Toolkit for Estimating Demand for Rural Intercity Bus Services (2011)

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38 The objective of this project was the development of sketch- planning tools to allow planners and operators to estimate the potential demand for rural intercity bus service; there- fore, the project effort shifted from the collection and analy- sis of data to this key element. Initial considerations in the development of these sketch-planning tools included the following observations, prior to the actual effort at calibrat- ing models. Need for Variety of Models/Tools The difference in the number of cases in each of the classifi- cations and the degree of variance (particularly in the regional private and rural public provider groups) suggested to the study team that the development of different tools or approaches might be required. It is likely that the behavioral response of the traveling public to conventional intercity bus service is more consistent across the country because the product is fairly standardized. In rural areas the frequency is low, the fares are similar across the country, the amenities are the same, and information availability and marketing are similar. Develop- ing a model or trip rates for this one type of service should be easier than for the other two types. For both the regional private and rural public services, the product is much less standardized. Fares vary considerably, frequencies vary greatly, the degree of connectivity (to the national network) varies a great deal, and user information and marketing efforts vary. It is likely that different tools, or a tool that is sensitive to these differences, would be needed for these types of services. Use of “a Priori” Expectations in Model Building The type of data collected for each route in the state-level matrices demonstrates the basic approach that was used in developing tools and a workbook, in that the tools and process proceeded from the assumption that rural intercity demand is a function of the following elements: • Overall population levels of origin points • Population of the destination city • Population characteristics • Length of the route or service • Basic service characteristics, including the frequency, the fare level, etc. • Impact of key institutions that are likely to concentrate demand • Connectivity of the service These factors were used to build upon the basic “gravity model” used as the basis for transportation demand fore- casting—that the demand for travel between two places is proportional to the populations and inversely proportional to the distance between them. In this case the “distance” or friction factor includes the actual distance, the fare level, and the frequency. This approach seems obvious, but it is impor- tant to state that these are the expectations regarding travel behavior, so that models or tools can be evaluated in terms of the consistency of the forecasts with these expectations. For example, a tool that forecasts higher ridership for lower frequency services, holding all other factors constant, would be suspect. Statistical Models or “Formulas” May Be Only One Element With a total of at least 133 cases, the potential existed for attempting statistical modeling using regression. The study team thought that, if there were problems obtaining a good fit or a satisfactory model for the entire sample, they would likely be because of issues related to the variety of service types. A concern was that if it became necessary or advisable to break the entire sample by classifications, there might not be enough C H A P T E R 5 Development of the Sketch-Planning Tool

cases in each subgrouping to allow for statistical modeling for each of them. For that reason alone, the resulting toolkit may well have to include a number of techniques to assist the service planner in estimating potential demand. Statistical Models Need To Be User Friendly To the extent that regression or other models were found to be reliable for either route-level or point ridership estimates, the study team thought that such models would need to be designed to utilize only easily available data and would be more of a “black box” downloadable tool that would simply have blank fields in which to enter the appropriate data and then provide the answers. The plan was to embody any needed formulas in the tools, rather than requiring the users to set up their own spreadsheets with formulas, enter the data, make adjustments, etc. Users with more interest in the statistical details of the models would be referred to a separate technical report (this document). As for the data, the study team thought that a simple source and means of assembling the data would be needed. An exam- ple of choosing simpler data over more complicated sources was the change in the data matrix (to be used for calibration) to readily available population data by jurisdiction, rather than the populations for 10-mile or 25-mile ridership sheds. Such areas may be more conceptually satisfactory but require a GIS to estimate the populations in such areas. Potential Use of Case Studies/Analogies For the regional private and rural public service classes, the study team expected that the services might need to be further clustered and then conclusions drawn about demand from these groupings, because of the difference in services. For example, one subgroup