Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component (2015)

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67 A P P E N D I X B This appendix provides full details of the statistical models used in this research. The level of detail provided here will be of interest to statisticians and modelers. Cross-Sectional Analysis of Urbanized Area VMT for the Entire United States Research Design In this analysis, a cross-sectional model is estimated to capture the long-run relationships between transportation and land use at a point in time, 2010. Each urbanized area has had decades to arrive at quasi-equilibrium among land use patterns, road capacity, transit capacity, and VMT. This quasi-equilibrium is captured via SEM. Method of Analysis SEM is a statistical technique for evaluating complex hypotheses involving multiple, interact- ing variables (Grace 2006). The estimation of SEM models involves solving a set of equations. There is an equation for each “response” or “endogenous” variable in the transit system. Endog- enous variables are affected by other variables and may also affect other variables. Variables that are solely predictors of other variables are termed “influences” or “exogenous” variables. They may be correlated with one another but are determined outside the transit system. Typically, solution procedures for SEM models focus on observed versus model-implied cor- relations in the data. The unstandardized correlations or co-variances are the raw material for the analyses. Models are automatically compared to a “saturated” model (one that allows all variables to inter-correlate), and this comparison allows the analysis to discover missing path- ways and, thereby, reject inconsistent models. Data Growing Cooler (Ewing et al. 2008) used data from the Texas A&M Transportation Institute (TTI) Urban Mobility database to estimate VMT models. In this research, data were instead gathered from several different primary sources. This was due to three critical shortcomings of the current TTI database, which contains 2010 data and was released in 2011: • Small sample size. The 2010 TTI database contains data for 101 large urbanized areas. This relatively small sample limits the statistical power of the analysis and the ability to discern sig- nificant relationships. It also makes it difficult to generalize results to smaller urbanized areas. • No land use variables. Previous versions of the TTI database contained one land use variable, the gross density of each urbanized area, but this measure has been dropped from more recent Statistical Models in Depth

68 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component versions. The lack of land use variables makes it impossible to use the current TTI data alone to examine the land use effects of transit on VMT. • Discrepancies with official databases. The TTI database contains estimates of transit pas- senger miles that differ from the official figures in the National Transit Database. The reason is unclear, but these discrepancies raised the question of whether the TTI database would be appropriate for use in this research. The research team gathered data from several primary sources for the cross-sectional analysis. For the sake of consistency, the boundaries used to compute explanatory variables had to be the same as the boundaries used to estimate the dependent variable, VMT per capita from FHWA Highway Statistics. The Highway Statistics definition of urbanized area is different from the Census definition. According to FHWA, “the boundaries of the area shall encompass the entire urbanized area as designated by the U.S. Bureau of the Census plus that adjacent geographical area as agreed upon by local officials in cooperation with the State.” Cervero and Murakami (2010) used the Census boundaries for their analysis and deleted urbanized areas from the sample if the Census and FHWA boundaries were hugely different. The research team for this project (TCRP Project H-46) chose not to make such approximations or lose many cases, and therefore set out to find FHWA- adjusted boundaries for urbanized areas in a geospatial shapefile format, which could then be used to conduct spatial analyses in geographical information systems (GIS) (see Figure 35). Source: Metropolitan Research Center, University of Utah Figure 35. 2000 Census and FHWA-adjusted urbanized area boundaries for Atlanta.

Statistical Models in Depth 69 Based on FHWA advice, the research team contacted individual state department of transpor- tation offices for their shapefiles. From this effort, shapefiles for all 50 states and 443 urbanized areas were obtained. The individual state files were then combined into one national shapefile by using the “merge” function in GIS. Many of the urbanized areas cross state boundaries, resulting in more than one polygon for each urbanized area. So, the “dissolve” function in GIS was used to integrate those polygons into one for each urbanized area. Several spatial “joins” were conducted in GIS to capture data from other sources. For exam- ple, the “centroid” function was used to join 2010 census tracts to FHWA-adjusted urbanized areas. Values of per capita income for census tracts were aggregated to obtain urbanized area averages (weighted by population). Variables The variables in the research models are defined in Table 11. The variables fall into three general classes: • Outcome variable, VMT per capita. • Exogenous explanatory variables. The exogenous variables, population and per capita income, are determined by regional competitiveness. The real fuel price is determined by Variable Definition Source Mean Standard Deviation Dependent variable vmt Natural log of daily VMT per capita FHWA Highway Statistics 3.09 0.25 Exogenous variables pop Natural log of population (in thousands) U.S. Census 12.45 1.16 inc Natural log of income per capita American Community Survey 10.13 0.19 fuel Natural log of metropolitan average fuel price Oil Price Information Service 1.03 0.06 flm Natural log of freeway lane miles per 1,000 population FHWA Highway Statistics −0.46 0.53 olm Natural log of other lane miles per 1,000 population FHWA Highway Statistics NAVTEQ 0.91 0.32 hrt Directional route miles of heavy-rail lines per 100,000 population* National Transit Database 0.04 0.23 lrt Directional route miles of light-rail lines per 100,000 population* National Transit Database 0.09 0.33 Endogenous variables popden Natural log of gross population density U.S. Census 7.33 0.44 rtden Natural log of transit route density per square mile National Transit Database 0.67 0.82 tfreq Natural log of transit service frequency National Transit Database 8.51 0.59 tpm Natural log of annual transit passenger miles per capita National Transit Database 3.76 1.12 * 1 was added to values so that urbanized areas with no rail mileage would have a zero value when log transformed. Table 11. Variables included in the urbanized area model.

70 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component federal and state tax policies and regional location relative to ports of entry and refining capacity. Variables representing highway capacity and rail system capacity were also treated as exogenous, as they are the result of long-lived policy decisions to invest in highways or transit. • Endogenous explanatory variables. The endogenous variables are a function of exogenous variables and are, in addition, related to one another. They depend on real estate market forces and regional and policy decisions: whether to increase transit revenue service and/or whether to zone for higher densities. All variables were transformed by taking natural logarithms. The use of logarithms has two advantages. First, it makes relationships among the variables more nearly linear and reduces the influence of outliers (such as New York and Los Angeles). Second, it allowed the research team to interpret parameter estimates as elasticities, which summarize relationships in an understand- able and transferable form. Model The SEM model was estimated with the software package Amos (version 7.0, SPSS 2007) and maximum likelihood procedures. The path diagram in Figure 36 is copied directly from Amos. Causal pathways are represented by uni-directional straight arrows. Correlations are represented by curved bi-directional arrows (to simplify the already complex causal diagram, some correla- tions are omitted). By convention, circles represent error terms in the model, of which there is one for each endogenous (response) variable. Figure 36. Causal path diagram explaining VMT per capita for urbanized areas.

