Improving ADA Complementary Paratransit Demand Estimation (2007)

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Before estimating regression equations, the data to be used are reviewed. This section provides summary statistics for all the data items collected and identifies issues that could affect the model- ing process. These issues include data items that could not be obtained from some representative systems, data items that needed to be modified or combined in some way in order to be suitable for regression analysis, and data items that are correlated with each other in ways that could affect the regression analysis. Summary Statistics Exhibits 3-1 through 3-6 provide summary statistics for the data items that were collected and are potentially relevant to estimating a system-level model of ADA paratransit ridership. (Con- tact data, non-quantitative data, and data about possible disaggregate modeling are not included.) “Base fare” was not part of the original list of required items, but was added after problems with the data for “average fare per passenger” were discovered. It is the full cash fare for an ADA para- transit trip before any discounts for advance purchase or use of a monthly pass, and before adding any zone charges. A number of data items were not obtained from a significant number of respon- dents and therefore cannot be used for modeling without unacceptably reducing the size of the already-small sample. These include the following: • Total ADA-certified rider trips. This differs from “total ADA paratransit trips” by excluding trips by attendants and companions. • Agency ADA trips. These are trips included within the count of total ADA paratransit trips that bring clients to agency services. Many agencies keep no records about this, even though trips to agency programs do account for much of their demand. • Average time on hold. Smaller systems that do not have automatic call distributors either do not have this information or provided only rough estimates. Although this variable could not be included in the model, an exploratory analysis was conducted, which is described at the end of Chapter 4. • Length of time since significant denials were eliminated. • Whether human service agencies provide at least 25% of the transportation needs of clients to come to agency services. Many agencies either never responded to the supplemental questionnaire on this topic or answered “don’t know” to the questions. Attempts to gather the same data from state-level contacts were not successful. Many respondents also did not provide any data about non-ADA services such as supplemen- tary taxi service or paratransit available to seniors regardless of disability. In this case, however, it was assumed that no response meant that no such service was provided, so a total of non-ADA service was computed for all representative systems. Note, however, that, in each category of non-ADA service, one-fourth or less of representative systems reported providing any trips. A 9 C H A P T E R 3 Preliminary Data Analysis

10 Improving ADA Complementary Paratransit Demand Estimation Valid N Non-Zero N Minimum Maximum Mean Std. Deviation Total ADA paratransit trips 28 28 11,327 3,982,892 469,028 753,715 ADA paratransit trips per capita 28 28 0.08 1.86 0.60 0.48 Total ADA certified rider trips 21 28 11,131 2,877,476 394,591 631,876 Agency ADA trips 13 13 1,562 764,000 101,087 206,682 Agency non-ADA trips 27 8 0 1,137,128 93,399 260,687 Taxi non-ADA trips 18 4 0 50,314 7,498 16,403 Senior non-ADA trips 16 6 0 524,642 35,564 130,524 Other non-ADA trips 15 7 0 117,004 21,022 34,986 Total non-ADA Trips 28 12 0 524,642 36,405 102,182 Valid N Non-Zero N Minimum Maximum Mean Std. Deviation Total ADA fare revenue 28 28 $2,700 $5,903,677 $805,548 $1,297,631 Fare per passenger 28 28 $0.18 $4.35 $1.78 $1.04 48.0$ 18.1$ 05.3$ 05.0$ 82 82 eraf esaB Effective on-time window* 28 28 10 60 30.4 10.0 Percent of pick-ups on-time 28 28 79.8% 99.1% 92.2% 4.9% Do they track drop-off on- time performance? 28 25.0% Average time on hold (m:ss) 24 24 0:15 3:00 1:08 0:38 *Effective On-time Window = the total variation in pick-up time, before or after the last time that was given to the customer, before the trip is no longer counted as being “on-time.” For example, if a vehicle is considered late beginning 20 minutes after the promised time, but customers are expected to be ready 10 minutes before the promised time, then the “effective window” is 30 minutes. Similarly, if pick-up times can be changed by up to 10 minutes without informing the customer, then the effective window may need to be adjusted. This measure was determined by combining responses about the advertised window and about scheduling practices. Exhibit 3-1. Trip data. Exhibit 3-2. Fare and service quality data. Valid N Non-Zero N Minimum Maximum Mean Std. Deviation Percent tested 28 20 0% 100% 52% 45% Percent fully eligible 28 28 13% 100% 72% 25% Percent conditionally eligible 28 21 0% 79% 21% 23% Percent not eligible 28 26 0% 15% 5% 4% Do they do conditional trip screening?* 28 Yes = 46% * Examples of specific conditions of eligibility used for trip-by-trip screening at the representative systems are given in Appendix B. Exhibit 3-3. Eligibility data.