might be those rural operators that interline with Greyhound or Jefferson. A second might expand that group to include rural intercity services that offer good connections, but not formal interlining. A third might be rural intercity routes that service major airports. Another might be less than daily services. These different and relatively unique subgroups may be too small, with only a few cases (or one), to develop anything statistically valid. A potential planner could learn something from these cases or subgroups by looking for services in areas that have similar characteristics to the proposed service area and then looking at the ridership response. This process is similar to urban transit route-level demand estimation procedures in which the planner looks for a route or several routes that are very comparable to a proposed service in terms of demographics, route length, fare, and frequency; determines the boardings per mile or service hour of these existing analogous services; and then applies that rate to the proposed service to estimate potential ridership. So the tool would need to provide infor- mation to allow the user to identify comparable services and obtain descriptive information about those services. Need to Include Information to Facilitate Project Design One other conceptual aspect is that the sketch-planning process will need to include a broader set of questions for the planner or operator to consider in the development of proposed projects, even before considering the ridership per se. The variety of projects that have been included in the survey data suggests that there may be many ways to provide for this type of service and a framework to begin the project design process is needed. Often the first consideration of the need for a rural intercity project will evolve out of the loss (or threatened loss) of existing intercity service or the identification of a need for long-distance trips as part of a local transportation coordina- tion planning effort. From that point the planner needs to begin consideration of such issues as the following: • Appropriate endpoints of the service – A service that has connections at both ends may offer more potential destinations and have higher ridership than a dead-end route – A service that makes a national network connection at a hub with many intercity departures will be less con- strained in terms of schedule than a route that connects at a small town with only one or two daily departures – Increasingly rural passengers seek a way to reach major air hubs where they can obtain lower air fares and more air choices. – Existing intercity carriers seek complementary services, not competing services—and so may not support routes that serve the same points they do at similar times. – Knowing the key places to stop to maximize ridership is important—colleges, bases, correctional facilities, etc. are critical to route design. • Schedules – Combining markets to include intercity connecting pas- sengers and more regional trips will provide for higher ridership, but schedules to accommodate both and pro- vide for efficient vehicle utilization can be difficult to design. – Daily fixed-route, fixed-schedule intercity bus service may be too much service for a given rural population, but if the frequency is to be less, determining which days are best may be an issue. If there is a tourism or a uni- versity component, Friday and Sunday may be required. If a human service or medical component is crucial, weekdays are required. 39

– A connecting intercity carrier will want to have fixed schedules, not demand-responsive or only on-call ser- vices, because schedule information is needed to quote service to an inbound passenger. – An intercity carrier providing rural intercity service will likely not be able to deviate to different hospitals in the destination city, wait for passengers, or make multiple stops at transit centers, etc.; therefore, if the primary market has a human service/medical component, local providers may need to be considered. • Connectivity – Connections are best made if they are located in the same place (the same terminal) and within a reasonable time period. – Rural intercity service connecting to scheduled un- subsidized intercity bus services needs to arrive in time that passengers can obtain tickets and find their outbound bus and, if the service is connecting with an inbound bus, it may need to be scheduled significantly later to allow for late arrivals. Rural providers are usually not able to guarantee a connection (by waiting until the connecting bus arrives, for example, or sending another bus). – Access to an intercity bus terminal can require a bus ter- minal licensing agreement with the carrier, and that can include liability waivers and insurance requirements for the rural carrier. – Full interlining with an intercity carrier may be one way to meet local needs for regional service, while offering the market the ability to connect both inbound and out- bound with the national network. • Institutional Considerations – Local rural transit operators will need to find local match support for intercity services and may therefore need to focus more on regional needs in service design. – Finding match support from jurisdictions along a route can be difficult, as they may be tempted to become “free-riders,” knowing the route will have to cross their