Estimating Paratransit Demand Forecasting Models Using ACS Disability and Income Data

Transcription

1 Estimating Paratransit Demand Forecasting Models Using ACS Disability and Income Data Presenter: Daniel Rodríguez Román University of Puerto Rico, Mayagüez Co-author: Sarah V. Hernandez University of Arkansas, Fayetteville Census for Transportation Planning Subcommittee Meeting 97 th Annual Meeting of the Transportation Research Board January 8, 2018

2 Outline The Demand Forecasting Problem Other Demand Forecasting Approaches Proposed Modeling Approach Using Census for Paratransit Demand Forecasting Application: Forecasting Paratransit Demand for the Ozark Regional Transit Paratransit Service Limitations and Future Work 2

3 Ridership The Demand Forecasting Problem Year (Source: US Census) Problem: Generate mid- to long-term forecast of paratransit ridership given projected demographic changes 3

4 Types of Paratransit Demand Forecasting Methods Time Series Analysis Regression Models Disaggregate Models Naturally, there are advantages and disadvantages to every modeling approach Some guiding questions in the selection of demand forecasting models: What is the purpose of the analysis? What is the quantity and quality of the available data? How much time do we have? Do we have the hardware and software resources? 4

5 Forecasting with Limited Resources Transit agencies commonly face significant resource limitations: Limited data Limited computing resources Limited time for analysis Limited staff assigned to demand model development Our contribution: An inexpensive fitting approach to ADA-compliant paratransit demand forecasting that relies on: Publicly available data (e.g., Census data) Prior information on travel behavior 5

6 Preliminary Ideas We want to predict paratransit demand ( y i ) at a time i using a model that is a function of: Demographic information (X i ) Model parameters (θ) y i = f X i, θ θ reflects travel behaviors The assumptions are that: there is limited travel behavior data BUT there is prior information regarding θ Let θ represent the prior information 6

7 Example: Linear Paratransit Demand Model Assume that: There are G population groups Each group g has a population X g Each individual in group g performs τ g daily paratransit trips The total ridership for a period i is specified as: y i = α i G g=1 τ g X ig Reasonable prior beliefs can be defined regarding the values of τ g 7

8 Sources of Prior Information The values of θ could originate from: Paratransit demand models form other regions Parameters in regional travel demand models Parameters in academic papers or technical reports Experience/professional judgement of transit agency staff 8

9 How to Determine θ Goal: Find the best θ given: Past aggregate ridership information Related demographic data Prior information/beliefs θ Here, the best set of model parameters θ is the one that minimizes the sum of squared differences: Between the observed values y i and the model predictions y i X i, θ + Between the fitted parameters θ and the target parameter values θ 9

10 Constrained Regularized Least Squares The best θ is the parameter set that solves this problem: Minimizes differences between y i and y i X i, θ Minimizes differences between θ and θ min θ I L = 1 I i=1 y i y i X i, θ λ n θ n θ n N n=1 subject to Bounds on values of θ θ n,min θ n θ n,max n 10

11 Obtaining Input Data Relevant to Paratransit Demand Forecasting from the Census Paratransit services are usually provided to people with disabilities The US Census has data products that contain information regarding people with disabilities For example, the American Community Survey (ACS) contains Table C18130: Disability status by age and income The population group estimates X g in the linear model can be obtained from ACS Uncertainty regarding X g can also be obtained 11

12 Incorporating Data Uncertainty in the Model Fitting Process Possible sources of uncertainty regarding X g : Sampling errors Paratransit coverage area The Census reports margin of errors (MOEs) for the ACS and other products This information can be used to generate different data scenarios ( alternative realities regarding input data X) Based on the scenarios, a paratransit demand model can be fitted that accounts for the variability 12

13 Unlinked Passender Trips Application: Forecasting Paratransit Demand for the Ozark Regional Transit Paratransit Service 15,000 10,000 5, Year The Ozark Regional Transit (ORT) Paratransit service operates in Arkansas Benton and Washington counties ORT complies with ADA regulations by providing complementary paratransit to those who have a disability and are functionally unable to get to or use ORT s fixed-route bus system 13

14 Application: Data and Model Assumptions Data Type Description Source Ridership information Demographic data Monthly ridership data for period Population by age groups and income levels Model assumptions: Linear model selected Four population groups considered: G1: non-elderly (under 65 years of age), low-income G2: non-elderly, not low-income G3: elderly (over 65 years of age), low-income G4: elderly, not low-income National Transit Database American Community Survey 14

15 Persons with Disabilities Persons with Disabilities Application: Population Projections Benton County 7,000 6,000 5,000 4,000 3,000 2,000 1,000 - G1 G2 G3 G Population groups: G1: non-elderly, low-income G2: non-elderly, not low-income G3: elderly, low-income G4: elderly, not low-income Washington County 7,000 6,000 5,000 4,000 3,000 2,000 1,

16 Annual Unlinked Passenger Trips Application: Results Population Group G1 G2 G3 G4 Trip Rate Parameter τ 1 τ 2 τ 3 τ 4 Target Prior τ Lower Bound τ min Upper Bound τ max Estimated trip rates τ RLS τ SAA RLS Observed SAA-RLS RLS 40,000 35,000 30,000 25,000 20,000 15,000 10,000 5,

17 Closing Remarks Limitations Definition of disability in ACS versus transit agency s definition Statistical rigor Level of aggregation Future work Incorporate Bayesian econometric methods Natural and statistically robust approach to incorporating prior beliefs regarding parameter values 17

18 Closing Remarks The models were estimated using the Python programming language (an open-source software!) GIS analysis was performed using QGIS (an open-source software!) 18

19 Thank you. The information previously presented can be found in the TRB Compendium: Paper # Regularized Least Squares Approach to Fitting Paratransit Demand Models with Limited and Uncertain Data Contact information: Daniel Rodriguez Roman: daniel.rodriguez6@upr.edu Sarah V. Hernandez: sarahvh@uark.edu 19