Statistical Models in Depth 71 Most of the causal paths shown in the path diagram are statistically significant (have nonzero values). The exceptions are a few paths that are theoretically significant, although not statisti- cally significant. The main goodness-of-fit measure used to choose among models was the chi-square statis- tic. Probability statements about an SEM model are reversed from those associated with null hypotheses. Probability values (p-values) used in statistics are measures of the degree to which the data are unexpected, given the hypothesis being tested. In null hypothesis testing, a finding of a p-value <0.05 indicates that the null hypothesis can be rejected because the data are very unlikely to come from a random process. In SEM, a model with a small chi-square and large p-value (>0.05) was sought because that indicates that the data are not unlikely given that model (that is, the data are consistent with the model). Results The VMT model in Figure 36 has a chi-square of 26.5 with 22 model degrees of freedom and a p-value of 0.23. The low chi-square relative to model degrees of freedom and a high (>0.05) p-value are indicators of a good model fit. The regression coefficients in Table 12 give the predicted effects of individual variables, all other things being equal. These are the direct effects of one variable on another. They do not Coefficient Standard Error Critical Ratio P-Value tfreq <--- pop 0.235 0.025 9.234 <0.001 rtden <--- lrt 0.495 0.131 3.787 <0.001 rtden <--- hrt 0.355 0.187 1.900 0.057 rtden <--- pop −0.103 0.042 −2.463 0.014 popden <--- olm −0.552 0.047 −11.748 <0.001 popden <--- rtden 0.197 0.017 11.528 <0.001 tpm <--- pop 0.141 0.041 3.440 <0.001 tpm <--- tfreq 0.796 0.077 10.406 <0.001 popden <--- tfreq 0.187 0.023 8.035 <0.001 tpm <--- rtden 0.839 0.049 17.124 <0.001 popden <--- flm −0.108 0.020 −5.383 <0.001 tpm <--- inc 0.902 0.208 4.345 <0.001 popden <--- pop 0.066 0.011 5.849 <0.001 popden <--- fuel 0.733 0.236 3.111 0.002 vmt <--- fuel −0.448 0.238 −1.883 0.060 vmt <--- popden −0.238 0.043 −5.577 <0.001 vmt <--- olm 0.040 0.051 0.784 0.433 vmt <--- flm 0.133 0.021 6.412 <0.001 vmt <--- inc 0.304 0.062 4.889 <0.001 vmt <--- tpm −0.016 0.011 −1.427 0.154 vmt <--- pop 0.078 0.012 6.635 <0.001 Table 12. Path coefficient estimates (regression coefficients) and associated statistics for direct effects in the 2010 VMT per capita model (see Figure 36).

72 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component Direct Indirect Total pop 0.078 −0.025 0.052 inc 0.304 −0.015 0.289 fuel −0.448 −0.175 −0.623 hrt 0 −0.021 −0.021 lrt 0 −0.03 −0.03 flm 0.133 0.026 0.159 olm 0.04 0.131 0.172 popden −0.238 0 −0.238 rtden 0 –0.06 −0.06 tfreq 0 −0.057 −0.057 tpm −0.016 0 −0.016 Table 13. Direct, indirect, and total effects of variables on VMT per capita in the cross-sectional model for 2010 (see Figure 36). account for the indirect effects through other endogenous variables. Also of interest are the total effects of different variables on VMT per capita, accounting for both direct and indirect pathways (see Table 13). A number of key factors affect VMT and in some cases urban area density: • Population growth is a driver of VMT growth. As urbanized areas grow, destinations tend to become farther apart (for example, the suburbs are farther from the central business district). Therefore, the direct effect of population size on VMT per capita is positive and significant due to the simple fact of their size. At the same time, as urbanized areas grow, they become denser and shift away from a singular focus on-road capacity to meet travel demands toward a balance of roads and transit. • Income. Another exogenous driver of VMT growth is income. As per capita income rises, people travel more by private vehicle, reflecting the general wealth of the commu- nity. The direct effect of per capita income on VMT per capita is positive and highly sig- nificant. Income has an indirect effect as well, through transit passenger miles per capita. Surprisingly, the effect of income on transit use is positive; hence the indirect effect on VMT is negative. Wealthier communities may provide more transit service, and higher income residents in large regions such as New York may use transit to commute in from the suburbs. • Freeway capacity. Controlling for other influences, areas with more freeway capacity are sig- nificantly less dense and have significantly higher VMT per capita. Areas with more highway capacity in arterials, collectors, and local streets are also significantly less dense (which affects VMT per capita indirectly), but the direct effect of other highway capacity on VMT per capita is not significant. From the standpoint of induced traffic, other roadways are more benign than freeways. • Transit has an effect opposite to that of highways. Areas with more service coverage and more service frequency have higher development densities, which lead to lower VMT per capita. They also have more transit passenger miles per capita, which lead to lower VMT per capita. The causal path through transit passenger miles constitutes the ridership effect of transit on

Statistical Models in Depth 73 VMT. The causal path through development density constitutes the land use effect of transit on VMT. • The two rail variables, HRT and LRT directional route miles per capita, are positively associated with route coverage, and through that variable, increase transit passenger miles per capita and reduce VMT per capita. Surprisingly, neither HRT route mileage nor LRT route mileage has a direct effect on the development density of urbanized areas. One pos- sible explanation for the failure of rail to raise densities is the oft-cited potential of rail extensions into the suburbs to cause sprawl, as long-distance commuters park and then ride into the city. • The real fuel price is negatively associated with VMT per capita, both directly and indirectly through an effect on development densities. The direct price elasticity, around -0.45, is what one would expect from the literature (the long-run elasticity being much greater than the short-run elasticity). There are persistent regional variations in real fuel prices, and these appear to affect both urban form and VMT per capita. • Urbanized area density is negatively related to VMT per capita. The elasticity, -0.24, sug- gests that every 1% rise in density is associated with a 0.24% decline in VMT per capita. With density serving as a proxy for all the “D” variables (density, diversity, design, and destination accessibility), the elasticity looks reasonable. Simulation of VMT Per Capita in a No-Transit Scenario The SEM models discussed above represent relationships using logarithmically transformed variables. Logged variables have the advantage of accounting for nonlinear relationships, reduc- ing the influences of outlying data points, and producing regression coefficients that can be interpreted as arc elasticities (percentage changes in VMT with respect to a 1% change in an independent variable). These models are well suited to predicting the effect of incremental changes in one variable or another. However, log models cannot answer the impacts that would occur in the extreme case of all transit service being eliminated. The log of zero is undefined (equal to negative infinity), so that transit variables in this scenario would be undefined. Therefore, the research team estimated a new SEM model with linear variables that, in the case of the transit variables, could be zeroed out in a no-transit scenario. The study sample consists of 315 federal-aid urbanized areas that, in 2010, collectively housed 200 million Americans or nearly two-thirds of the U.S. population. Included are all large urbanized areas and most smaller urbanized areas. Some urbanized areas were lost for lack of complete datasets, particularly lack of fuel price data. Some urbanized areas were also lost for lack of complete transportation sys- tems, including transit service and some freeway capacity. Variables are defined in Table 14. The variable of ultimate interest is VMT per capita. Other endogenous variables are gross population density, transit route density, transit service fre- quency, and transit passenger miles per capita. Endogenous variables are variables that are influ- enced by other variables in the modeling transit system and that may influence other variables. The remaining variables, such as miles of light rail, lane miles of freeway per 1,000 population, and average fuel price, are exogenous. Exogenous variables are variables that influence other variables, but whose values are determined outside the transit system. The model’s path diagram (see Figure 37) is very similar to the path diagrams of the loga- rithmic models. Some causal links were added (straight single-headed arrows); several correla- tional arrows (curved two-headed arrows) were deleted from the diagram to make it appear less complex.