boundaries. – Use of the FTA Pilot Project method of obtaining match by using the in-kind value of the capital used in un- subsidized service can be one way to satisfy the match re- quirement. – Private intercity carriers may have more ability to provide the local match support from other sources—or through use of the Pilot Project with their other routes—and thus may be more fitting for some intercity projects. Originally the study team thought that these and other such considerations needed to be included in the sketch- planning tool as a series of steps with questions and answers that would then lead to the appropriate questions regarding potential demand—which might involve different types of models or techniques depending on the service design of the project. However, a full rural intercity bus planning guide- book is beyond the scope of this project, and provision of this information would have to be limited to that needed to pro- vide context for estimating demand: • Description of the demand estimation steps and their role in the overall planning process • Attributes that are potentially under the control of the plan- ner (routing, service types, reservations, frequency, fare level, stops at the destination, schedule connectivity, ticketing, information, etc.) and the potential impact • Demand-forecasting tool or tools included in the guidebook • Data required, its source, and processing requirements • Local data requirements (for example, tourism visitation, etc.) and potential sources • Appropriate way to input service and other variables in the forecasting process • Default values for use where local data is not available • Methods for computing the forecasts • Checks on reasonableness The study team anticipated that the guide would include a workbook with text, tables, and graphics and that spread- sheets or other software applications would be included; how- ever, in the end all of this information was included on the CD accompanying this report. The plan for the toolkit included the idea of examples that would follow a hypothetical case through the process to results, with examples worked for each type of tool or process included in the overall guide. The study team still felt the need to provide some guidance at the beginning of the toolkit product regarding the factors that the planner should consider in developing a project. Much of this was presented and discussed in the interim report, and the TCRP B-37 panel is correct in saying that a full intercity planning toolkit is beyond the scope of this project. Development of Demand Models At the end of the reclassification of the data we felt that we had a data set that was as complete and well defined as it would be given the need to have a finite schedule and that there are finite resources. Having spent as much effort on the data, we were optimistic about being able to quickly develop a usable tool for estimating rural intercity demand. However, this was unsupported optimism as we began a search for pat- terns in the data. Trip Rates: Population Issues Initially the study team thought that the population served would be the primary explanation of demand and that some 40

variations in the service characteristics plus the other un- observed variances would account for the rest. The study team began the analysis by calculating basic trip rates for all the services in the database using the corridor populations. It be- came apparent that there was an immediate problem relating to the populations, one that has been seen elsewhere in the literature. A route that serves a number of points, many of which might be non-urbanized, terminates in a major metro- politan area. The major metropolitan area has a very large population and, if that is included in the corridor population, the calculated trip rates vary enormously. Conceptually this population is also problematic for inclusion in the model because it likely has lots of intercity bus service available. To investigate this further, the study team took all of the corridor populations and split them into components— urbanized areas and non-urbanized areas. Further work with the data essentially revealed that, for the most part, providing service to otherwise unserved non-urbanized places is impor- tant to driving ridership on a rural intercity route, but that the urbanized area with other services is essentially an independ- ent factor. Providing intercity bus service between Wadena, Minnesota, and the Twin Cities results in ridership for Wadena that would not exist otherwise, but new ridership out of the Twin Cities as a result of the Wadena connection is not meas- urable (beyond the Wadena folks returning home). Trip rates calculated based on the populations of non-urbanized areas alone varied widely. The demand literature often starts with the basic gravity model, which generally posits that the demand between two cities is a function of their populations and the distance between them. Thomas J. Cook and Judson J. Lawrie utilized this approach to estimate intercity bus route demand as part of their study for the North Carolina Department of Trans- portation (8). Two large urban areas in proximity generate a lot of travel between them. The same populations at a greater distance generate less travel. Generally the formula to represent this phenomenon is the population of one urban area times the population of the