Population Synthesis

Background and Literature Review

Creating a synthetic population, or in other words, enumerating a complete set of households and persons (with key attributes) for a modeling region is a necessary first step for the application of advanced travel models such as hybrid trip-based models and Activity Based Models (ABM).

The synthesized household and person characteristics reflect the distribution of key variables in the study region and match observed marginal distributions at an aggregate level.

Having access to detailed person and household characteristics in the model opens the door for model estimation to include a range of variables that define trip and travel making behavior. Even for traditional trip-based models, development of a synthetic population and household database can help generate various cross-tabulations at desired geographic levels that may not be available otherwise.

For the TRM, a population synthesis forms the core basis for applying a state-of-the-art hybrid travel demand model. The aim of the synthesis is focused on matching both household and person marginals at the Traffic Analysis Zone (TAZ) level. Another crucial requirement is a solution that is practical to apply and runs in minutes without sacrificing accuracy of the results. To that end, the updated population synthesis procedure in TransCAD 9.0 is employed.

This documentation briefly summarizes the basic idea of population synthesis, some of the advancements made in recent years and points the reader to published literature for additional details. It also details the creation of disaggregate curves, which convert aggregate zonal data into targets for the synthesis process. The technical approach for population synthesis in the TRM is briefly illustrated, following details regarding the application. Finally, the results of the application are demonstrated.

Basic Idea (Simple IPF)

The basic idea of population synthesis is best illustrated by Figure 1. In simple forms of population synthesis, there are two inputs: disaggregate household (HH) and person seed tables and HH marginals summarizing the distribution of key characteristics of HH at some aggregate level of geography.

The seed data tables consist of a sample of household (HH) and person records, typically obtained from a survey of the study region, and tagged to a high-level geography such as Public Use Microdata Areas (PUMAs). Public Use Microdata Sample (PUMS) data from the American Community Survey (ACS) typically forms this seed, although this sample can be enhanced by incorporating data from a travel survey and reweighing the combined records.

Various aggregate marginals, typically ACS marginals at the census block or block group level in the base year or sometimes at higher levels of geography for future years provide control totals that the synthesized databases must match. It is also a well-accepted practice to fit curves using the census marginal distributions, which can then be applied to generate marginals at a TAZ level for example. These TAZs are usually smaller than census block groups but larger than census blocks.

Figure 1 Simple population synthesis process flow diagram

An Iterative Proportional Fitting (IPF) step then estimates the number of each type of household (identified in the seed) to be generated for each of the smallest geographic entities. This is achieved by identifying the number of households of each type that will add up to various household marginals. This is best illustrated for a single block group using the schematic in Figure 2. In this example, the two classifications of interest are HH by Size and HH by Number of Vehicles. The row and column marginals highlighted in yellow are the input control totals and the goal of the process is to fill in the cells of the matrix (i.e. the values TS1_V0 etc.) such that the row and column totals are respected. The value TS1_V0 represents the number of single person, zero car HHs that need to be synthesized for this block group.

Figure 2 IPF

The term “Nested” in Figure 1 indicates that the household marginals may themselves be specified at different (but nested) geographies: for example, the vehicle ownership marginals may be at the traffic analysis zone (TAZ) level while the income marginals may be at the level of Census blocks or block groups. Nested synthesis will drill all the marginals down to a common geography (usually the smallest/finest among all input geographies.

Finally, for each smallest geographic entity, the required number of households of each type determined by IPF are sampled or drawn from the surveyed (seed) households using externally supplied (initial) weights (generally based on the survey sampling). The selected households are accumulated in a HH output file, and all persons living within each sampled household are automatically copied into a person output file. Together, the HH and person files comprise the synthetic population once the sampling is complete.

The most important drawback of this process is the lack of control on person marginals. Since the algorithm only controls for household variables, the obtained distribution of person attributes in any given zone is largely a lottery. There is no guarantee that the chosen households will yield, for instance, the correct distribution of age, gender, etc., in the synthetic population. This can have adverse effects from a modeling application perspective, for example if the distributions of working-age persons, students or seniors are incorrect.

