Ram M. Pendyala and Karthik C. Konduri School of Sustainable Engineering and the Built Environment Arizona State University, Tempe

Transcription

1 Ram M. Pendyala and Karthik C. Konduri School of Sustainable Engineering and the Built Environment Arizona State University, Tempe Using Census Data for Transportation Applications Conference, Irvine, Oct 25-27, 2011

2 Outline Motivation for population synthesis What is population synthesis? Standard IPF procedure Motivation for enhanced population synthesis New Iterative Proportional Updating (IPU) Algorithm Explanation of procedure Geometric Interpretation Census Databases for Population Synthesis Case Studies Population Evolution Model Model Components Conclusions

3 Microsimulation Models of Travel Increasing interest in microsimulation models for travel demand forecasting Microsimulation models simulate travel at the level of the individual decision-maker while recognizing inter-dependencies among activities, trips, persons, time, and space Microsimulation models of travel increasingly based on activitybased paradigm of travel behavior Explicit recognition of derived nature of travel demand Enhanced representation of time-space interactions and constraints

4 Microsimulation Models of Travel (continued) Activity-based microsimulation modeling approaches offer ability to address emerging policy questions of interest By simulating activities and travel at the level of the individual traveler, these models are able to address impacts of: Greenhouse gas emissions reduction targets Flexible working arrangements Impact of information and communication technology (ICT) Interactions between micro-scale land use changes and travel Pricing-based policies Non-motorized transportation mode enhancements

5 Why Population Synthesis? We need disaggregate household and person sociodemographic data for entire population of model region Such data for the entire population is generally not available This leads to the need to synthesize a regional population from known statistical distributions on the population We have: Disaggregate data for a sample of the population (PUMS, travel surveys) Marginal distributions for the entire region (census summary files, agency forecasts)

6 What is Population Synthesis? Population synthesis involves generating a synthetic population by expanding the disaggregate sample data to mirror known aggregate distributions of household and person variables of interest.

7 Standard IPF-Based Procedure Standard IPF (iterative proportional fitting)-based procedure based on Beckman et al (1996) Procedure Choose household-level control variables Obtain the marginal distributions on these variables from census summary files (SF) Generate a seed matrix of the joint distribution from a microdata sample data set (PUMS, travel survey) Expand the seed matrix using an IPF-procedure to match the given marginal control totals while maintaining the joint distribution implied by the seed matrix

8 Standard IPF-Based Procedure (continued) Selection probabilities are estimated for households in the microdata sample Households are drawn using the selection probabilities to match the expanded cell frequencies The resulting synthetic population is checked for goodness-offit and households are redrawn if necessary The synthetic population is comprised of all individuals within the synthesized (drawn) households

9 Motivation for Enhancement Key limitation of the standard IPF-based procedure Controls only for household attributes and not person attributes Synthetic populations fail to match distributions of person characteristics of interest The method ignores differences in household composition among households within a cell Hence the need to re-assign weights to sample households based on household composition

10 Recent Literature The issue has been recognized by researchers and a number of solutions have been proposed Guo and Bhat (2007) Arentze and Timmermans (2007) Pritchard and Miller (2009) Srinivasan et al (2009) Ye et al (2009) Lee and Yingfei (2011) Muller and Axhausen (2011)

11 PopGen: A New Population Synthesizer Incorporates a new Iterative Proportional Updating (IPU) algorithm for estimating household weights The algorithm estimates sample household weights such that BOTH household and person distributions are matched Simple, practical, and computationally tractable algorithm with an intuitive interpretation Basic idea behind IPU algorithm in PopGen Reallocate weights among sample households of a type to account for differences in household composition

12 PopGen Methodology Step 1: Estimate Household and Person Type Constraints household and person sample data household and person level marginal distributions Adjust priors to account for zero-cell problem Adjust marginals to account for the zero-marginal problem Run Iterative Proportional Fitting (IPF) procedure to estimate household and person type constraints

13 PopGen Methodology (continued) Step 2: Estimate Household Weights household and person sample data household and person type constraints from Step 1 Run the Iterative Proportional Updating (IPU) algorithm to estimate sample household weights that satisfy both household and person type constraints

14 PopGen Methodology (continued) Step 3: Generate the Synthetic Population household and person sample data household weights from Step 2 Apply rounding procedures to get the frequency of different household types in the synthetic population Estimate household selection probabilities using the computed weights Draw sample households based on selection probabilities for each household to match cell frequencies Repeat the process until a synthetic population with the best fit is obtained

15 PopGen Terminology Household Type Not to be confused with a household attribute household type Refers to a combination of household-level variables of interest Represents a cell in the joint distribution of a set of householdlevel variables Person Type Similar to above formed by a combination of multiple personlevel variables of interest