second, divided by the distance between them squared. Under this theory, then, an urban area has a gravitational pull that is proportional to its population (mass). So, to follow in the example, there will be more people riding from Wadena, Minnesota, to the Twin Cities than from Wadena to Thief River Falls. So, after the data was separated into urbanized and non-urbanized populations, the study team attempted to develop trip rates for the non-urbanized points and a gravitational “attraction” factor for the urban- ized points. As Cook and Lawrie (8) realized, the gravity model approach gets much more complicated once a route has numerous intermediate stops that offer alternative destinations. Travel between an origin, an intermediate point, and a destination is not simply the sum of demand between (1) the origin and the intermediate stop and (2) the origin and the destination. In the study efforts to calculate an attraction factor for the largest population center on a given route did not result in a systematic pattern. At this point the trip rate approach was not yielding a usable basis for a tool. Alternative Approach: Multiple Regression Another path the study team followed at the same time was to try to develop a regression model to predict ridership as a function of the populations served and the service charac- teristics, along the lines of the models originally developed for NCHRP’s 1981 effort at an intercity bus service planning handbook. The demand models were published in several places (4, 9). Multiple regression is a commonly used tool for estimating the effect of independent variables (in this case population and service characteristics) on a dependent variable (ridership). The study team initially used the regression functions in Microsoft® Excel, focusing on population—again under the assumption that the population served would explain much of the variance in ridership. At this stage of the process, the population categories used included an urban and non-urban designation as provided by the Census and the service type designation was intercity bus or non-intercity bus as classi- fied in Task 6. The population was used as the independent variable, and ridership as the dependent variable. Based on the category types, several combinations were analyzed. Given the small number of observations, or routes, and the use of only one independent variable in each analysis, emphasis was placed on the R-squared result. Figures 5-1 and 5-2 show the results of two of the analyses. In Figure 5-1 the data set used was the intercity bus category. The population, the independent variable, of the entire cor- ridor was used—urban and non-urban. Observed annual ridership was used as the dependent variable. The graph shows the predicted ridership values, based on the regression analysis, and the actual values obtained for each observation. In this case the resulting R2 = 0.139. This result means that there is a really weak relationship between the corridor population and the ridership. In this case, approximately 14 percent of the variance in the ridership variable can be explained by the regres- sion equation using the corridor population as the independent variable. The same approach was tried with the non-intercity bus category of providers, and Figure 5-2 presents the results. Again, the population of the entire corridor was used—urban and non-urban—as the independent variable. The ridership was used as the dependent variable. The graph shows the predicted ridership values, based on the regression analysis, and the actual values obtained for each observation. This time R2 = 0.021. Although slightly higher than for the intercity bus 41

42 0 10000 20000 30000 40000 50000 60000 70000 0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 Corridor Population R id er s Riders Predicted riders Figure 5-1. Line fit plot for intercity bus corridor population. 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 Corridor Population R id er s Riders Predicted riders Figure 5-2. Line fit plot for non-intercity bus corridor population. category, it still means that there is essentially no relationship between the corridor population and the ridership. In this case approximately 2 percent of the variance in the ridership variable could be explained by the regression equation using the corridor population as the independent variable. However, as can be seen in both graphs, there is a line when the residuals are plotted, and so the study team did not give up on the regression approach. The data sets were converted to an SPSS format, and efforts were made to develop models that were plausible in terms of the signs of the independent variables (more population should mean more ridership, so it would have a plus sign, higher fares would decrease rider- ship, so it should have a minus sign). Again the study team tried models for separate data sets for the regional providers and the intercity bus providers and tried pooling the data to see if the larger sample would help. The explanatory power of the resulting models did not improve significantly. Scatter plots were then used to see if there are patterns to the relation- ship between any of the variables and ridership. The scatter plots helped explain the poor regression results—either there is no discernable pattern or there are patterns reflecting a very limited variation in a particular variable.