74 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component Regression coefficients for direct causal relationships and associated significance levels are shown in Table 15. The regression coefficients give the predicted effects of individual variables on one another, all other things being equal. These are the direct effects of one variable on another, not accounting for the indirect effects through other endogenous variables. The model has a chi-square of 15.0 with 18 model degrees of freedom and a p-value of 0.67. This indicates an extremely close fit between the model and the data. The two main transit service variables, transit service frequency (tfreq) and transit route density (rtden), affect VMT (vmt) directly through transit passenger miles (tpm) and indi- rectly through gross population density (popden). The resulting equations for vmt, tpm, popden are: vmt 28.87 6.105 fuel 0.002 popden 0.471 olm 4.564 f lm 0.355 inc000 0.001 pop000 0.006 tpm = − ∗ − ∗ + ∗ + ∗ + ∗ + ∗ − ∗ tpm 491.6 0.025 pop000 0.004 tfreq 4.198 rtden 4.134 inc000 59.882 hrt 146.800 fuel = − + ∗ + ∗ + ∗ + ∗ + ∗ + ∗ popden 746.1 354.711 olm 55.895 rtden 0.046 tfreq 316.547 flm 0.108 pop000 1092.585 fuel 144.573 lrt = − − ∗ + ∗ + ∗ − ∗ + ∗ + ∗ + ∗ Variable Definition Source Mean Standard Deviation Dependent variable vmt Daily VMT per capita FHWA Highway Statistics 22.7 5.5 Exogenous variables pop000 Population (in thousands) U.S. Census 635.7 1,559.7 inc000 Income per capita (in thousands) American Community Survey 25.5 5.1 fuel Average fuel price metropolitan average fuel price Oil Price Information Service 2.79 0.16 flm Freeway lane miles per 1,000 population FHWA Highway Statistics 0.72 0.38 olm Other lane miles per 1,000 population FHWA Highway Statistics NAVTEQ 2.60 0.80 hrt Directional route miles of heavy-rail lines per 100,000 population National Transit Database 0.085 0.545 lrt Directional route miles of light-rail lines per 100,000 population National Transit Database 0.193 0.785 Endogenous variables popden Gross population density U.S. Census 1,683.2 824.9 rtden Transit route density per square mile National Transit Database 2.82 3.21 tfreq Transit service frequency National Transit Database 5,831.4 3,315.1 tpm Annual transit passenger miles per capita National Transit Database 79.7 122.5 Table 14. Variables in the urbanized area model.

Statistical Models in Depth 75 These equations allowed the research team to estimate how the absence of transit would affect VMT for the average urbanized area. Plugging mean values for the sample into the three equa- tions, the research team estimated a mean vmt value of 22.19, a mean tpm of 79.5, and a mean popden of 1,675. These values apply to a status quo scenario. They are entirely comparable to the actual mean values for the sample, 22.7, 79.7, and 1,683, respectively. If tfreq, rtden, hrt, lrt, and hrt are zeroed out in a no-transit scenario, tpm falls from 79.5 to 39.3, popden falls from 1,675 to 1,221, and hence vmt rises from 22.19 to 23.36, a 5.3% rise. One could argue that despite the multivariate equation that says tpm would be 39.3 under this scenario, the actual value of tpm for the no-transit scenario would be zero. Plugging this value into the first equation, vmt would rise from 22.19 to 23.59, a 6.3% rise. The increase in vmt for the typical urbanized area was bounded between 5.3% and 6.3% if transit service were eliminated. How much of the difference in vmt between the no-transit scenario and status quo is due to the ridership effect of transit through tpm, and how much is due to the land use effect through popden? Using predicted values of both mediating variables (39.3 and 1,221, respectively), the difference in vmt between scenarios is 1.17 vehicle miles per day. Of that, 22% is the ridership effect and 78% is the land use effect. Using the predicted value of popden (1,231) and the more plausible value of tpm (0), the difference in vmt between scenarios is 1.40 vehicle miles per day. Of that, 35% is the ridership effect and 65% is the land use effect. Figure 37. Causal path diagram explaining VMT per capita for urbanized areas.

76 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component Cross-Sectional Analysis of Household VMT in Nine Diverse Regions This multivariate analysis pools household travel and built environment data from nine diverse regions of the United States. The model is distinct from many earlier studies for several important reasons: • Large, diverse database. What most distinguishes this study from the many earlier studies of household travel behavior is the external validity (generalizability) that comes with such a large and diverse database. A study using data from cities such as Portland, Oregon, or Houston, Texas, could be challenged for relevance to other regions of the country, particu- larly when different dependent and independent variables are used in each study. Research that pools data from nine diverse regions and uses consistently defined built environmental variables to predict several consistently defined travel outcome variables should be ready for use in large metropolitan areas across the United States. • Multilevel modeling. Another characteristic that distinguishes this study from earlier ones is the use of multilevel modeling (MLM). MLM overcomes the limitations of ordinary least Estimate Standard Error Critical Ratio P-Value tfreq <--- pop000 .889 .108 8.223 <0.001 rtden <--- lrt .129 .214 .604 0.546 rtden <--- hrt .502 .333 1.506 0.132 rtden <--- pop000 .000 .000 −1.106 0.269 tfreq <--- lrt 750.004 213.148 3.519 <0.001 popden <--- olm −354.711 38.112 −9.307 <0.001 popden <--- rtden 55.895 9.134 6.119 <0.001 tpm <--- pop000 .025 .004 6.216 <0.001 tpm <--- tfreq .004 .002 2.415 0.016 popden <--- tfreq .046 .009 4.953 <0.001 tpm <--- rtden 4.198 1.735 2.419 0.016 popden <--- flm −316.547 66.378 −4.769 <0.001 popden <--- pop000 .108 .018 5.943 <0.001 popden <--- fuel 1092.585 187.035 5.842 <0.001 tpm <--- inc000 4.134 1.012 4.086 <0.001 popden <--- lrt 144.573 32.719 4.419 <0.001 tpm <--- hrt 59.882 10.287 5.821 <0.001 tpm <--- fuel 146.800 34.614 4.241 <0.001 vmt <--- fuel −6.105 1.917 −3.185 0.001 vmt <--- popden −.002 .000 −3.139 0.002 vmt <--- olm .471 .421 1.119 0.263 vmt <--- flm 4.564 .677 6.743 <0.001 vmt <--- inc000 .355 .053 6.757 <0.001 vmt <--- pop000 .001 .000 3.011 0.003 vmt <--- tpm −.006 .003 −2.332 0.02 Table 15. Path coefficient estimates (regression coefficients) and associated statistics for direct effects in the 2010 VMT per capita model (see Figure 37).