small number of non-zero observations is a concern for regression analysis. Results based on such variables are, in effect, based on a very small number of observations. All of these variables, except for those about human service agency transportation, have been excluded from further analysis. The summary data about human service agency transportation are a compilation of responses. Respondents were asked, “Thinking of human service agencies in your ADA paratransit service area, to the best of your knowledge, what portion of the transportation needed by their clients to agency programs or services do the agencies provide or pay for?” They were asked to respond using categories of 0%, 25%, 50%, 75%, and 100%. Preliminary Data Analysis 11 Valid N Non-Zero N Minimum Maximum Mean Std. Deviation Fixed-route revenue vehicle miles 28 28 313,640 443,483,860 26,447,402 81,247,775 RVM per capita 28 28 3.0 55.4 14.9 9.5 Active fixed-route fleet 28 28 11 9040 625 1687 Active ADA-accessible fixed-route fleet 28 28 11 9040 620 1688 Do they track wheelchair boardings? 28 Yes = 46% Valid N Non-Zero N Minimum Maximum Mean Std. Deviation Total ADA service area population 28 28 19,503 8,008,278 1,041,089 1,563,730 Pct males age 65+ 28 28 2% 7% 5% 1% Pct males age 75+ 28 28 1% 3% 2% 1% Pct females age 65+ 28 28 3% 11% 7% 2% Pct females age 75+ 28 28 2% 6% 4% 1% Pct non-white or Hispanic 28 28 6% 65% 32% 17% Pct population below poverty line 28 28 3% 33% 13% 6% Pct of housing units with no vehicle 28 28 5% 56% 11% 9% Pct with sensory disability 28 28 1% 5% 3% 1% Pct with physical disability 28 28 2% 12% 7% 2% Pct with mental disability 28 28 1% 8% 5% 1% Service land area (square miles) 28 28 16 1,803 357 375 Population per square mile 28 28 280 26,402 3,111 4,679 Days with >.1" of snowfall 28 21 0 31 6.6 7.6 Valid N Percent “Yes” Do agencies provide some DD/MR trips? 20 85% Do agencies provide some ADC trips? 20 65% Do agencies provide some senior meal trips? 20 55% Do agencies provide some dialysis trips? 18 39% Do agencies provide some Medicaid trips? 17 76% Exhibit 3-4. Fixed-route service data. Exhibit 3-5. ADA service area data. Exhibit 3-6. Human service agency transportation data.

A preliminary statistical analysis was conducted to determine how to use these responses using regression on total ADA paratransit trips per capita. It was found that systems that gave non- zero responses have significantly higher ADA paratransit trips per capita than systems that gave zero responses (i.e., agencies serve none of their clients’ transportation needs). The differences were significant with 95% confidence for Developmental Disabilities/Mental Retardation (DD/MR) and Adult Day Care (ADC) trips and 90% confidence for Senior Meals and Dialysis trips. However, there was no discernable difference based on the specific non-zero responses (i.e., whether respondents believe that the agencies provide 25%, 50%, 75%, or 100% of the needed trips). The full analysis is shown in Exhibit 3-7. 12 Improving ADA Complementary Paratransit Demand Estimation Y variable = Total ADA trips per capita R-squared Parameter Estimate Standard Error t value Pr > |t| Pr > F 0.2439Full Model 1.33392Percent of DD/MR_0 Percent of DD/MR_25 Percent of DD/MR_50 Percent of DD/MR_75 Percent of DD/MR_100 0.40957 0.03963 0.07713 0.04344 0.2804Full Model 0.91312Percent of Adult Day Care _0 Percent of Adult Day Care _25 Percent of Adult Day Care _50 Percent of Adult Day Care _75 Percent of Adult Day Care _100 Full Model Percent of Senior Meals _0 Percent of Senior Meals _25 Percent of Senior Meals _50 Percent of Senior Meals _75 Percent of Senior Meals _100 Full Model Percent of Dialysis _0 Percent of Dialysis _25 Percent of Dialysis _50 Percent of Dialysis _75 Percent of Dialysis _100 Full Model Percent of Other Medicaid _0 Percent of Other Medicaid _25 Percent of Other Medicaid _50 Percent of Other Medicaid _75 Percent of Other Medicaid _100 Full Model Percent of Other_0 Percent of Other_25 Percent of Other_50 Percent of Other_75 Percent of Other_100 0.06093 0.08728 0.24394 0.02009 0.2001 0.71651 0.22775 0 0.05928 0.18518 0.1539 0.0928 0.0298 0.58255 0 0 0.2562 0.1731 0.2533 0.2518 0.8085 0.6852 0 0 –0.41326 0 0.0278 0.2215 0.9448 0.8745 0.9551 0.0226 0.8608 0.9078 0.6097 0.9787 0.0548 0.5589 . 0.918 0.7065 0.0817 0.531 0.7698 . . 0.4735 0.6159 0.8065 0.3902 0.6408 . . 0.6032 . 0.5082 2.36 1.26 -0.07 -0.16 0.06 2.45 0.18 -0.12 -0.52 -0.03 2.02 0.59 . -0.1 -0.38 1.82 0.64 -0.3 . . 0.73 0.51 0.25 -0.88 -0.47 . . -0.53 . 0.67 0.5662 0.32554 0.5662 0.48285 0.76346 0.37241 0.34334 0.74482 0.47106 0.74482 0.35404 0.38401 . 0.56958 0.48574 0.32053 0.47782 0.42833 . . 0.6026 0.50816 0.6026 0.50816 0.4175 . . 0.78491 . 0.565590.37964 0.19752 0.44547 0.14943 0.25861 0.43946 0.12674 0.30373 Exhibit 3-7. Exploratory analysis of human service agency transportation variables.