Trip Rate Approach: Rates from the National Household Travel Survey Given the issues with the regression efforts, one other approach was tried. The U.S. Department of Transportation periodically conducts a detailed survey of transportation users to identify many different characteristics of travel behavior. A report on the travel survey results regarding long-distance travel (10) suggested that although no report on intercity bus usage per se had been published, there might be data from the survey that would at least provide trip rates and mode split. The article also showed regional variations in overall long-distance trip rates, along with differences by income level. The study team contacted the author of the article and dis- cussed the needs for TCRP Project B-37, and she agreed to do some runs of the survey data including urbanized and non- urbanized trip rates, rates by region, rates by income, and national rates by the same breakdowns. Based on this discus- sion, a major concern was that there would be too few survey responses for the intercity bus mode in any one cell, if the data was also split by urbanized and non-urbanized, and then by income and region. The study team decided to request overall trip rates, and then apply a mode split factor based on mode splits for the overall survey. Table 5-1 presents the resulting trip rates. The appropriate mode split is an issue. The 2001 National Household Travel Survey (NHTS) data provided only the overall trip rates, so the mode split rates presented in the table are calculated by KFH Group. The 2001 NHTS overall mode split found a 3 percent mode share for intercity bus and intercity passenger rail combined. However, when the study team applied that mode split and compared the results to its observed ridership, the predicted ridership was too high. The American Travel Survey of 1997 found that overall intercity bus had a 2 percent mode share, but that only 16 percent of that was scheduled buses. However, that study had a different trip length threshold. The 2001 study found an overall bus mode share of 0.09 per- cent for the long-distance trips over 50 miles. Applying this mode share to the data from the sample set produced more close matches to the actual ridership, and rounding it to 1 percent improved it further. Based on the NHTS data, the study team decided that at least one approach to the toolkit would involve the use of these rates. The remaining issue for the toolkit was how to operationalize this model to make usage easy. Continued Development of the Regression Model The study team decided to seek some assistance in the devel- opment of the regression model, and an outside consultant, Jason Sartori, was identified to assist in this role. Based on the issues previously identified with including the population of the “destination” (defined as the largest population stop on the route), the study team developed a data set of the route data that had been collected with the populations separated into a variable called “destination population” and one that included the population of the origin locations. Population was also provided in the data set divided into urbanized and non-urbanized. Also, before trying to estimate a model, the study team looked back at the scatter plots and identified some of the outliers, primarily routes that had been included but that had dramatically different characteristics. The San Luis Obispo Route 10 is one such example. It connects two urban areas and makes stops to allow connectivity to the national inter- city bus network, but it has the frequency and span of serv- ice characteristic of a local transit route, along with local stops on the way. Its ridership was much higher than any of the other routes. The study team elected to drop it from the analysis. There were other similar cases. The Yosemite Area Regional Transit (YARTS) route to Yosemite caused the study team to try estimating with and without it. It has very little population served and no destination population but has a relatively high ridership, and so seemed to be an outlier. The study team later found that including it in the data set reduced the over- all R2; therefore, essentially only models based on a data set that did not include the YARTS route have been included. Stepwise regression was used to generate a model that included the urbanized area population, airport service, provi- sion by an intercity provider, and average origin population— all of which seemed plausible. It had an R2 of 0.708 (adjusted R2 = 0.64), much better than any previous result. Additional work yielded a model that the study team considered usable: R Adjsuted R c2 20 712 0 690= =. , . Ridership average origin popul= − +2803 536 0 194. . ation the number of stops on the route ( ) + (314 734. ) + ( ) + 4971 668 578 . airport service or connection 3 653. service provided by intercity provider( ) 43 cIn a regression equation, the term “R2” refers to the fraction of the sample variance of the dependent variable that is explained by the regressors. “Adjusted R2” is a modified version of R2 that does not necessarily increase when a new regressor is added to that regression. In general, a higher value of R2 means that the model has more explanatory power. See pp. 193–195 in Introduction to Econometrics, James H. Stock and Mark W. Watson, 3rd Edition, Pearson Education, Boston.