Person Marginals and Iterative Proportional Updating (IPU)

The Iterative Proportional Updating (IPU) process (Xe et al, 2009) has been proposed and applied (most notably in PopGen) as a way of matching person marginals while essentially retaining the simplicity of the IPF framework. In this approach, before sampling households for a particular geographic entity (zone) using the initial weights in the seed, these sampling weights are first adjusted (or raked) to explicitly match both household and person marginals for the zone. In this process, note that the same seed household(s) may be weighted differently for different zones, which adds precision compared to the use of a priori weights supplied externally. Further, this household re-weighting may be applied at a different (usually more aggregate) geography than that used for simulating the population. A modified version of the published approach in the literature using IPU is applied to the TRM region and is discussed in detail in the next section.

Other Techniques

Several optimization methods have also been published in the literature. For a general literature review, see Ramadan and Sisiopiku, 2019. While these methods might tackle certain issues of the IPU approach, these methods tend to be customized. Owing to the nonlinear and non-convex nature of the resulting formulation, the performance can be problem dependent and can result in long run times, local optima, and sensitivity to the scale of the objective function.

Disaggregate Curves

The first step in synthesizing the population of residents in the TRMG2 is to develop univariate or one-dimensional marginal distributions describing the population in each zone based on the limited demographic variables forecast for each zone, typically averages. In other words, the model starts by determining the number of single person, two person, three person, etc., households in each zone based on the average household size in the zone.

Rather than use stratification curves to convert simple zonal input variables such as average household size into a distribution of households by size, some travel model population synthesizers require the user to supply the number of households by size. However, this puts a considerable burden on data development for future year scenarios which is difficult for agencies lacking staff dedicated to demographic forecasting.

Therefore, to keep the data development burden as light as possible, Caliper has retained the approach of using stratification curves in the TRMG2, although the specific implementation has changed. These curves simply encode information on the extent to which, for example, a zone with 3.5 persons-per-household on average will have a high percentage of 3- and 4-person households and a zone with an average of 1.5 persons-per- household will have more 1- and 2-person households.

In the Triangle, the marginal distribution curves estimated are:

  • Size (1-4+)
  • Income
    • Low: $0 - $24,999
    • Medium-Low: $25,000 - $74,999
    • Medium-High: $75,000 - $149,999
    • High: $150,000 and above
  • Workers (0-3+)

These curves are estimated from Census data, and the data is taken from different data products and geographies depending on availability. For example, the data needed to estimate the worker curve is only available from the American Community Survey (ACS) product known as the Census Transportation Planning Package (CTPP). Vehicle and income information is available from the ACS 5-year file directly, and size information is available from multiple products.

Household Size

The base year zonal SE data contains a range of zonal average household sizes, as shown by the blue histogram bars below. The Census block group histogram, shown in orange, has a similar range of household sizes which makes it a good candidate for model estimation. Although the differing level of aggregation between block groups and zones results in the distribution having different dispersion or variance, the fact that both distributions are centered on the regional average of 2.5 persons per household implies their consistency.

In the graph below, each green dot is the share of 1-person households in a block group based on the block group’s average household size. (Click on the siz2, siz3, and siz4 entries in the legend to the right of the chart to turn them off and focus on the green, 1-person households.) Multiple block groups that have the same average household size will usually have slight differences in their shares of 1-person households. For example, block groups with an average household size of 2.0 generally have 37-47% 1-person households; whereas, block groups with close to 3.5 persons per household on average typically have only 5-15% 1-person households. The same is true of the dots of different colors representing 2-, 3-, and 4+ households. A polynomial equation is fit to each set of colored dots. For any average household size, these polynomials can be evaluated to determine the percent of households in each size category.

For example, for a zone with an average household size of 2.3, the percent of households by size would be:

  • 1-person: 0.32 (green curve)
  • 2-person: 0.35 (orange curve)
  • 3-person: 0.15 (purple curve)
  • 4-person: 0.18 (pink curve)

At the extremes of average household size, manual edits were required to adjust curve behavior due to the low number of observations in these ranges. This same treatment was applied to create all marginal tables.