Statistical Models in Depth 77 squares regression by accounting for the dependence of households in each region on the characteristics of that particular region, dependence that violates the independence assump- tion of ordinary least squares. MLM thereby produces more accurate coefficient and standard error estimates (Raudenbush and Bryk 2002). While MLM is just beginning to be used in planning studies, it has a rich history in education and public health research. • Two-stage “hurdle” models for two of the dependent variables. A third characteristic that distinguishes this study from earlier studies is the estimation of two-stage “hurdle” models for two of the dependent variables, household VMT (vmt) and household transit trips (ttrips). The study dataset is “zero inflated,” which means these two dependent variables have an exces- sive number of zero values that violate conventional distributional assumptions. The solution to this problem is to estimate so-called hurdle models (Greene 2012, pp. 443, 824–826). The research team is aware of no previous application of hurdle models to the planning field. Data The research team gathered and pooled data for nine metropolitan regions for the neighborhood-level analysis of the ridership and land use effects of transit on VMT. One region, Portland, Oregon, is represented twice in the combined dataset, once for 1994, early in the development of LRT, and then for 2011, after much LRT development, thereby permitting lon- gitudinal comparisons. The early Portland dataset was dropped for purposes of cross-sectional analysis. The resulting dataset consists of 254,691 trips by 26,009 households in nine regions (see Table 16). The regions are diverse, with Boston and Portland at one end of the transit service continuum and Houston and Kansas City at the other. All surveys provide XY coordinates for households and their trips. This allows travel to be modeled in terms of the precise built environment in which households reside and travel occurs. For individual trips, trip purpose, travel mode, travel time, and other variables are available from the survey dataset. Distance traveled on each trip was either supplied or computed with GIS from the XY coordinates. For travelers, individual age, employment status, driver’s licensure, and other variables are available from the survey dataset. For households, household size, household income, vehicle ownership, and other variables are available from the survey dataset. This allowed the research team to control for sociodemographic influences on travel at the household level. Additional geocoded household travel datasets have been acquired for Boston, Denver, Houston, Los Angeles, Minneapolis-St. Paul, Philadelphia, and San Antonio (see Table 17). The acquisition of a second database for Boston (1991 and 2011) allowed the research team to drop the early databases from the cross-sectional samples. In addition, having three regions (Boston, Survey Date Surveyed Households Surveyed Trips Austin 2005 1,446 14,196 Boston 1991 2,595 20,217 Eugene 2011 1,672 16,409 Houston 1995 1,954 19,417 Kansas City 2004 3,000 30,416 Portland 2011 4,500 46,854 Sacramento 2000 3,520 33,519 Salt Lake City 2012 3,516 38,595 Seattle 2006 3,896 35,068 Total 26,099 254,691 Table 16. Combined dataset.

78 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component Houston, and Portland) with widely spaced travel surveys and with transit expansion in between the travel surveys, permitted longitudinal as well as cross-sectional analyses. Other datasets have been collected for the same years as the travel surveys in order to estimate values of many “D” variables for 1⁄4-, 1⁄2-, and 1-mile radius buffers around each household. These include a geocoded parcel land use layer, geocoded street and transit layers, and travel time skims, population, and employment by traffic analysis zone (TAZ) as supplied by the regions’ metropolitan planning organizations. Parcel-level assessor data in the survey area were acquired from each individual county to estimate the amount and type of each land use within the buffers. Parcel features were con- verted to centroid points, allowing parcel attributes to be joined to the buffer polygons. Roadway centerlines were used for collection of intersection points, where centerline intersections were counted and summarized. Transit stop geographic locations were collected from all operators serving the travel survey area. All stops were merged according to bus or rail categories. Bus and rail stop locations were joined to buffers for stop counts. Population density was determined by weighting census block group population estimates with residential parcel square footage for population density. Population density per square foot was then applied to residential parcels intersecting each buffer. Employment data were obtained at the TAZ level from metropoli- tan planning organizations and, along with interzonal travel times from metropolitan planning organizations, were used to compute employment accessible within 10-, 20-, and 30-minute automobile travel times and within 30-minute transit travel times. Employment for individual household buffers were generated by weighting the size of the TAZ in proportion to the buffer. The proportion was multiplied by the number of jobs in each intersecting TAZ. Variables To increase statistical power and external validity, household travel data from nine diverse regions were pooled. The data and model structure are hierarchical, with households nested within regions. The variables extracted from these datasets and used in subsequent analyses fall into four categories (see Table 18). Three of the categories are specific to households. Each household has a different set of variable values. One of the categories is specific to regions. All households within a given region share these characteristics. Variables are the following: • VMT (vmt), the household variable of ultimate interest. This is an outcome variable to be explained or predicted. • Transit trips (ttrips) and activity density (actden—population plus employment divided by land area) in the 1⁄2-mile buffer around households. These are mediating variables on the causal pathway between household VMT and the exogenous variables. These are also out- come variables to be explained or predicted. Survey Year Households Trips Boston 2011 7,661 103,124 Denver 2010 7,302 84,819 Houston 2009 5,807 79,393 Los Angeles 2000 16,939 190,169 Minneapolis-St. Paul 2010 10,363 79,232 Philadelphia 2000 4,217 47,071 San Antonio 2006 NA NA Table 17. New household travel datasets.

Statistical Models in Depth 79 • Transit variables that measure the relative level and type of transit service at the neighbor- hood level. These are the key independent variables in the research. They are the percentage of regional employment accessible within 30 minutes by transit from a household location (emp30t) and a dummy variable for the presence of a rail station within 1⁄2 mile of the house- hold (rail). • Built environmental variables, accounting for the land use diversity, street network design, and automobile accessibility to jobs at and around the household location. • Household control variables accounting for the socioeconomics of households. There are three: household size, number of employed members, and household income. Category Symbol Definition Level Primary outcome variable vmt Household daily VMT Household Intermediate outcome variables ttrips Household daily transit trips Household actden Activity density within 1/2 mile (sum of population and employment divided by gross land area in square miles) Household Exogenous transit variables emp30t Proportion of regional employment accessible within 30-minute travel time via transit (in-vehicle time only) Household rail Rail station within 1/2 mile (dummy variable; yes=1, no=0) Household Exogenous built environmental variables jobpop Job-population balance within 1/2 mile of a household (index ranging from 0, where only jobs or residents are present within a 1/4 mile, to 1, where there is one job per five residents) Household entropy Land use mix within 1/2 mile of a household (entropy index based on net acreage in different land use categories that ranges from 0, where all developed land is in one use, to 1, where developed land is evenly divided among uses) Household intden Intersection density within a 1/2 mile of a household (number of intersections divided by gross land area in square miles) Household int4way Percentage of four-way intersections with 1/2 mile of a household (four-way intersections or intersections where more than four streets meet divided by total intersections) Household emp10a Percentage of regional employment accessible within a 10-minute travel time via automobile Household emp20a Percentage of regional employment accessible within a 20-minute travel time via automobile Household emp30a Percentage of regional employment accessible within a 30-minute travel time via automobile Household Household control variables hhsize Number of household members Household employed Number of household members employed Household income Household income (in 1,000s of 2012 dollars) Household Regional control variables rpop Total regional population (in 1,000s) Regional remp Total regional employment (in 1,000s) Regional ract Total regional activity (sum of population and employment in 1,000s) Regional rind Regional compactness index (index measuring compactness vs. sprawl based on a combination of four factors that measure density, land use mix, degree of centering, and street accessibility); higher values signify great compactnessa Regional aFor more information on the regional sprawl index and how it is calculated, see Measuring Sprawl and Its Impact (Ewing, Pendall, and Chen 2002). Table 18. Category, definition, and scale of variables proposed for inclusion in the neighborhood level model.