44 Long Distance per Capita Trips by Census Division Trips of 50 miles or more in one-way distance Per Capita Trips by Urban/Rural Households & Household Family Income* Urban/Rural Household HHFAM INC* Number of People Long-Distance Trips LD Trips/Capita ICB Share=1% ICB Share=2% ICB Share=3% Urban < 30K 59,348,622.92 327,949,593.66 5.53 0.055 0.111 0.166 Urban < 75K 88,593,298.79 807,776,271.10 9.12 0.091 0.182 0.274 Urban 75K + 55,637,088.46 663,604,914.52 11.93 0.119 0.239 0.358 Rural < 30K 18,722,965.77 151,956,962.19 8.12 0.081 0.162 0.244 Rural < 75K 28,337,614.59 377,763,186.60 13.33 0.133 0.267 0.400 Rural 75K + 10,199,602.81 159,067,326.23 15.6 0.156 0.312 0.468 9 ALL 277,208,169.00 2,604,814,821.20 9.4 0.094 0.188 0.282 Average: 0.104 0.209 0.313 Long Distance per Capita Trips by Census Division Trips of 50 miles or more in one-way distance Trips by Census Division & Household Family Income* Census Division HHFAM INC* Number of People Long-Distance Trips LD Trips/Capita ICB Share=1% ICB Share=2% ICB Share=3% NewEngld < 30K 3,164,287.73 22,695,408.84 7.17 0.072 0.143 0.215 NewEngld < 75K 6,401,005.62 64,394,625.85 10.06 0.101 0.201 0.302 NewEngld 75K + 4,192,850.13 55,388,951.02 13.21 0.132 0.264 0.396 MidAlntc < 30K 9,894,519.59 41,919,624.66 4.24 0.042 0.085 0.127 MidAlntc < 75K 15 324 978 69 137 637 345 44 8 98 0 090 0 180 0 269 , , . , , . . . . . MidAlntc 75K + 9,959,485.73 119,025,927.86 11.95 0.120 0.239 0.359 EastNrth Centrl < 30K 11,138,639.80 69,420,001.97 6.23 0.062 0.125 0.187 EastNrth Centrl < 75K 20,031,885.86 188,393,709.44 9.4 0.094 0.188 0.282 EastNrth Centrl 75K + 10,298,491.86 133,207,476.73 12.93 0.129 0.259 0.388 WestNrth Centrl < 30K 5,017,050.58 42,342,757.94 8.44 0.084 0.169 0.253 WestNrth Centrl < 75K 9,207,670.32 114,177,285.66 12.4 0.124 0.248 0.372 WestNrth Centrl 75K + 3,930,515.27 49,322,058.12 12.55 0.126 0.251 0.377 South Atlntic < 30K 16,758,745.92 102,591,451.45 6.12 0.061 0.122 0.184 South Atlntic < 75K 22,163,512.85 215,829,448.14 9.74 0.097 0.195 0.292 South Atlntic 75K + 13,469,831.04 174,907,253.98 12.99 0.130 0.260 0.390 East Sth Centrl < 30K 5,461,116.94 35,716,211.45 6.54 0.065 0.131 0.196 East Sth Centrl < 75K 6,500,175.49 82,797,429.04 12.74 0.127 0.255 0.382 East Sth Centrl 75K + 2,482,333.75 34,510,845.13 13.9 0.139 0.278 0.417 West Sth Centrl < 30K 9,455,112.62 62,117,096.67 6.57 0.066 0.131 0.197 West Sth Centrl < 75K 11,588,203.34 136,015,598.64 11.74 0.117 0.235 0.352 West Sth Centrl 75K + 5,492,763.94 71,375,972.38 12.99 0.130 0.260 0.390 Mountain < 30K 4,627,980.70 35,812,442.91 7.74 0.077 0.155 0.232 Mountain < 75K 8,398,920.27 81,316,645.54 9.68 0.097 0.194 0.290 Mountain 75K + 3,647,887.17 41,251,332.13 11.31 0.113 0.226 0.339 Pacific < 30K 12,554,134.80 67,291,559.95 5.36 0.054 0.107 0.161 Pacific < 75K 17,314,560.95 164,977,369.95 9.53 0.095 0.191 0.286 Pacific 75K + 12,362,532.36 143,682,423.41 11.62 0.116 0.232 0.349 ALL ALL 277,208,169.00 2,604,814,821.20 9.4 0.094 0.188 0.282 Average: 0.098 0.197 0.295 Table 5-1. Per capita long-distance trips (50 miles or more one way) from the National Household Travel Survey.