16 PopGen Terminology (continued) A measure of fit ( value) Measures the absolute relative deviation between the IPU-adjusted cell frequency and the IPF-estimated household/person type constraints Average value across all constraints is used as a goodness-of-fit measure Average value is also used to monitor and set convergence criterion for the IPU algorithm

17 PopGen Terminology (continued) A measure of fit ( value) j d i, j w c i j c j d i,j w i = adjusted cell frequency c j = the j th IPF-estimated constraint

18 Illustration of IPU Algorithm Household ID Initial Weights Frequency Matrix Household Type 1 Household Type 2 Person Type 1 Person Type Person Type 3 Weighted Sum Constraints

19 Illustration of IPU Algorithm (continued) Adjustment with respect to household type constraints Household ID Initial Weights Household Type 1 Household Type 2 Person Type 1 Person Type 2 Person Type 3 Weights 1 Weights Weighted Sum Constraints Weighted Sum Weighted Sum /3 = /5 = 13.00

20 Illustration of IPU Algorithm (continued) Adjustment with respect to person type constraints Household ID Initial Household Household Person Person Person Weights Type 1 Type 2 Type 1 Type 2 Type 3 Weights 1 Weights 2 Weights 3 Weights 4 Weights Weighted Sum Constraints Weighted Sum Weighted Sum Weighted Sum Weighted Sum Weighted Sum /3 = /5 = / = /76.80 = /67.68 = 1.54

21 Illustration of IPU Algorithm (continued) Household ID Initial Weights Household Type 1 Final Results Household Type 2 Person Type 1 Person Type 2 Person Type 3 Weights IPU Weights Without Reallocation Constraints δ δ IPU

22 Average value (log-scale) Illustration of IPU Algorithm (continued) Improvement in Average Value 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E Number of Iterations

23 IPU: Geometric Interpretation Consider the following household structure and population constraints Household ID Household Type 1 Person Type 1 Weights w w 2 Constraints 4 3 Weights can be estimated by solving the following system of linear equations w w 1 2 w 3 2 4

24 IPU: Geometric Interpretation (continued) When solution is within the feasible region w 1 B S D A w2 = 3 C E S Starting Point B Adjustment for Household Constraint C Adjustment for Person Constraint D Adjustment for Household Constraint E Adjustment for Person Constraint continue to convergence O I I Solution w 2

25 IPU: Geometric Interpretation (continued) When solution is outside the feasible region w 1 A S w2 = 5 S Starting Point B Adjustment for household constraint C Adjustment for person constraint D Adjustment for household constraint E Adjustment for person constraint O B D I 1 C E I 2 I w 2 continue to convergence I Solution outside feasible region I 1 Corner solution where household constraint is satisfied I 2 Corner solution where person constraint is satisfied

26 Synthetic Population Synthetic population generation process can be divided into three steps Estimating whole frequencies Calculating selection probabilities Drawing households

27 Estimating Frequencies IPF-estimated household type constraints provide target frequencies Rounding procedures are employed to convert decimal values to whole frequencies Rounding procedures implemented in PopGen Arithmetic Rounding (default) Bucket Rounding Stochastic Rounding

28 Selection Probabilities Synthetic households are drawn probabilistically based on IPU-estimated weights Selection probabilities are estimated for each household type that needs to be synthesized No additional adjustments to match person constraints are needed The individuals from the synthetic households comprise the synthetic population

29 Illustration of Estimating Selection Probabilities Household ID Household Type 1 Household Type 2 Person Type 1 Person Type 2 Person Type 3 Final Weights Household Type 1 Household Type 2 Cumulative Cumulative Sum Probability Sum Probability

30 Drawing Households Rounded frequencies and the selection probabilities from earlier steps are used to generate a synthetic population For each household type, we use the corresponding selection probabilities to draw households The persons in the drawn households comprise the synthetic population for the target year As the drawing procedure is probabilistic, the fit of the synthetic population is checked The drawing procedure is repeated until a synthetic population with the best fit is obtained

31 Illustration of Drawing Households Household ID Household Type 1 Household Type 2 Cumulative Sum Probability Cumulative Sum Probability Consider Household Type 1 2. Generate a random number between 0 and 1, e.g < 0.23 < Household ID 2 is added to the synthetic population 5. The process is repeated until 35 households of Household Type 1 are included 6. The process is repeated for Household Type 2 Frequency 35 65