80 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component • Region size and urban form variables, accounting for regional random effects shared by all households in a given region. Statistical Methods Nesting of households within regions creates dependence among observations, in this case the dependence of households within a given region. All households within a given region share the characteristics of the region. Regions such as Boston and Houston are likely to generate very different travel patterns irrespective of household and neighborhood characteristics. This dependence violates the independence assumption of ordinary least squares regression. Stan- dard errors of regression coefficients based on ordinary least squares will consequently be under- estimated. Moreover, ordinary least squares coefficient estimates will be inefficient. One solution to the problem of nested data is MLM, also called hierarchical modeling (Raudenbush and Bryk 2002). The essence of MLM is to isolate the variance associated with each data level and then seek to explain as much of it as possible with available variables. The more explained variance, the better. MLM modeling is just beginning to be used in the planning field. For this research, the research team began by partitioning variance between the household level (Level 1) and the region level (Level 2). Outcomes were then modeled in terms of variables specific to each level. Given the large sample of households, many household level variables were likely to prove significant, thereby reducing unexplained variance at Level 1. This was not the case at the regional level, with only nine regions. Variables such as regional population and density were unlikely to prove significant due to limited degrees of freedom. Still, there was sig- nificant variance in transportation outcomes from region to region, and MLM captures it in the random effects terms of the Level 2 equations. The modeling task was further complicated by the large number of zero values for two of the three dependent variables. The vmt frequency distribution had an excessive number of zero val- ues, specifically 1,878 of the 26,000 households with no VMT at all (see Figure 38). These were households that relied on alternative modes of transportation. The other variable—ttrips—had an excessive number of zero values too, in this case 21,934 households with no transit use at all (see Figure 42). Use of transit was the exception rather than the rule in the United States. In the planning literature, the problem of zero inflation is often handled by adding one (1.0) to the value of a dependent variable and then log transforming the variable. The 1 becomes a 0 when transformed. This is not econometrically correct, however, since households with zero values may be qualitatively different than those with positive values. “In some settings, the zero outcome of the data-generating process is qualitatively different from the positive ones. The zero or nonzero values of the outcome is the result of a separate decision whether or not to ‘par- ticipate’ in the activity. On deciding to participate, the individual decides separately how much to, that is, how intensively [to participate]” (Greene 2012, p. 824). The proper solution to the problem of zero inflation is to estimate two-stage “hurdle” models (Greene 2012, pp. 443, 824–826). The stage 1 models categorize households as either generating VMT or not, or generating transit trips or not. The stage 2 models estimate the amount of VMT generated for households with positive (nonzero) VMT and the number of transit trips gener- ated for households with positive (nonzero) transit trips. Setting aside for the moment the dependence of cases (which are handled with MLM) and zero inflation (which are handled with hurdle models), two of the three dependent variables— vmt and actden—were continuous but highly skewed to the left (see Figure 38 and Figure 40. The two were transformed by taking their natural logarithms (as in Figure 39 and Figure 41). With logarithmic transformations, these variables were very nearly normally distributed.

vmt Fr eq ue nc y Figure 38. Histogram of household VMT. Invmt Fr eq ue nc y Figure 39. Histogram of the natural logarithm of household VMT.

actden Fr eq ue nc y Figure 40. Histogram of the household buffer activity density. Inactden Fr eq ue nc y Figure 41. Histogram of the natural logarithm of household buffer activity density.

Statistical Models in Depth 83 17 For examples, see “Safe Urban Form: Revisiting the Relationship between Community Design and Traffic Safety” (Dumbaugh and Rae 2009) and “Does Street Network Design Affect Traffic Safety?” (Marshall and Garrick 2011). These dependent variables were modeled with Hierarchical Linear and Nonlinear Modeling software, HLM 6.08. For vmt, the research team first modeled the dichotomous outcome of a household having positive VMT or not, using hierarchical logistic regression. The team then modeled the continuous variable lnvmt using hierarchical linear regression. For actden, the pro- cess only involved one step since all values are positive; the team simply modeled the continuous variable lnactden using hierarchical linear regression. The process of modeling the third dependent variable—ttrips—was somewhat trickier. This dependent variable was a count with many zero values (households making no transit trips—see Figure 42) and the rest with positive integer values whose frequency dropped off rapidly as the number increased (household making one or more transit trips—see Figure 43). Not only did the household’s choice have to be first modeled between using transit or not, using hierarchi- cal logistic regression, but then another type of hierarchical regression had to be used to model cases with positive values. Treating the positive values separately allowed them to be modeled with HLM 6.08. Two basic methods of analysis were available when the dependent variable was a count with nonnegative integer values, many small values, and few large ones. The methods were Poisson regression and negative binomial regression, both fairly new to the planning field. These meth- ods had mostly been used in crash studies because of the highly skewed nature of crash counts.17 ttrips Fr eq ue nc y Figure 42. Histogram of household transit trip counts.

84 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component ttrips Fr eq ue nc y Figure 43. Histogram of transit trip counts for households making transit trips. The two models—Poisson and negative binomial—differ in their assumptions about the dis- tribution of the dependent variable. Poisson regression is the appropriate model form if the mean and the variance of the dependent variable are equal. Negative binomial regression is appropriate if the dependent variable is overdispersed, meaning that the variance of counts is greater than the mean. Because the negative binomial distribution contains an extra parameter, it is a robust alternative to the Poisson model (Hilbe 2011, p. 140). Popular indicators of overdispersion are the Pearson and c2 statistics divided by the degrees of freedom, so-called dispersion statistics. If these statistics are greater than 1.0, a model is said to be overdispersed (Hilbe 2011, pp. 88, 142). By these measures, the study had overdispersion of transit trip counts in the dataset, and the negative binomial model was more appropriate than the Poisson model. Results Modeled results for the three dependent variables are shown in Table 19 and Table 20 for vmt, Table 21 for actden, and Tables 22 and 23 for ttrips. The hurdle models required two tables each. Generalizing, Level 1 independent variables have the expected signs and are highly significant. Level 2 independent variables have the expected signs but, due to limited degrees of freedom, never reach conventional significance levels. The best-fit model for the dichotomous variable, any VMT (1=yes, 0=no), is presented in Table 19. The likelihood of any VMT increases with household size, number of employed house- hold members, and real household income. These sociodemographic variables are associated