Where: Ridership = annual one-way passenger boardings Average origin population = sum of the populations of origin points (all points on the route except that with the largest population) Number of stops = count of points listed in public timetables as stops Airport service or connection = route serves an airport with commercial service either directly or with one trans- fer at a common location Intercity provider = service operated by a car- rier meeting the definition of an intercity bus carrier (see Definition of Intercity Bus Service in Chapter 6.) All variables are significant at the 5 percent level or better, and the included variables and their signs are plausible. One would expect that ridership would increase with a greater origin population and with more stops on the route. The pos- itive impact of the airport connection is also plausible, given the changes in commercial airline service over the past few decades (deregulation, increased service, lower fares). Similarly, the model reflects some advantages in ridership terms of having an intercity bus provider, which offers the advantages of interlining. The impact of the intercity bus provider and the airport service both reflect the advantages of connectivity to a broader network. Some other attempts at improving the model included a version calibrated with the YARTS route, but it did not perform as well. Interaction variables were also tried but were not sig- nificant. An effort to include destination population in the model reduced its explanatory power, and it was not significant; nor was a log transformation of destination population. Efforts to include regional dummy variables were complicated by having few cases in some regions, so adjustments in regions were needed. Including the regional variables improved the model slightly, but only in one region did the ridership predic- tion vary much from a model without the regional adjustment. The study team elected not to include the regional dummy variables, as they would complicate the toolkit. Prediction and Confidence Intervals When one uses a regression equation to predict ridership values, one can calculate prediction and confidence intervals around those values, and the study team did this. A confidence interval provides the range within which one can be confident the population mean of the dependent variable falls, for a given set of values for the independent variables. For instance, as seen in Table 5-2, the study team can state that it is 95 percent confident that, among all bus lines that are intercity with an airport and six stops on the line and serve an average origin population of 35,000, the mean annual ridership will fall between 12,233 and 19,667. In contrast, a prediction interval provides the range within which one is confident that a specific future value will fall. In this case, the study team can be 95 percent confident that a specific future bus line, given these same characteristics (intercity, airport, six stops, and 35,000 average origin popu- lation), will have an annual ridership between 1,878 and 30,022. Here, because the ridership for a specific individual future line is being predicted, as opposed to the average of all lines with those same characteristics, the prediction interval is much larger than the confidence interval. Combined Approaches—Adjustment Factor Another effort to improve predictive accuracy involved an effort to combine the trip rate model and the regression model. 45 INPUTS AvgOriginPop 35,000 Average population of the origins (total origin population/number of origins) Stops 6 Number of stops along route Airport 1 Airport on the line (1) or not on the line (0) Intercity Bus 1 Intercity bus (1) or Non-intercity bus (0) Interval Level 95% Prediction and confidence interval level (e.g., 95%) OUTPUTS Point Predicted annual ridership for route with AvgOriginPop = 35000, Stops = 6 Prediction 15,950 Airport = 1, Intercity Bus = 1 PI Upper Limit 30,022 Upper limit of the 95% prediction interval PI Lower Limit 1,878 Lower limit of the 95% prediction interval CI Upper Limit 19,667 Upper limit of the 95% confidence interval CI Lower Limit 12,233 Lower limit of the 95% confidence interval Table 5-2. Prediction and confidence intervals.

