDa paratransit Demand Models 49 • The impedance function: An average of the travel time to go from the home location to each possible destination zone and the time to return back home again. • The attraction function: A composite function of the number of jobs and households in each possible destination zone that attract trips to that zone. Multiple-destination tours: For this minority of tours, the model is applied once for each out-of-home destination along the trip. The specification is much the same as above for single- destination tours, but with two differences in the impedance function: • After the first out-of-home destination has been predicted, the impedance function is measured from the previous destination location rather than from the home location. • Instead of using the average of the time to go to the (next) destination and back again, it uses only the time to go to the (next) destination from the current location, and then a second variable that measures the travel time to go from each possible destination location back to the home location. The use of this second variable prevents the possibility that we would simulate a series of one-way trips that end up a great distance from the home location, which would be unrealistic because the tour eventually needs to end up back at home. (In fact, when we are predicting the last out-of-home destination in the tour, this variable is exactly the travel time for the last trip in the tour that returns to home.) The destination choice model was estimated using a full sample of all 5,386 possible des- tination zones for each trip. In the past, a subsample of destinations would typically be used to estimate such a model, but the current logit model estimation software and hardware can estimate a model on a large number of alternatives in just a few minutes, so it is possible to use the full sample, which is more efficient than sampling both in terms of statistics and analyst time. The model estimation results are summarized in Table 3-12. Trip mode Trip type Tour mode ADA paratransit Special transit Scheduled transit Car passenger Car driver Walk/ wheelchair From home ADA paratransit 95.3% 0.2% 0.5% 3.6% 0.2% 0.3% From home Special transit 100.0% 0.0% 0.0% 0.0% 0.0% From home Scheduled transit 80.6% 3.2% 0.0% 16.1% From home Car passenger 97.3% 0.0% 2.7% From home Car driver 100.0% 0.0% From home Walk/wheelchair 100.0% NHB ADA paratransit 55.0% 0.8% 0.8% 19.4% 0.0% 24.0% NHB Special transit 0.0% 12.5% 0.0% 0.0% 87.5% NHB Scheduled transit 54.5% 9.1% 0.0% 36.4% NHB Car passenger 99.2% 0.0% 0.8% NHB Car driver 100.0% 0.0% NHB Walk/wheelchair 100.0% To home ADA paratransit 90.2% 0.0% 0.8% 7.3% 0.0% 1.8% To home Special transit 81.3% 6.3% 0.0% 0.0% 12.5% To home Scheduled transit 48.4% 0.0% 0.0% 51.6% To home Car passenger 99.1% 0.0% 0.9% To home Car driver 100.0% 0.0% To home Walk/wheelchair 100.0% Table 3-11. Trip mode choice model: choice distribution fractions.