The model implements the curves above using a look-up table. The table below shows a segment of rows from the look-up table the model uses to dis-aggregate zonal data into households by size.

Household Size Lookup Table, Sample Rows
Average Household Size 1-person 2-person 3-person 4-person
2.00 0.3983 0.3666 0.1164 0.1187
2.01 0.3947 0.3675 0.1178 0.1200
2.02 0.3910 0.3683 0.1193 0.1214
2.03 0.3874 0.3691 0.1207 0.1228
2.04 0.3840 0.3698 0.1221 0.1241
2.05 0.3805 0.3705 0.1235 0.1255
2.06 0.3770 0.3712 0.1249 0.1269

Household Workers

The chart below shows the model and Census distributions of workers per household. The Census Transportation Planning Program (CTPP) data was used at the TAZ level, which contains more than enough observations to estimate a robust curve across the entire range of zonal values. The distribution of workers per household in the zonal data (developed from ACS) has a slightly different distribution from the older CTPP data set. However, the difference is small enough (1.2 vs 1.3 workers per household) that the CTPP data is deemed suitable for use.

Similar to the household size curve, Census data tables were used to calculate the share of households by number of workers at different levels of zonal average workers per household. The chart below shows the raw data from CTPP TAZ as well as the fitted curves.

Household Income

Before developing curves for median income, Caliper had to determine appropriate income groups. ACS data is already grouped to some extent, which limits the possible breakpoints in the final grouping. The histogram below shows the final income grouping and count of households in each group.

The prediction metric used for income is the median income of the zone divided by the regional median ($65,317). This provides an estimation range on a similar scale as the other variables for convenience ( e.g. 0.2 - 3.0 instead of $0 - $250,000).

The chart below shows the distribution of model and Census data. The model has zones without households (and thus zero median income), but otherwise the distributions are similar, particularly allowing for the slightly different levels of aggregation.

The chart below shows the raw observations and fitted curves.

Household Vehicles

The TRMG2 model utilizes an auto-ownership model, and as a result does not require disaggregation by household vehicles.

IPU Approach for TRM

The population synthesis for TRM is based on an updated algorithm in TransCAD 9. While earlier versions of TransCAD did have a population synthesis procedure, it was based on basic IPF as illustrated in the previous section without explicit control of person marginals. The IPU based enhancements provide a natural framework for incorporating person marginals.

Figure 3 shows the general schematic of the IPU enhancement over IPF. Note the additional inserted steps which creates the loop. As mentioned earlier, the HH seed weights are adjusted for each zone to match HH and person marginals for that zone.

Figure 3: Population Synthesis with IPU

The weight adjustment for each zone is performed using an incidence table shown in Figure 4. The rows in the table are HHs from the seed database. This can include either all the HHs in the seed or only include those that belong to the parent geography (PUMA) of the zone. The latter is used in TransCAD.

The columns represent the various marginal categories. For each row (HH), the values in the corresponding column indicates which category the HH belongs to or how many people in the household belong to the category. For instance, assume one HH category with 2 marginal columns (HH Veh 0 and HH Veh 1+) and one person category with three age marginals, then the HH with ID 5 has 1+ vehicles and has three persons (two in age category 2 and one in age category 3). Multiplying the ‘HH Veh 0’ column vector (cell by cell) with a corresponding weight vector will yield the number of HHs with zero vehicles in the zone. This is indicated in the ‘Column Sum’ row. The ‘Marginals’ row consists of the target values for this zone.

Figure 4: Incidence Table and IPU Adjustment

One iteration of the IPU consists of a complete set of column adjustments from left to right, one at a time. During each adjustment of the IPU, an adjustment factor is calculated as a simple ratio of the marginal total divided by the column total. This adjustment factor is used to multiply the current weight of all HHs that contributed to the total in the column. The weights of the other HHs are left unmodified.