Preliminary Data Analysis 13 Despite the prevalence of missing data, the human service agency transportation variables were kept in the analysis because of their obvious importance from a policy point of view. In order to avoid unacceptable loss of sample size, systems which did not respond or which responded “don’t know” were grouped with those that gave responses of 0%. This admittedly rough assumption is based on the reasoning that, if human service agencies were organized to provide significant amounts of transportation, paratransit staff would be likely to know about it. The data were examined for extreme values that would tend to skew model results. Three vari- ables were identified as problematic, even after normalizing observations on a per-capita basis: • Percent of housing units with no vehicle available. • RVM of fixed-route service per capita. • Non-ADA trips per capita. The most extreme situation involves “percent of housing units with no vehicle available.” The mean value for this variable is 11%. The maximum is 56% represented by New York City. The next highest observation is 16%, represented by the Port Authority of Allegheny County (Pittsburgh) and the Southwest Ohio Regional Transit Authority (Cincinnati). If this variable is included in the model, the coefficient that is estimated for it will mainly show the difference between New York City and all other systems, rather than differences among the majority of systems. For “revenue vehicle miles of fixed-route service per capita,” New York City is again the extreme case with a value of 55.4 compared to a mean of 14.9. The situation is not as extreme as for the no-vehicle variable, since there are four systems with values of 20 or more (King County, WA; Wenatchee, WA; Pittsburgh, PA; and Portland, OR). In addition, this variable is one that lends itself to transformation using logarithms; when this is done, the problem of extreme val- ues is greatly reduced. For “Non-ADA trips per capita” Ottumwa, IA and Charlottesville, VA (JAUNT) stand out from the rest (as shown below): Non-ADA System Trips per Capita Ottumwa Transit Authority 1.75 JAUNT, Inc. 1.14 Port Authority of Allegheny County 0.38 Capital Area Transportation Authority 0.23 Eastern Contra Costa Transit Authority 0.11 King County Metro Transit 0.10 Merrimack Valley Regional Transit Authority 0.10 Central New York Regional Transportation Authority 0.09 Lane Transit Agency 0.04 Regional Transportation District 0.02 Southwest Ohio Regional Transit Authority 0.02 All others (17 systems) 0 Correlation Analysis As a next step, Exhibit 3-8 shows how each variable of interest correlates with total ADA para- transit trips per capita. Trips per capita is used because of the great variation in population among the representative systems, ranging from Ottumwa, Iowa, with a population of 19,503 to New York City with a population of 8,008,278. Other variables that are clearly related to city size