50 Improving aDa paratransit Demand estimation: regional Modeling The impedance function: Separate impedance functions can be used for the six different trip modes. The destinations for car drive-alone and shared-ride trips are the most sensitive to automobile travel time, with coefficients of –0.181 and –0.172, respectively—both with very high t-statistics. The travel time coefficients for ADA paratransit, scheduled transit, and other special transit are all very similar, at around –0.120. The lower ADA paratransit sensitivity to general- ized ADA paratransit travel time is an indication that these trips are somewhat longer than private car trips, on average. The walk/wheelchair trip impedance is based on automobile path distance rather than travel time. (NCTCOG does not have a separate walk network with best paths for pedestrians, but such an input could be used with this model system in other regions if it is available.) The coefficient for walk distance is –0.570. The impedance function uses automobile time, rather than transit in-vehicle and out-of- vehicle time, as the measure for scheduled transit. As discussed earlier, the NCTCOG transit matrices are quite sparse, so using transit times from those matrices would require making many destinations unavailable for transit trips when in reality those destinations are con- nected by transit. Given (1) the relatively minor role of scheduled transit in the model system, (2) transit matrices can be considerable work to process, and (3) many regions do not have transit matrices at all, this simplification was judged appropriate in the current study context. In the future, if the model system is applied in a region with much higher scheduled transit mode shares and more complete transit data, it would be possible to adjust the models to accommodate them. Model name Tdes4 # Observations 1332 Final log- likelihood -7961.4 Rho squared w.r.t. 0 0.304 Impedance function By trip mode ADA paratransit Car drive- alone Car shared- ride Other special transit Regular transit Walk/ wheelchair Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Variable T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. Automobile time (minutes) -0.124 -0.181 -0.172 -0.120 -0.120 -27.4 -8.0 -20.0 -6.8 -6.8 Automobile distance (miles) -0.570 -10.4 Intra-zonal 0.503 0.635 0.908 -10.0 -10.0 2.932 1.4 0.8 3.5 const Const 11.5 Automobile time back home (min) (Multi- stop tours -0.103 -0.118 -0.118 -0.177 -0.177 -.088 only, segmented by tour mode) -8.3 -9.3 -9.3 -3.9 -3.9 -1.3 Attraction size variable function by trip purpose medical trip work trip school trip adult daycare trip shopping / meal trip recreation trip social visit trip personal business trip Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Variable T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. T-stat. Service employment 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 const* const* const* const* const* const* const* const* Retail employment 0.49 12.45 0.81 1.94 -1.1* 10.2* -0.3 1.9* Basic employment 1.87 2.2* Hospital/medical center 6.45 employment 13.3* Households 0.15 0.66 2.90 0.85 -2.2* -0.9* 2.2 -0.5* * For size variable functions, the base size variable (Service employment) has coefficient constrained to 1.0 and the t-statistics for the other variables in the function are relative to a coefficient of 1.0. Table 3-12. Trip destination choice model results.

the aDa paratransit Demand Models 51 Even though the NCTCOG zone system is detailed, with over 5,000 zones in the region, some observed trips in the survey data are intra-zonal, meaning that the origin and destination address are in the same TAZ. In those cases, there is no zone-to-zone travel time information to use in the models, so a separate dummy variable is added for the origin zone alternative to represent the probability of making an intra-zonal trip. As one would expect, this probability is clearly highest for walk/wheelchair trips, but also positive for private car and ADA paratransit trips, indicating that intra-zonal car and ADA paratransit trips do occur. There are no intra-zonal trips observed by scheduled transit or other special transit, so the intra-zonal constant for those modes is con- strained to a large negative value. The final variable in the impedance function is the automobile time back to the home loca- tion, applied only for multi-stop tours, as explained earlier. For this variable, the segmentation is by the tour mode, rather than the trip mode, because we do not know for sure that other trips in the tour are made by the same mode as the current trip. For ADA paratransit and automobile tours, which make up the majority of cases, the coefficient for this variable is very accurately estimated and 20 to 35% lower than the main automobile time coefficient for the current trip. For walk tours, the travel time back to home is less significant, but such tours tend not to stray very far from home in the first place. The attraction function: The size variable function is a specific feature of destination choice models. A “base” size variable is designated—in this case service employment—and the coef- ficient for that variable is constrained to 1.0, while the estimated coefficients for any other size variables determine their importance relative to the base variable. So, the results at the bottom of Table 3-12 indicate that hospital/medical center employment has an effect that is 6.45 times as large as service employment in attracting medical trips. The largest effect for other purposes is for shopping/meal trips, where retail employment has an effect that is 12.45 times as large as for service employment. (In fact, we combined those two trip purposes because they are both carried out almost exclusively at retail establishments.) Other noteworthy results are that households are important in attracting social visit trips; basic employment is important in attracting work trips; and recreation trips and personal business/errand trips are attracted by a combination of service jobs, retail jobs, and households. Model Calibration Ridership Targets for DART and MITS Forecasts As a first step in calibrating the models, reported trips in the ADA paratransit travel survey were compared to actual ADA paratransit trips made by ADA-eligible adults, excluding atten- dants or companions as reported by the two ADA paratransit systems for the time period around the time of the ADA paratransit travel survey. The survey diary days were weekdays, mainly during spring of 2010. The calculations are shown in Table 3-13. DART provided annual ridership and ridership for the year of survey and also for the period April–June 2010. FWTA provided only annual rider- ship. The DART ridership figures show 163,219 weekday trips made by ADA-eligible adults in the period. That period included 65 weekdays, for an average of 2,511 trips per spring weekday. Applying the ratio of DART spring weekday ridership to annual ridership to the MITS annual ridership gives an estimate of 1,214 trips per spring weekday for MITS. Dividing the annual trips (row B) by the spring weekday trips (row C) gives a factor of 284.5 to convert to a spring weekday from an annual total. (Note that there are 260 weekdays in a year, so a factor greater than 260 means that spring ridership is somewhat lower than average.)