For instance, the column sum for the first column is 3 whereas the desired marginal is 35. Thus, a factor of 35/3 = 11.67 is applied to the first three households that contributed totals to the first column. After the first column adjustment, HHs 1, 2 and 3 have a weight of 11.67 while the other HHs have a weight of 1. In the second iteration, the column sum (using the current weights is 5) and the marginal is 65. Thus, the adjustment factor of 13 (=65/5) is used to multiply the weights of the last five HHs to bring them up to 13. After this adjustment, HHs 1 to 3 still have a weight of 11.67 as they did not contribute to the second column sum. This mechanism is repeated for one column at a time.

Once a single iteration across all the columns is complete, an objective function is calculated and checked for convergence. The objective function calculations are general and can take many forms. For example, the fit \(\delta_{j}\) for column \(j\) may be computed as:

\[\delta_{j} = \frac{\sum_{i}^{}\left\lbrack w_{i}d_{\text{ij}} \right\rbrack - m_{j}}{m_{j}}\]

where \(w_{i}\) is the weight of household \(i\); \(d_{\text{ij}}\) is the contribution of household \(i\) to column \(j\); and \(m_{j}\) is the marginal for column \(j\). The overall objective function \(\delta\) could then be expressed as:

\[ \begin{matrix} \delta = \sum_{j}^{}\left( \delta_{j} \right)^{2} \end{matrix} \]

In the incidence table above, \(\delta = (3 - 35)/35\) for the first column and its absolute value is 0.914. After obtaining the \(\delta\) values for each column, the second equation then can be used to determine the objective function as 4.563.

The adjustment continues from left to right starting at the first column if the desired convergence metric has not been achieved.

Key Differences between TransCAD’s IPU and existing IPU approaches (PopGen)

The originally published IPU method in the literature was implemented in the PopGen software. In this original IPU algorithm, two separate IPFs are run, one on the HH marginals and one on the person marginals. The results of the second IPF on the person marginals are used to populate detailed person-level columns in the incidence table that specify the full, joint distribution of person
attributes. So, if there are multiple marginals to match such as HHs by Size (1,2,3,4+), number of vehicles (0,1,2,3+) and number of workers (1,2,3,4+) and Persons by Age (assume 5 categories) and Gender, then the incidence table has 64 HH columns, one for each combination of size, vehicles and workers and 10 person columns, one for each age category and gender combination. Since only one-dimensional marginals are typically known, the marginal values in the incidence tables come from the IPF run and the second IPF must be performed on the person characteristics to populate the person columns.

This version of IPU has several drawbacks. One, the process is slow, especially if there are a lot of marginals and the process can take hours. Second, the solution introduces a couple of other issues that must be dealt with and these issues have garnered significant attention in literature. One of these issues is a zero-cell problem, where the seed data is stretched thin and certain combinations may not be present in the seed. The second issue is a zero-marginal problem, but this can be solved by replacing the zero in the marginal row with epsilon values. There are several techniques to address these issues, which have been implemented in PopGen, but addressing these issues adds further runtime.

In the TransCAD approach, for want of minimizing these issues and at the behest of maintaining fast run times, only the one-dimensional marginals are used to form the incidence table. Thus, in the hypothetical example, the incidence table has 12 HH columns (as opposed to 64) and 7 person columns (as opposed to 10).

The enhanced TransCAD IPU method has been applied successfully for the Las Vegas RTC model as well as the California Central Coast ABM model. In both cases, not only was the match to the one-dimensional marginals (especially the persons) very close but the joint distribution observed from the synthesis was also very reasonable. These applications take a fraction of time compared to that reported on similar sized problems with the original IPU method or optimization methods.

The next few sections discuss the application of the procedure to the TRM and the results.

Application for the TRM

For the TRM region, several marginals have been synthesized at the zone layer. These marginals at the HH level include:

  • HHs by Size (1, 2, 3 and 4+)

  • HHs by number of workers (0, 1, 2 and 3+)

  • HHs by Income

    • Low [0, 35000)

    • Medium Low [35000, 75000)

    • Medium High [75000, 150000)

    • High 150000+

Several disaggregate curves developed from the ACS 2014-2018 data are used to obtain these marginals from zonal average values which are more easily supplied for future scenarios than full distributions. The curves determine the respective marginal splits based on average HH size, ratio of TAZ income to regional income and average number of workers in the TAZ.