32 Synthetic Population: Performance χ 2 goodness-of-fit statistic A goodness-of-fit measure to check match against person-level distributions The corresponding p-value represents the level of confidence at which the synthetic population matches the given constraints A synthetic population is drawn repeatedly until a desired p-value is achieved or a maximum number of draws is reached Maximum number of draws is user specified and dependent on geographic context 2 j n j c j c j 2 n j = frequency of synthetic persons of the j th person-type c j = the j th IPF-estimated person-type constraint

33 Case Studies Case Study Southern California (SCAG) Synthesis Year 2008 Sample Data Source Census percent PUMS ACS percent PUMS* Marginal Distributions SCAG TAZ Data SCAG TAZ Data Baltimore Metropolitan (BMC) 2000 Census percent PUMS BMC TAZ Data

34 Case Studies: Control Variables Case Study Household-level Control Variables Southern California (SCAG) Baltimore Metropolitan (BMC) Presence of children (2), household type (5), household size (7), age of householder (2), family type (2), income (4) 1120 household type constraints Household size (5), worker count (4), income (4) 80 household type constraints

35 Case Studies: Control Variables (continued) Case Study Person-level Control Variables Southern California (SCAG) Age (10), gender (2), race (7) 140 person type constraints Baltimore Metropolitan (BMC) Person total (1) 1 person type constraint

36 Population Synthesis Summary Case Study Households Person Actual Synthesized Actual Synthesized Southern California (SCAG) Baltimore Metropolitan (BMC) Census PUMS 3-yr ACS PUMS Census PUMS 5,925,576 5,925,576 18,904,466 18,451,705 5,925,576 5,925,576 18,904,466 18,083,857 1,642,882 1,642,882 4,391,673 4,404,711

37 Performance: Aggregate Comparisons Household Size (Controlled) SCAG Using Census PUMS SCAG Using 3 yr ACS PUMS Actual Synthesized Actual Synthesized 1,800,000 1,600,000 1,400,000 1,200,000 1,000, , , , , ,800,000 1,600,000 1,400,000 1,200,000 1,000, , , , , BMC Using Census PUMS Actual Synthesized

38 Performance: Aggregate Comparisons Household Income (Controlled) SCAG Using Census PUMS SCAG Using 3 yr ACS PUMS Actual Synthesized Actual Synthesized 2,000,000 2,000,000 1,500,000 1,500,000 1,000,000 1,000, , ,000 0 < $25K >= $25K - $50K >= $50K - $100K >= $100K 0 < $25K >= $25K - $50K >= $50K - $100K >= $100K BMC Using Census PUMS Actual Synthesized < $11.8K >= $11.8K and < $26K >= $26K and < $44.2 K >= $44.2K

39 Performance: Aggregate Comparisons Age (SCAG Controlled, BMC Uncontrolled) SCAG Using Census PUMS SCAG Using 3 yr ACS PUMS Actual Synthesized Actual Synthesized 3,500,000 3,000,000 2,500,000 2,000,000 1,500,000 1,000, ,000 0 < 5 >= 5 >= 15 >= 25 >= 35 >= 45 >= 55 >= 65 >= 75 >= 85 and < and < and < and < and < and < and < and < ,500,000 3,000,000 2,500,000 2,000,000 1,500,000 1,000, ,000 0 < 5 >= 5 >= 15 >= 25 >= 35 >= 45 >= 55 >= 65 >= 75 >= 85 and < and < and < and < and < and < and < and < BMC Using Census PUMS (Compared Against Census 2000 SF) Actual Synthesized < 5 >= 5 and < 14 >= 15 and < 24 >= 25 and < 34 >= 35 and < 44 >= 45 and < 54 >= 55 and < 64 >= 65 and < 74 >= 75 and < 84 >= 85

40 Performance: Aggregate Comparisons Race (SCAG Controlled, BMC Uncontrolled) SCAG Using Census PUMS SCAG Using 3 yr ACS PUMS Actual Synthesized Actual Synthesized 10,000,000 8,000,000 6,000,000 4,000,000 2,000, ,000,000 8,000,000 6,000,000 4,000,000 2,000,000 0 BMC Using Census PUMS (Compared Against Census 2000 SF) Actual Synthesized

41 Actual Actual Actual Actual Performance: Disaggregate Comparisons BMC Case Study - Household Size Category 1 Person 2 Persons Synthesized Synthesized 3 Persons 4 Persons Synthesized Synthesized

42 Actual Performance: Disaggregate Comparisons BMC Case Study Person total Synthesized

43 Performance: Synthesized vs Marginals vs CTPP Matches given marginals almost perfectly Variable Category Synthesized CTPP Marginal Number of workers in the household No workers 407, , ,448 1 worker 704, , ,987 2 workers 631, , ,257 3 or more workers 148, , ,505 1 person 535, , ,158 Household size 2 persons 560, , ,022 3 persons 331, , ,526 4 or more persons 463, , ,530