52 Improving aDa paratransit Demand estimation: regional Modeling The second section of the first table is based on full client databases provided by DART and MITS (excluding anyone who did not make any trips and did not register in the previous 12 months). Each client record contains the count of the number of trips the person made in the previous 12 months. (The total number of clients and trips are in rows E and F.) If we apply the same factor from row D, we obtain the expected number of trips from those clients on a spring weekday (row G). For both DART and MITS, the values in rows F and G are about 10% lower than the values from the total ridership statistics in rows B and C. One possible reason for this is that just as our sample could contain records for people who had recently registered but not (yet) made any trips on the system, there could also be people who had made trips on the system in the prior year but were no longer in the client database because they had moved or otherwise left the system. In any case, the two estimates are reasonably close. The third section of the first table is similar to the second section, but now based only on the 800 final survey respondents, after expansion to match the full client database. We had oversampled on frequent riders, and the sample expansion adjusts for that, although not per- fectly, as the expanded sample trips in the last 12 months (row I) is about 8% below the figure for the full client database (row F). The most striking difference, however, is that the average number of expanded ADA paratransit trips reported per survey diary day is over twice as high as the number that would be expected based on the observed number of trips made in the last 12 months (row K versus J). The reported number of ADA paratransit trips is about 115% too high for both MITS and DART respondents (row L). The second table in Table 3-13 takes the comparisons in rows H-L and reports them separately for each observed frequency segment used for sample stratification. For the high observed fre- quency categories, the reported trips are “only” about 50% higher than expected. For the lower observed frequency categories, however, the reported trips are 4 to 5 times higher than expected. This means that those people were much more likely to use ADA paratransit on one or both of the two diary days than they had been in reality over the previous year. Even though people in the lower frequency categories were less likely to report ADA paratransit diary trips than those in the higher frequency categories, this difference was not as strong as would be expected based Based on operator ridership data DART MITS A. Total annual ADA paratransit trips by ADA-eligible persons 718,178* 347,270* B. Total annual ADA paratransit trips by ADA-eligible adults 714,336* 345,421** C. Trips per spring weekday by ADA-eligible adults 2,511* 1,214** D. Factor to convert from annual to spring weekday trips (=B/C) 284.5 284.5 Based on operator client databases DART MITS E. Full client database – ADA-eligible adults 7,335 4,591 F. Full client databases – trips in last 12 months 654,667 312,792 G. Calculated expected trips per Spring weekday (=F/D) 2,301 1,099 Based on survey sample expanded to full client databases DART MITS H. Survey expanded sample – ADA-eligible adults 7,282 4,533 I. Survey expanded sample – trips in last 12 months 605,666 284,870 J. Calculated expected trips per spring weekday (=I/D) 2,129 1,001 K. Reported diary trips per spring weekday (expanded) 4,570 2,189 L. Factor – reported / expected trips (=K/J) 2.15 2.18 * Statistics provided by operators, ** assumes same distributions for DART and MITS Area / frequency category DART high DART medium DART low MITS high MITS medium MITS low MITS none - new Survey Expanded sample (H) 2,200 2,811 2,271 1,130 1,466 1,104 833 Avg. trips last 12 months 219.45 30.56 16.28 207.61 26.73 10.04 0 Expected trips per weekday (J) 1,697 302 130 825 138 39 0 Reported diary trips / day (K) 2,436 1,473 661 1,245 596 199 149 Factor reported / expected trips (L) 1.44 4.88 5.09 1.51 4.33 5.11 Table 3-13. Actual and surveyed ADA paratransit ridership.