Statistical Models in Depth 85 Coefficient Standard Error T-Ratio P-Value constant 6.53 0.41 16.0 < 0.001 hhsize 0.506 0.039 13.0 < 0.001 employed 0.323 0.045 7.16 < 0.001 income 0.010 0.001 12.3 < 0.001 entropy −0.974 0.130 −7.57 < 0.001 intden −0.0010 0.0003 −3.08 0.003 int4way −0.013 0.002 −6.15 < 0.001 emp20a −0.010 0.004 −3.43 0.001 ttrips* −0.326 0.014 −23.1 < 0.001 lnactden* −0.478 0.048 −9.90 < 0.001 pseudo R2 0.21 *Intermediate variables. Table 19. Best-fit logistic model for the any household VMT (1  yes, 0  no). Coefficient Standard Error T-Ratio P-Value constant 3.54 0.09 41.2 < 0.001 hhsize 0.141 0.005 25.6 < 0.001 employed 0.230 0.008 27.5 < 0.001 income 0.0025 0.0002 16.5 < 0.001 jobpop −0.063 0.025 −2.57 0.011 entropy −0.083 0.026 −3.17 0.002 intden −0.0006 0.0001 −6.45 < 0.001 int4way −0.0032 0.0004 −8.61 < 0.001 emp20a −0.0027 0.0004 −6.43 < 0.001 ttrips* −0.063 0.004 −14.6 < 0.001 lnactden* −0.112 0.008 −13.5 < 0.001 pseudo R2 0.22 *Intermediate variables. Table 20. Best-fit linear model for the natural logarithm of household VMT (for positive VMT). Coefficient Standard Error T-Ratio P-Value constant 6.87 0.21 33.1 < 0.001 intden 0.0022 0.0001 1.89 0.058 int4way 0.0150 0.0014 10.7 < 0.001 emp30t* 0.0274 0.0064 4.31 < 0.001 rail* 0.0895 0.0175 5.12 < 0.001 pseudo R2 0.37 *Exogenous transit variables. Table 21. Best-fit linear model for the natural logarithm of buffer activity density.

86 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component with increased likelihood of automobile use. The likelihood of any VMT declines with land use entropy within a 1⁄2-mile buffer around a household, with intersection density within the buf- fer, with the percentage of four-way intersections within the buffer, and with the percentage of regional employment accessible within a 20-minute drive time. Basically, those who live in highly accessible places (characterized by these “D” variables) are better able to make do without automobile trips. Most importantly, the likelihood of any VMT declines with the two mediating variables in this model: number of transit trips made by household members (ttrips) and activity density within 1⁄2 mile of households (lnactden). For households with VMT, household VMT increases with the household size, number of employed household members, and real household income (see Table 20). VMT declines as the following “D” variables increase within 1⁄2 mile of households: job-population balance, land use entropy, intersection density, percentage of four-way intersections, and percentage of regional employment accessible within a 20-minute drive time. Those who live in highly accessible places (characterized by these types of “D” variables) generate less VMT than those in less accessible places. Most importantly, household VMT declines with the two mediating variables in this model: number of transit trips made by household members (ttrips) and activity density within 1⁄2 mile of households (lnactden). The best-fit model for activity density is presented in Table 21. Activity density increases as intersection density and percentage of four-way intersections increase. A dense grid of streets Coefficient Standard Error T-Ratio P-Value constant −4.09 0.51 −8.04 < 0.001 hhsize 0.242 0.017 14.4 < 0.001 employed 0.183 0.027 6.73 < 0.001 income −0.0044 0.0005 −8.99 < 0.001 jobpop 0.185 0.081 2.29 0.022 entropy 0.477 0.087 5.50 < 0.001 intden 0.0020 0.0002 7.89 0.003 int4way 0.0073 0.0012 6.14 < 0.001 emp30t* 0.0147 0.0018 8.18 < 0.001 rail* 0.0522 0.0143 3.65 < 0.001 pseudo R2 NA * Exogenous transit variables.. Table 22. Best-fit logistic model for any transit trips (1  yes, 0  no). Coefficient Standard Error T-Ratio P-Value constant 0.46 0.07 6.44 < 0.001 hhsize 0.148 0.027 5.39 < 0.001 jobpop 0.116 0.031 3.78 < 0.001 entropy 0.281 0.084 3.34 0.001 emp30t* −0.00002 0.0006 −0.03 0.97 rail* 0.0092 0.0018 5.01 < 0.001 pseudo R2 0.16 * Exogenous transit variables. Table 23. Best-fit negative binomial model for household transit trips (for positive transit trips).

Statistical Models in Depth 87 can support more intense development than can a sparse hierarchy of streets. Activity den- sity also increases with the two exogenous transit variables, percentage of regional employment accessible within 30 minutes by transit and presence of a rail station within 1⁄2 mile of a house- hold. As economic theory suggests, better transit accessibility translates into higher density. The best-fit model for the dichotomous variable, any transit trips (1=yes, 0=no), is presented in Table 22. The likelihood of a household having any transit trips increases with household size and number of employed members, and declines with household income. The likelihood also increases with job-population balance, land use entropy, intersection density, and percentage of four-way intersections within 1⁄2 mile of the household. These variables, plus activity density, vir- tually define transit-oriented development. Controlling for these variables, transit trips increase with the two transit service variables: percentage of regional employment accessible within 30 minutes by transit and presence of a rail station within 1⁄2 mile of a household. Consistent with the empirical literature, better transit accessibility translates into greater transit usage. For households with transit trips, many variables that proved significant in other equations are not significant in this one (see Table 23). The number of household transit trips increases with household size, job-population balance within 1⁄2 of a household, and land use entropy within the same 1⁄2 mile. The number of household transit trips also increases with access to rail. However, the number of transit trips is not affected by the percentage of regional employment accessible by transit. This does not mean that employment accessibility has no effect on transit use, since it affects the likelihood of having any transit trips. It just means that those who use transit anyway do not make more transit trips as employment accessibility increases. The study sample is much smaller when limited to households with transit trips (just over 4,000 vs. 26,000 for the full sample). But the sample is large enough to produce significant results if the associations among the variables are moderately strong. Apparently, variables such as household income cut both ways when it comes to transit use. There may be a propensity to substitute the automobile for transit among the higher income users, but at the same time, a propensity to con- sume more transit at higher income levels. The two effects may cancel each other out. Transit’s Land Use Effect For transit accessibility to employment, the ridership effect of transit on VMT occurs through the causal pathway: transit accessibility to employment -> transit trips -> ridership effect on VMT The land use effect occurs through a different causal pathway: transit accessibility to employment -> activity density -> land use effect on VMT Likewise for rail access, the ridership effect of transit on VMT is: rail access -> transit trips -> ridership effect on VMT while the land use effect is: rail access -> activity density -> land use effect on VMT The equations estimated previously outputted natural logarithms, log odds, and expected values of variables. They were transformed to compute effect sizes. The simplest transformation was for activity density, whose natural logarithm was the dependent variable in Table 21. Values of the natural log computed with this equation were exponentiated: activity density = exp (log of activity density)