44 Population Evolution Model Marginals are often generated at individual geography-level for specific forecast years Population is synthesized for each forecast year and activitybased travel demand model is applied to estimate the demand Issues: Estimation of travel demand for intermediate years Reflection of underlying socio-economic and demographic processes across forecast years

45 Population Evolution Model (continued) Instead of generating a synthetic population for every forecast year, evolve the base year synthetic population (annually) to obtain population for any future year Synthetic households and persons are subjected to a host of socio-economic and demographic evolutionary processes: Immigration and emigration Person-level life cycle events Household-level changes over time Population evolution allows intermediate year simulations while reflecting dynamics across forecast years

46 Population Evolution Prototype Developed and implemented for Baltimore Metropolitan Council (BMC) region Emigration Immigration Aging Mortality Fertility Income Occupation Labor Participation Child Leaving Model Education Marriage/ Divorce Household Formation Household Dissolution

47 Household Migration: Emigration Description Simulation Model Data Households moving out of the study region Select households from sample to match given household- and person-level distributions of emigrating households and locate them Procedure similar to population synthesis; IPF is used to estimate frequency of households and IPU is employed for selection probabilities Sample Census PUMS Control distributions Maryland Department of Planning

48 Emigration Control totals of person-level attributes of emigrants Person Attributes Anne Arundel County Baltimore City County Name Baltimore County Caroline County Carroll County Frederick County Male Female Person Total White alone Black or African American alone American Indian & Alaska Native alone Asian alone Native Hawaiian & other Pacific Islander alone Some other race alone Two races or two or more races Person Total to 9 years old to 14 years old to 19 years old to 24 years old to 29 years old to 34 years old to 39 years old

49 Household Migration: Immigration Description Simulation Model Data Households moving into the study region Select households from sample to match given household- and person-level distributions of immigrating households and locate them Procedure similar to population synthesis; IPF is used to estimate frequency of households and IPU Is employed for selection probabilities Sample Census PUMS Control distributions Maryland Department of Planning

50 Emigration Control totals of household-level attributes of immigrants Household Attributes Anne Arundel County Baltimore City County Name Baltimore County Caroline County Carroll County Frederick County Married-couple family HH with children < Married-couple family HH without children < Other family Household with children < Other family Household without children < Non-family Household Household Total Under $25, $25,000 to $49, $50,000 to $74, $75,000 to $99, $100,000 to $199, $200,000 and over Household Total

51 Person-level Evolution: Aging Description Simulation Model Reflect the aging of individuals from year-toyear Increase the age of individuals by 1; update household attributes NA Data NA

52 Person-level Evolution: Mortality Description Simulation Model Reflect the mortality of individuals from yearto-year Remove person from the household; update household and person attributes Rate-based model is employed to calculate the probability of mortality Data Mortality Rates by person characteristics Centers for Disease Control and Prevention

53 Mortality Rates by Race, Gender, and Age American Indian or Asian or Pacific Black or African Alaska Native Islander Americxan White Female Male Female Male Female Male Female Male < 1 year years years years years years years years years years years years years

54 Person-level Evolution: Fertility Description Simulation Model Data Mimics the addition of individuals through birth event Add an individual; update household and person attributes Binary logit model is applied to calculate the probability of female giving birth or not Model estimated using National Survey of Family Growth data

55 Fertility Binary logit model Variables Coefficient T-test Constant Age (Years) Age Square (Years 2 ) Female is in marriage Female is full-time employed Female is part-time employed Female is Black Female is Hispanic White Model Statistics Sample Size 7356 LL(b) LL(0) Adj

56 Person-level Evolution: Education Description Simulation Model Data Reflects the enrollment and education attainment processes Update the education status if continues enrollment Rate-based model is employed to estimate the probability to discontinue Education continuation rates by current education level and person-characteristics Census PUMS

57 Education Enrollment discontinuation rates Non-Hispanic White Hispanic White Black or African Asian or Native Two or more Other American Hawaiin major No Schooling Completed st grade to 4th grade th grade or 6th grade th grade or 8th grade th grade th grade th grade th grade, no diploma High school graduate Some college, but less than 1 yea One or more years of college, no Associate degree Bachelor s degree Master s degree

58 Person-level Evolution: Individuals Moving Out Description Simulation Model Data Mimics children moving out from family households for college Remove person from the household; update household and person attributes; create a new household and locate Multinomial logit model is applied to estimate probability of living on-campus, living offcampus, or living with parents Model estimated using Census PUMS