the aDa paratransit Demand Models 53 on previously observed behavior. This is most likely a survey-related bias that needs to be cor- rected in model calibration. It appears that respondents who travel infrequently may have made it a point to schedule the trips they needed to make on their assigned survey days. The number of trips to calibrate toward is that based on actual aggregate ridership statistics (row C)—roughly 2,500 ADA paratransit trips per weekday on DART, and 1,200 on MITS. Calibration Procedure The actual model calibration adds constants to the stay-at-home portion of the tour genera- tion model and the ADA paratransit alternative of the tour mode choice model, using the fol- lowing procedure: 1. Run the uncalibrated model, and get predictions of ADA paratransit trips, designated as PAR(u), and trips by other modes, designated as OTH(u), within each area and frequency stratum (the columns of the table above). 2. Set target ADA paratransit demand, PAR(t), in each area/stratum. 3. Calibrate the tour generation model so that the total number of trips in each stratum is approxi- mately equal to PAR(t) + OTH(u) (fewer ADA paratransit trips but no change in other modes) 4. Calibrate the tour mode choice model so that the predicted ADA paratransit trips in each stratum is approximately equal to PAR(t) and the trips by other modes is near OTH(u). The results of the calibration procedure are shown in Table 3-14. The numbers are given approximately, rounded to the nearest 25 trips, because there is some simulation error due to stochastic simulation of choices, so the model system gives somewhat different results if a different random number sequence is used. (Each sample observation is simulated multiple times to reduce the simulation error substantially.) The calibration was done using both the “sketch” version and the full “regional” version, with both methods giving approximately the same aggregate results. The resulting total calibrated in-scope ADA paratransit trips per day is approximately 2,350 for DART and 1,225 for MITS—both very close to the actual ridership statistics. Sensitivity Tests The calibrated model was run using Dallas-Fort Worth data to explore how its predictions vary, given changes in demographic variables. These tests involved factoring the input census- tract numbers that feed into the ADA registration rate model, affecting the size of the predicted Transit Operator and Frequency Category DART high DART medium DART low DART new MITS high MITS medium MITS low MITS new Calibration constant in tour generation model (on Stay Home alternative) 0.0 0.9 1.0 0.8 0.0 0.9 1.0 0.8 Calibration constant in tour mode model (on ADA paratransit alternative) 0.0 -1.8 -2.3 -1.5 0.0 -2.0 -2.5 -1.5 Trips by ADA paratransit – uncalibrated 1,650 1,550 1,050 325 925 850 600 175 Trips by other modes- uncalibrated 1,900 2,350 2,050 475 1,175 1,450 1,300 275 Trips by ADA paratransit – calibrated 1,650 400 175 125 925 175 75 50 Trips by other modes – calibrated 1,900 2,450 2,025 500 1,175 1,500 1,200 300 Table 3-14. Model calibration constants and results.