have been similarly stated in per capita terms, including RVM of fixed-route service, fixed-route ADA accessible fleet, and non-ADA paratransit trips. At this preliminary stage, only four variables are significantly correlated with ADA paratran- sit trips per capita. They are highlighted with gray in Exhibit 3-8 and are as follows: • Fare per passenger • Base fare • Percent fully eligible • Percent conditionally eligible In addition, whether or not conditional trip screening is used has a nearly significant correlation. The variables that show no significant correlation all have possible relevance based on experi- ence and theory, so they could not be eliminated. For example, it is possible that correlations not 14 Improving ADA Complementary Paratransit Demand Estimation Exhibit 3-8. Correlation of potential variables with total ADA paratransit trips per capita. Variable Pearson Correlation Significance (2-tailed)** 82.0 12.0 atipac rep spirt ADA-noN Fare per passenger -0.57 0.00 Base fare -0.47 0.01 12.0 52.0- wodniw evitceffE 46.0 90.0-Pct on-time 67.0 60.0- detset tcP Pct fully eligible 0.47 0.01 Pct conditionally eligible -0.42 0.03 82.0 12.0- elbigile ton tcP 80.0 43.0- *gnineercs pirt lanoitidnoC 74.0 41.0 atipaC rep MVR 28.0 40.0- atipac rep teelf ADA Track wheelchair boardings* 0.05 0.80 16.0 01.0- +56 selam tcP 67.0 60.0- +57 selam tcP 24.0 61.0- +56 selamef tcP 05.0 31.0- +57 selamef tcP 91.0 62.0- cinapsiH ro etihw-non tcP 85.0 11.0- ytrevop woleb tcP Population per square mile -0.15 0.45 94.0 41.0-Pct no vehicle 35.0 31.0 ytilibasid yrosnes htiw tcP 95.0 11.0- ytilibasid lacisyhp htiw tcP 66.0 90.0- ytilibasid latnem htiw tcP Days with >-0.1" of snowfall -0.04 0.83 Agenda provide some DD/MR trips* -0.13 0.50 Agencies provide some ADC trips* -0.25 0.20 Agencies provide some Senior Meal trips* -0.14 0.47 Agencies provide some Dialysis trips* 0.02 0.92 Agencies provide some Medicaid trips* 0.00 1.00 *1 = Yes, No = 0 **Shaded rows are significant at 95% (?5% probability that the true correlation = 0 ) using a two-tailed test.

Preliminary Data Analysis 15 seen at this level of analysis may become evident once other factors are controlled for. To provide additional basis for considering these variables, correlations among the variables were examined. Exhibits 3-9 and 3-10 show all the correlations among variables that were found significant with 95% significance. The correlations fall into three categories: • Probably Meaningful Correlations: These correlations appear to indicate important con- nections among variables that would be important to include in a model. These correlations could help to explain why some variables that would be expected to show a significant impact on demand appeared not to in Exhibit 3-8. • Possibly Chance Correlations: These correlations, while statistically significant, have no apparent explanation and may indicate problems with the data. With a small sample and a large number of variables, it would be expected that, on average, 5% of the possible variable combinations would have some apparent correlation in the sample, even though there is no correlation in the total population from which the sample was drawn. Such chance correla- tions represent a pitfall for model development, since they could result in a model that is not generalizable to systems other than those in the sample. • Closely Related Measures: These correlations show that some obviously related variables are so closely connected that they should not be used together in a model. Instead one of them should be selected or they should be combined. Examples in each of these categories are discussed next. Probably Meaningful Correlations Fare per passenger with eligibility variables: Systems with higher than average fare per pas- senger tend to have fewer fully eligible riders, have more conditionally eligible riders, and are more likely to use conditional trip screening. All of these would be expected in systems that have Exhibit 3-9. Correlations among variables. Variable of Interest Correlated Variables Non-ADA trips per capita Pct non-white or Hispanic 44.- Fare per passenger Base fare .64 Pct fully eligible -.46 Pct conditionally eligible .41 Conditional trip screening .40 Base fare Fare per passenger .64 Pct below poverty -.42 04. emit-no tnecreP wodniw evitceffE Pct with sensory disability .53 Pct with physical disability .38 enoN detset tcP Pct fully eligible Fare per passenger -.46 Pct conditionally eligible -.95 Pct not eligible -.41 Pct conditionally eligible Pct not eligible Pct fully eligible -.41 RVM per capita .41 Pct no vehicle .39 Conditional trip screening Fare per trip .40 All age variables .45 - .46 RVM per Capita Pct no vehicle .81 Total or ADA fleet per capita .83 - .85 Population per square mile .80 ADA fleet per capita RVM per capita .85 Pct no vehicle .60 Population per square mile .57 Track wheelchair boardings enoN Pct on-time Effective window .40 All age variables .52 - .59 Pct fully eligible -.95 Fare per passenger .41 Pct fully eligible -.95