59 Individuals Moving Out Model of residence location choice for college students Variables Coefficient T-test Living On-Campus Constant Age (Years) Female Annual Household Income ( $1,000) Non-Hispanic White Living Off-Campus Constant Female Annual Household Income ( $1,000) Non-Hispanic White Hispanic White Black Asian Living with Parents (Utility is fixed at 0) Model Statistics Sample Size LL(b) LL(0) Adj

60 Person-level Evolution: Employment Description Simulation Model Data Reflects the participation in labor force, occupation type, and income Update the labor participation decision, occupation, and income; update household and person attributes Binary logit model of labor participation, multionomial logit model of occupation, ordered logit model of income Models of labor participation, occupation, and income estimated using Census PUMS (but no information on dynamics or history dependency; fresh simulation each time)

61 Employment Model for labor force participation Variables Coefficient T-test Constant Age (Years) Age Square (Years) Education Years Female In-marriage Female Number of kids Male In-marriage Non-Hispanic white Hispanic white Asian/Native Hawaiian/ Pacific Islander Model Statistics Sample Size LL(b) LL(0) Adj

62 Person-level Evolution: Household Formation Description Simulation Model Data Mimics the decision of individuals to get married and form new households Simulate decision to marry, and match spouses from pool of eligible males and females Binary logit model of marriage for males and females Model estimated using National Survey of Family Growth

63 Employment Model of marriage decision for males and females Variables Coefficient T-test Constant Age (Years) Age Square (Years 2 ) Black Hispanic White Full-time Employed Model Statistics Sample Size 4638 LL(b) LL(0) Adj Marriage model for males Marriage model for females Variables Coefficient T-test Constant Age (Years) Age Square (Years 2 ) White Full-time Employed Model Statistics Sample Size 4877 LL(b) LL(0) Adj

64 Person-level Evolution: Household Dissolution Description Simulation Model Mimics the decision of individuals to get divorced Simulate decision to divorce, and dissolve the household and locate the new household; update household and person attributes Binary logit model of getting divorced Data Model estimated using National Survey of Family Growth

65 Employment Model of divorce decision Variables Coefficient T-test Constant Age (20 25 Years) Age (25 30 Years) Age (Elder than 40 Years) Hispanic White Fulltime Employed Model Statistics Sample Size 2621 LL(b) LL(0) Adj

66 Population Evolution Prototype Implementation The prototype was developed using the software infrastructure that supports OpenAMOS an open-source activity-travel demand model system PopGen was used to generate base year synthetic population for year 2008 for Harford county in the BMC model region and population was evolved for 10 years past that i.e. from All the models identified earlier were implemented except for the household formation model (spouse matching component)

67 Preliminary Results Race distribution White alone Black or African American alone Asian alone Some other race alone Two or more major race groups American Indian, Alaska Native and other Pacific Islander

68 Preliminary Results Gender distribution Male Female

69 Preliminary Results Household Size distribution

70 Preliminary Results Worker Count distribution

71 Population Evolution Challenges The prototype considers some basic dimensions of householdand person-level attributes of interest There are a host of other household- and person-level socioeconomic and demographic processes that are of interest Formation of non-family households, e.g., roommates Vehicle fleet composition and evolution, bicycle ownership Mobility options, e.g., driver s license and transit pass holding status ICT availability We need a better understanding of evolutionary processes and enhance their representation

72 Population Evolution Challenges (continued) Availability of data Data from a single source that can uniformly be used to estimate and model choice dimensions of interest avoid introducing sample biases Richer data needed to estimate and apply advanced models Modeling simultaneous choices, e.g., Education and Occupation choices Endogeneity of choices, e.g., auto ownership and residential/ workplace location choices (typically in land use model) Accounting for inter-person dependencies in the population evolution choice dimensions Sequencing/hierarchy of choice dimensions

73 Summary and Conclusions State of practice moving towards disaggregate microsimulation modeling of travel demand Need to generate synthetic population for base year and evolve populations for subsequent years to apply microsimulation models of travel demand The current Census information is adequate for base year synthetic population generation However, the applicability of Census to estimate models of various socio-economic and demographic evolutionary processes is limited

74 Summary and Conclusions Often researchers look for alternative survey resources to model these processes. This may potentially introduce survey biases ACS data offers valuable opportunity to capture dynamics of households on annual basis Create a panel PUMS sample that can be traced over long periods of time; households rotate in and out of panel sample Estimate models of evolution (changes in demographics) from a single consistent data source and introduce history dependency (e.g., labor force participation at time point t+1 is highly dependent on labor force participation at time t; should not simulate choice as a fresh start each year)

75 Questions?