In this case, the regression approach was used to develop an adjustment factor that would then be applied to the estimated demand from the trip rate approach. The idea was that this approach would make maximum use of the available infor- mation. Stepwise regressions were run on the error terms for the NHTS-based trip rate predictions, for each assumed mode split. Table 5-3 summarizes the variables found to impact how far off these predictions were from the actual ridership values. These regressions were used to estimate the inaccuracy (error term) of the NHTS trip rate predictions. This effort was performed to help identify the impact of specific variables on the error term, which could then be used to determine how to adjust the mode share predictions on a case-by-case basis. For example, the coefficients associated with the error model for the NHTS trip rate model using regional trip rates and a 1 percent mode split would be used to estimate a predicted error term. Subtracting the result from the pre- dicted value would give an adjusted prediction. The process is as follows: 1. Stepwise regression identified length, stops, jails, average population of origins, and total population of all stops as significantly impacting the error terms (the distance between the method’s predicted values and the actual rid- ership values). 2. Using this adjustment regression equation, a predicted error term for each observation was calculated. 3. These predicted error terms were then subtracted from the regional 1 percent (RegRate1.0) method’s predicted rider- ship levels to calculate an adjusted ridership prediction for each observation. This approach did yield some improvement in accuracy, as can be seen in the following section. Analysis of Accuracy Again with the help of Jason Sartori, the study team ana- lyzed the accuracy of the trip rate model in comparison to the regression model described previously. Table 5-4 shows how well the various approaches performed compared to actual ridership values. The second column shows the degree to which the 1 percent trip rate model was able to predict the actual ridership. The third column shows the accuracy of the trip rate predictions after they were adjusted using the error term model described previously. The fourth column highlights the accuracy of the regression model predictions, using the 46 Factor RegRate1.0 RegRate0.9 RegRate1.1 NatRate2.0 RegRate2.0 RegRate3.0 Length X X X X X Stops X X X X X X Jails X X X X X AvgOriginPop X X X X X TOT_POP X X X Rail X POP_UA X X POP_UC X X Note: “RegRate” is defined as a model using regional trip rates. “NatRate” is a model using the national trip rate. The numbers refer to the interstate bus mode share, in percentages. Length = One-way length of route in miles Stops = Number of scheduled stops on the route Jails = Route serves a stop with a state or federal correctional facility AvgOriginPop = Average population of origins (total origin population divided by number of origins) TOT_POP = Total population of all stops Rail = Route serves a rail passenger station POP_UA = Population of urbanized areas on the route POP_UC = Population of urban clusters on the route Table 5-3. Factors influencing accuracy of alternative models. Regression Predictions Within 50% of actual ridership Within 10% of actual ridership Within 5% of actual ridership 1% Trip Rate Prediction 45.60% 14.00% 8.80% Adj. 1% Trip Rate Prediction 54.40% 15.80% 5.30% 59.60% 17.50% 5.30% Table 5-4. Accuracy of trip rate and regression models.

regression equation identified previously. While the trip rate prediction provided the largest share of predictions within 5 percent of the actual ridership, the regression equation had the largest share (nearly 60 percent) of predictions within 50 percent of the actual ridership level. The study team was concerned that this was not suffi- ciently accurate for a demand estimate, but when the range of ridership estimates produced for major transit invest- ments are compared to actual ridership, an accuracy rate at this level is not unheard of. Another concern was that this model might not be a better tool than the 1981 Ecosometrics regression models (described in the literature survey), so the study team ran those models on the same data and found that its new regression model is more accurate. Table 5-5 presents the accuracy of the Ecosometrics regression demand model predictions. The new methods are more accurate for the rider- ship being observed on current rural intercity bus routes. Conclusions It may be that over the past 30 years rural intercity bus ser- vice has become much more specialized. The remaining routes that were used to calibrate the model are either (1) exceptional unsubsidized routes, likely with higher demand (or revenue) than the routes now abandoned, or (2) subsidized routes. The subsidized routes have been through a selection process that may well be related to particular needs or demands that make each unique—for example, a link to a university town. Previ- ously there was more rural intercity bus service (more data), and the demand was likely more generic. The results of this effort to develop the models led the study team to proceed with the development of a toolkit using the best of the model approaches developed here: the regression model and the adjusted trip rate model. The results of that effort are presented in Chapter 6. 47 Ecosometrics Regression Predictions Routes 20-60 mi Routes 20-120 mi Routes 121+ mi Routes 20+ mi 14.63% 2.44% 2.44% 6 of 41 1 of 41 1 of 41 9.76% 2.44% 0.00% 4 of 41 1 of 41 0 of 41 33.33% 13.33% 6.67% 5 of 15 2 of 15 1 of 15 66.67% 66.67% 33.33% 2 of 3 2 of 3 1 of 3 Within 50% of actual ridership Within 10% of actual ridership Within 5% of actual ridership Table 5-5. Accuracy of 1981 Ecosometrics regression demand models.