88 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component The calculations were more complicated for transit trips. From the logistic equation in Table 22, the research team first computed the odds of any transit trips by exponentiating the log odds and then the probability of any transit trips with the formula for the probability in terms of the odds: odds of any transit trips = exp (log odds any transit trips) probability of any transit trips = odds of any transit trips/(1 + odds of any transit trips) From the negative binomial equation in Table 23, the expected number of transit trips for households with any transit trips were also calculated by exponentiating: number of transit trips (for households with transit trips) = exp (log of expected number of transit trips) The expected number of transit trips for all households was the product of the two: number of transit trips (for all households) = probability of any transit trips × number of transit trips (for households with transit trips) A parallel set of calculations was applied to VMT. From the logistic equation in Table 23, the odds of any VMT were computed by exponentiating the log odds and then the probability of any VMT with the formula for probability in terms of odds: odds of any VMT = exp (log odds any VMT) probability of any VMT = odds of any VMT/(1 + odds of any VMT) From the semi-logarithmic equation for households with any VMT, the expected VMT were computed, again, by exponentiating: VMT (for households with VMT) = exp (log of VMT) The expected VMT for all households was the product of the two. VMT (for all households) = probability of any VMT × VMT (for households with VMT) To estimate land use effects for the two exogenous transit variables, transit accessibility to employment (emp30t) and rail access (rail), base values of each endogenous variable were first calculated using average values of exogenous variables for the sample households, with this exception: the research team assumed no rail access in the base case (rail = 0). Values for the base case are shown in Table 24. For the base case, activity density was computed from the equation in Table 21; the number of household transit trips was computed from the equations in Table 22 and Table 23. Using resulting values of activity density and transit trips, household VMT was computed from the equations in Table 19 and Table 20. For comparison with the base case, two scenarios were created that represented enhanced tran- sit service at the neighborhood level. For the first scenario, the research team bumped up transit accessibility to employment by 10 percentage points from 19.9% to 29.9%, assuming the neigh- borhood had better access to employment via transit. For the second scenario, the team bumped up the rail access dummy variable from 0 to 1, assuming the neighborhood had rail access. The team then went through the similar calculations as in the base case. First, activity density and transit trips were calculated with the equations in Tables 21, 22, and 23. Then, household VMT was computed three ways for each scenario from the equations in Tables 19 and 20. In the first calculation, revised values of both activity density and transit trips were used to obtain an estimate of household VMT that included the ridership and land use effects of the scenario. In the second calculation, the revised value of transit trips and the base value of activity density were hhsize 2.23 employed 1.25 income 73.0 jobpop 0.59 entropy 0.39 intden 169.4 int4way 27.6 emp20a 38.5 emp30t 19.9 rail 0 Table 24. Values of exogenous variables in the base case.

Statistical Models in Depth 89 used to obtain an estimate of household VMT due to the ridership effect only. In the third calcula- tion, the revised value of activity density and the base value of transit trips were used to obtain an estimate of household VMT due to the land use effect only. Finally, subtracting VMT for each sce- nario from VMT in the base case, the ridership and land use effects of the scenarios were obtained. Results for the two scenarios are shown in Table 25 and Table 26. Longitudinal Analysis of LRT Expansion in Portland, Oregon Two of the 10 regional household travel databases in this study are for Portland, Oregon. One survey was conducted in 1994, the second in 2011. The 17-year separation between the dates of these two surveys allowed the research team to study the effect of transit investments on VMT in and around transit stations. With a bit of manipulation, ridership effects could be separated from land use effects. This is a classic quasi-experimental study design referred to as a pretest-posttest (pre- intervention–post-intervention) design with a comparison group. The intervention is the con- struction of a new LRT line between the two survey years, which affects development patterns and travel behavior of households proximate to the new line. The comparison group consists of households in another transportation corridor not directly affected by the new line. It was Base Case Scenario Percentage Difference Daily transit trips per household 0.218 0.249 +14.5% Neighborhood activity density (population + employment per square miles) 3,645 4,794 +31.5% Average daily VMT per household (ridership + land use effects) 20.08 19.35 −3.63% Average daily VMT per household (ridership effect only) 20.08 20.03 −0.22% Average daily VMT per household (land use effect only) 20.98 19.39 −3.40% Table 25. Results for a scenario with enhanced neighborhood access to employment (10 percentage point bump in transit accessibility to employment). Base Case Scenario Percentage Difference Daily transit trips per household 0.218 0.231 +5.8% Neighborhood activity density (population + employment per square miles) 3,645 4,794 +9.4% Average daily VMT per household (ridership + land use effects) 20.08 19.35 −1.25% Average daily VMT per household (ridership effect only) 20.08 20.03 −0.08% Average daily VMT per household (land use effect only) 20.98 19.39 −1.15% Table 26. Results for a scenario with enhanced neighborhood access to rail (from no rail within 1⁄2 mile to rail within 1⁄2 mile)

90 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component assumed that changes in the treated group would have paralleled those in the comparison group in the absence of any intervention. Deviations from general trends were assumed to be due to the intervention itself—in this case, the opening of an LRT line. Case Study Selection This case study focuses on the Westside LRT line (western portion of the Blue Line). The por- tion of interest starts west of downtown Portland and extends through Beaverton out to Hillsboro. The 15-mile section, with 17 stations, opened in 1998, after the first household travel survey and well before the second. Much of the alignment is through land that was ripe for development or redevelopment. Station areas have had many years to densify and thereby affect travel behavior. This represents the best opportunity for a pre-intervention–post-intervention comparison. The comparison group for this study is another corridor heading southwest from downtown Portland to Tigard and beyond. This is a highway corridor, in contrast to the treated corridor, running along the SW Pacific Highway and (for the first few miles) Interstate 5. This portion of the corridor is 12.5 miles long and has 14 interchanges or major intersections. In a quasi-experimental study, the comparison group should be as similar as possible to the treated group. If the two groups were equivalent, this would be a true experiment. They can never be truly equivalent in planning practice, and a quasi-experiment is the best available for this study. The two corridors are similarly situated in the region and relative to downtown. In the next section, the study tests for rough equivalence of travel and other statistics before the intervention. The existence of big differences before the intervention would create statistical problems, most notably the likelihood of regression to the mean. As for the other rail lines in Portland, the Eastside LRT line was completed in 1986, 8 years before the 1994 household travel survey. It had already had much of its ultimate impact on development patterns by the time of the survey. The Airport LRT Red Line, opened in 2001, mostly travels through land that is industrial (surrounding the airport). Only one station serves a residential neighborhood, and it is bounded by highways. The Downtown Streetcar also began service in 2001. Any reasonable buffer around its stations would encompass LRT stations as well, making it difficult to isolate the streetcar’s effect on land use. The Interstate LRT Yellow Line, opened in 2004, may not exemplify the potential of rail to affect development patterns due to its alignment along the Interstate. Portland’s fifth LRT line, the Green Line connecting downtown Portland to Clackamas County, was opened in 2009, too recently to have had much effect on development patterns in the corridor. Data and Variables This study uses geocoded household travel data from surveys conducted in 1994, 4 years before the opening of the Westside LRT line, and 2011, 13 years after the opening. The 1994 survey was a 2-day travel survey. The research team selected the travel day with the largest number of trips for each household. Even so, it appears that trips were underreported on average, as households are less diligent about reporting trips over 2 days than 1 day. The 2011 survey was a 1-day survey that covered a larger sample of households. This study also uses socioeconomic data for surveyed households, built environmental data for buffers around household locations, and transit service data for households and buffer areas. Variables used in this study are defined in Table 27. Measures of household size, employment, VMT, and trip frequency refer only to household members who completed travel diaries. Data for other household members were not available.