54 Improving aDa paratransit Demand estimation: regional Modeling registered population, and then making corresponding changes to the survey expansion factors in the ADA population synthesis procedure. Three scenarios were tested: 1. Higher incomes: In this scenario, the fraction of households in each census tract with income below the poverty level was decreased by 10%, and the median income in each census tract was increased by 10%. Also, the expansion factor for any sample members in the lowest income category (less than $15K) was decreased by 10% relative to the rest of the sample (The “lowest income” dummy variable is the only income variable that appears in the tour and trip level models, so this is the only distinction that needs to be made to the sample to reflect the effect of income changes.) 2. Aging of the population: In this scenario, the fraction of the population in all age groups over age 60 was increased by 10%. Also, the expansion factor for any sample members in those same age groups was increased by that same amount relative to the other sample members. 3. Larger households: In this scenario, the fraction of the households in each census tract that are single-person households was decreased by 10%, and the average household size in each tract was increased by 10%. Also, the expansion factor for all sample members in single- person households was decreased by 10% relative to the other sample members. Each of these scenarios was run in two ways: • Only on the expanded survey sample, with no change in the number of people registered: This used the “sketch version” of the model to estimate the sensitivity of ADA paratransit trips in terms of the number of trips per registered individual, without considering changes in the number of individuals registered and without detailed spatial expansion. • On the full model system: This used the full “regional” version of the model, including run- ning the ADA registration rate model at the census-tract level, and re-expanding the survey sample to be representative of registered people in each tract. The results are shown in Table 3-15. First, the results of running the model in sketch mode are shown, giving predicted changes in ADA paratransit trips per registered person. Second, results of the registration model alone are shown, predicting changes in the number of registered persons. The third and fourth rows show results for running the model in full regional mode, which adds a prediction of changes in travel patterns. Each scenario assumed a 10% change in some variable(s), and the resulting change in trips or registered people was used to calculate an approximate elasticity. For example, a predicted increase in trips of 1% would imply a +0.1 elasticity (1%/10%). The results indicate that a rise in incomes would tend to increase the average number of trips per registered person, but would cause a more substantial drop in the number of persons who register, so the overall effect is a negative elasticity of ADA paratransit demand with respect to income of roughly -0.2. An increase in household size shows effects in the same direction, with a similar large drop in the number of registered persons, but with only a slight increase in the Model Mode and Predicted Quantity Scenario Higher incomes Older population Larger households Sketch Mode: Travel day simulation models Elasticity of ADA paratransit trips per registered person +0.40 -0.43 +0.13 Full Regional Mode - Registration rate model: Elasticity of number of ADA-registered persons -0.58 +0.18 -0.53 Full Regional Mode: Travel day simulation models Elasticity of ADA paratransit trips per registered person +0.41 -0.39 +0.10 Full Regional Mode - all model components Elasticity of total ADA paratransit trips -0.18 -0.22 -0.44 Table 3-15. Sensitivity test results.

the aDa paratransit Demand Models 55 number of ADA paratransit trips per person, for a net negative elasticity of roughly -0.4. Aging of the population (increase in the fraction of people over age 60) shows effects in the opposite direction, with a slight increase in the number of registered persons, but a larger offsetting drop in the number of ADA paratransit trips per registered person, for a resulting slightly negative net elasticity of about -0.2. It would be interesting to test the effect of automobile ownership also, net of any changes in income. We did not include automobile ownership/availability in the tract-level registration rate model, because this variable is endogenous to many travel demand model systems. That is, it is not used as an input, but is predicted, because for many households automobile ownership decisions depend on the relative accessibility by various modes. In further research along this line, it may be worthwhile to include automobile ownership as exogenous, because it is unlikely that the level of ADA paratransit service would significantly affect automobile availability levels among the eligible population.

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TRB’s Transit Cooperative Research Program (TCRP) Report 158: Improving ADA Paratransit Demand Estimation: Regional Modeling presents a sketch planning model and regional models designed to help metropolitan planning organizations and transit operators better estimate the probable future demand for Americans with Disability Act (ADA) complementary paratransit service, as well as predict travel by ADA paratransit-eligible individuals on all public transportation modes.

Both models permit more detailed forecasts and deeper understanding of the travel behavior of ADA paratransit-eligible people. All model parameters and coefficients are contained in the report and a fully implemented version is available on a CD-ROM that is included with the print version of the report.

The CD-ROM is also available for download from TRB’s website as an ISO image. Links to the ISO image and instructions for burning a CD-ROM from an ISO image are provided below.

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