16 Im proving ADA Com plem entary Paratransit Dem and Estim ation Variables of Interest Correlated Variables Pct males 65+ Pct on-time .59 Conditional trip screening .45 All age variables >.90 All disability variables .61 - .74 Pct males 75+ Pct on-time .54 Conditional trip screening .46 All age variables >.90 All disability variables .57 - .73 Pct non-while or Hispanic -.38 Pct females 65+ Pct on-time .56 Conditional trip screening .46 All age variables >.90 All disability variables .63 - .76 Pct females 75+ Pct on-time .52 Conditional trip screening .45 All age variables >.90 All disability variables .60 - .73 Some senior meals .40 Pct non-white or Hispanic Non-ADA trips per capita -.44 Pct males 75+ -.38 Population per square .51 .67 - .86 .67 - .80 mile Days with >-.1" of snowfall -.46 Some Medicaid -.40 Base farePct below poverty Population per square mile Pct non white or Hispanic Pct no vehicle Pct not eligible .39 RVM per capita Population per square mile .92 Pct with sensory disability Pct with physical Pct on-timedisability disability Pct with mental All disability variables All disability variables .71 - .76 .57 - .63 All age variables All age variables Some Medicaid Days with >-.1" of snowfall Pct non-white or Hispanic Some DD/MR* Some ADC* .40Pct females 75+Some Senior Meals* Some Dialysis* Some Medicaid* All human svc vars* -.53 to -.57 Pct with sensory disability .37 Pct with mental disability .39 Pct non-white or Hispanic -.40 *Agencies provide some of these trips. Correlation is Kendall's Tau b All human svc vars* All human svc vars* All human svc vars* All human svc vars* -.42 .38 .39 -.46 -.38 -.60 -.37 -.60 -.46 -.57 -.37 to -.54 .80 ADA fleet per capita .60 Pct on-time .53 All age variables .71 - .77 All disability variables .80 - .86 Some Medicaid .37 .51 RVM per capita .79 ADA fleet per capita .57 Pct no vehicle .92 Exhibit 3-10. Correlations among variables, Part 2.

focused strongly on controlling costs. However, none of these eligibility variables is correlated with the base fare. Base fare with poverty: Systems in places with higher rates of poverty tend to have lower-than- average paratransit base fares. The correlation between poverty rate and the average fare per passenger is somewhat weaker and significant with only 91% confidence. These connections are reasonable and might be expected as a response to affordability issues. Since both poverty and fares are expected to influence paratransit demand, these negative correlations suggest that it is important to have both fare and poverty variables in a model. Otherwise the excluded variable could result in biased estimates for the remaining variable. The correlations, while significant, are too weak to cause unreliability in the model results. Effective window with percent of on-time pick-ups: It is to be expected that systems with longer windows that define which trips can be considered on-time would be able to report a higher percentage of on-time pick-ups than systems that hold themselves to a tighter standard. Possibly Chance Correlations Percent of on-time pick-ups with age and disability variables: Systems with higher per- centages of older people or people with sensory or physical disabilities in their service areas tend to report a higher percent of on-time pick-ups. Conceivably, systems in areas with high percentages of older people or people with disabilities are more concerned with providing high- quality service. However, reported on-time performance is subject to great variation in relia- bility. Some systems rely entirely on driver reports or passenger complaints, while others use automated, on-board monitoring equipment. Note that the age and disability variables are not correlated with effective window, suggesting that it may perform better in a model than reported on-time performance. Conditional trip screening with age variables: Systems where there are more older people are somewhat more likely to use conditional trip screening. Closely Related Measures Eligibility variables: Percent of applicants found fully eligible is very highly correlated with the percent found conditionally eligible. This is to be expected, since most applicants will be in one of these two categories: that is, the two add up to close to 100% less those found not eligi- ble. These two variables should not be used together. The remaining eligibility variables (percent found not eligible and whether or not conditional trip screening is used) are weakly correlated or not correlated with the others. Fixed-route transit and urbanization variables: RVM of fixed-route service per capita, active fleet per capita, ADA accessible fleet per capita, population density, and the percentage of house- holds without access to a vehicle are all strongly correlated. Lack of access to a vehicle, when measured at the level of an entire metropolitan area, appears to be more closely connected to urbanization than it is poverty. Total active fleet per capita and ADA accessible fleet per capita are very highly correlated since all but six of the systems reported 100% accessible fleets, and only three have less than 90% accessible fleets. All age and disability variables: There are strong correlations among all of these variables. This suggests that the age variables, if used, should be combined—for example, as total percent of population age 65 and older. There is no easy way to combine the disability variables. Preliminary Data Analysis 17