Person marginals matched include

  • Persons by Age Group

    • Children (0 < age <= 18)

    • Adults under 65 (18 < age < 65)

    • Seniors (age >= 65)

The zone socio economic data contains derived percentages of kids, adults under 65 and seniors (from ACS data). These are used to compute the three age classifications above that serve as person marginals.

The seed HH and person data come from ACS PUMS that have 45,825 and 110,146 records respectively. The seed data has the necessary fields to generate indicators for the various dimensions being matched using the fields NP (Number of persons in the HH), HHINC and ADJINC (to compute the income classification) in the HH database; and the fields Age and ESR (Employment Status) in the person database to compute the age classification and the number of workers in the HH.

There are 18 PUMA zones in the TRM region and Figure 5 highlights some key data. The TAZ boundaries are shown in green and the colored areas are the PUMA zones.

Figure 5: PUMAs in the TRM region

The running time of the entire population synthesis for the TRM (with the IPU) is 2 minutes. These running times represent a small fraction of running times reported for similar problems in the literature.

Results

The population synthesis on TRM generates 731,913 HHs and 1,783,548 persons. The number of HHs in the SE data is 731,875 and the population in households is 1,826,973. The percentage errors are 0.005% on the HHs and 2.38% on the overall population.

The fit to various marginals is illustrated in the following charts. The input SE marginals (by TAZ) are on the x-axis while the synthesized marginals (aggregated to TAZ) are plotted on the y-axis. Each graph also includes the regression line equation, R-squared and the percent RMSE.

Figure 6: Comparison of HH Size Marginals

Figure 7: Comparison of HH Workers Marginals

Figure 8: Comparison of HH Income Marginals

As expected, the fit to the HH marginals shown in Figures 6, 7 and 8 are pretty much spot on. This is testament to the IPF procedure having converged successfully.

The subsequent charts show fit to person marginals. Figures 9 and 10 show fit to total HH population and the fit to total number of workers. Since the HH marginals match HH by size and HH by number of workers, these charts are also expected to show a great fit.

Figure 8: Comparison of total HH population

Figure 9: Comparison of workers

Note that for a run without the IPU option, the fit to the marginals in Figures 6 to 9 are pretty similar.

Figures 10 to 12 show the fit of population in three age categories. Unlike the previous figures, the incorporation of the IPU here makes a significant difference. In these graphs, the orange line and the orange points represent the fit of the TRM population synthesis with the IPU option enabled. The blue line and the blue points represent the fit of a similar population synthesis without the IPU options. These graphs are produced to illustrate both the good fit of the final TRM synthesis and illustrate the efficacy of the IPU.

Figure 10: Comparison of Number of Kids (IPU vs Non-IPU)

Figure 11: Comparison of Adults Under 65 (IPU vs Non-IPU)

Figure 12: Comparison of Seniors (IPU vs Non-IPU)

Conclusion

The updated population synthesis for the TRM is based on the improved population synthesis available in TransCAD 9, which is a variant of the population synthesis with IPU published in the literature. The TAZ marginals are derived by fitting curves on the ACS 2014-2018 data. The ACS PUMS for these years form the seed databases for the synthesis procedure. The marginals matched include HH by Size, HH by Number of Workers, HH by Income Group and Persons by Age. The population synthesis is extremely fast with a run time of 2 minutes and the fit to the marginals is great. The resulting synthesis is demonstrative of the person and HH characteristic distribution in the TRM region and can be confidently used in the application of the state-of-the-art hybrid model for the Triangle Region.

References

Balakrishna, R., S. Sundaram and J. Lam. An Enhanced and Efficient Population Synthesis Approach to Support Advanced Travel Demand Models. Presented at the 99th TRB Annual Meeting.

Ye., X., K. Konduri, R.M. Pendyala, B. Sana and P. Waddell. A methodology to match distributions of both household and person attributes in the generation of synthetic populations. Presented at the TRB annual meeting, 2009.

Ramadan, O.E., and V.P. Sisiopiku. A Critical Review on Population Synthesis for Activity- and Agent-Based Transportation Models. Transportation Systems Analysis and Assessment, IntechOpen, 2019.




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