Statistical Models in Depth 91 Variables Definition Explanation Location Household within 2 miles of a Westside LRT station or an SW Pacific Highway intersection A 2-mile buffer was used to produce a large enough sample of households for statistical purposes Household socioeconomic variables hhsize Household size Only includes household members who completed travel diaries employed Employed household members Only includes household members who completed travel diaries income Household income in 1,000s of 2012 dollars Income inflated by the personal consumption expenditure price index vehicles Household vehicles Number of cars and other vehicles owned by household Household built environmental variables actden Activity density within the 2-mile buffer in 1,000s of persons per square mile Population + employment divided by gross land area in square miles jobpop Job-population balance within the 2-mile buffer Index ranging from 0, where only jobs or residents are present within 1/4 mile, to 1, where there is one job per five residents entropy Land use mix within the 2-mile buffer Entropy index based on net acreage in different land use categories that ranges from 0, where all developed land is in one use, to 1, where developed land is evenly divided among uses intden Intersection density within the 2-mile buffer Number of intersections divided by gross land area in square miles int4way Percentage of four-way intersections within the 2-mile buffer four-way intersections or intersections where more than four streets meet divided by total intersections emp10a Percentage of regional employment accessible within a 10-minute travel time via automobile Midday travel times emp20a Percentage of regional employment accessible within a 20-minute travel time via automobile Midday travel times emp30a Percentage of regional employment accessible within a 30-minute travel time via automobile Midday travel times Household travel variables vmt Average household VMT per day Adjusted for average vehicle occupancy by household size from 2009 National Household Travel Survey wtrips Average number of household walk trips Only includes household members who completed travel diaries btrips Average number of household bike trips Only includes household members who completed travel diaries ttrips Average number of household transit trips Only includes household members who completed travel diaries atrips Number of household automobile person trips Only includes household members who completed travel diaries trips Number of household person trips by all modes Only includes household members who completed travel diaries adist Average length of automobile trips Only includes household members who completed travel diaries n Sample size Table 27. Variable definitions.

92 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component All variables are defined and measured consistently for the two survey years. Household income is adjusted for consumer price inflation. Even adjusting for inflation, incomes rose sub- stantially between 1994 and 2011 across the prosperous Portland region. Importantly, the study team used a 2-mile network distance to define the study area around the transit stations on the Westside LRT line and around the intersections on the SW Pacific Highway. This relatively large buffer produces a large enough sample of households for statisti- cal purposes. A 1-mile network buffer would have left a sample of only 40 households living in the transit corridor surveyed in 1994, and a 1⁄2-mile network buffer would have left only eight households. By using a larger buffer, the team is not suggesting that the effects of LRT on transit use and activity density are identical in the first 1⁄2 mile around stations and second 1⁄2 mile, or the first mile and the second mile. It is suggested, however, that average effects over a larger area can be used to define transit’s impacts on VMT. Statistical Methods The analysis was conducted in two parts. The first part used independent samples difference- of-means tests to see if household travel and other variables differ between the LRT corridor and the comparison corridor, and between the first survey and the second survey. The research team looked for gross effects of the new LRT line on household travel and development patterns around the stations. The second part of the analysis estimated a household VMT model in terms of household socio- economic variables; built environmental variables for their surroundings; and the variables of greatest interest, household transit trips and activity density. Once estimated, the model could be used to predict the ridership effect of LRT on household VMT through increased transit usage and the land use effect of LRT on household VMT through increased activity density around stations. Difference-of-Means Tests The research team began with the results of difference-of-means tests. Table 28 permits a pre- intervention comparison of the Westside LRT corridor and the SW Pacific Highway corridor. Location LRT Control T-Ratio P-Value hhsize 2.28 2.04 2.28 0.023 employed 1.25 1.16 1.18 0.24 income (1,000s) 60.2 60.1 0.05 0.96 vehicles 1.86 1.74 1.66 0.097 actden (1,000s) 5.29 6.26 −4.21 <0.001 vmt 23.1 21.9 1.50 0.13 wtrips 0.83 0.83 0.04 0.97 btrips 0.08 0.08 0.08 0.94 ttrips 0.16 0.27 −1.89 0.06 atrips 8.12 7.33 1.49 0.14 trips 9.78 9.02 1.28 0.20 adist 4.87 4.96 −0.31 0.76 n (varies but max) 194 440 Table 28. Westside LRT corridor vs. SW Pacific Highway corridor in 1994.

Statistical Models in Depth 93 This may be the most important comparison of all, as large differences would introduce the likelihood of regression to the mean. In 1994, the two corridors were equivalent in most respects. There was no significant difference in mean number of employees per household; mean income per household; and mean frequencies of walk, bike, automobile, and total trip making. Also, most importantly, there was no significant difference in mean household VMT. Interestingly, activity density was significantly higher in the highway corridor, and transit trip frequency was marginally higher (approaching significance at the 0.05 level). Vehicle ownership was margin- ally lower in the highway corridor. By these measures, the highway corridor was actually more urbanized in 1994 than was the transit corridor. By 2011, the introduction of LRT had changed the LRT corridor, and it now differed signifi- cantly from the highway corridor. Compare the 2011 values in Table 29 to the 1994 values in Table 28. Real household incomes had risen in both corridors, but not nearly as fast in the tran- sit corridor. Vehicle ownership, which had been higher in the transit corridor, was now lower. Activity density, which had been lower in the transit corridor, was now significantly higher. The mean walk and transit trip rates rose in both corridors, but much faster in the transit corridor. Looking at relative numbers, it might be expected that the increase in walk trips had a greater impact on VMT than the increase in transit trips. Most importantly for this research, while the mean household VMT rose in both corridors, it rose much faster in the highway corridor. The rapid rise in household VMT mirrors the region as a whole. Hence the LRT corridor is bucking the trend. The difference in household VMT is entirely due to mode shifts in the LRT corridor, as the average automobile trip rates and lengths are not significantly different. The final comparison is between household data for the transit corridor before and after the Westside LRT line opened (see Table 30). Average household income increased significantly between the years, which partially accounts for the higher overall trip rate and the longer aver- age automobile trip length in 2011. Vehicle ownership actually declined in the transit corridor, bucking the regional trend. Activity density increased by almost 30%, as land near stations was rezoned, in many cases for transit-oriented development (dense mixed-use development). The increase in density was greater in the first mile around the transit stations than the second mile (a 2-mile buffer was used in this study to achieve a meaningful sample size). Walk and tran- sit rates both increased dramatically after LRT, the former by 158% and the latter by 438%. Location LRT Control T-Ratio P-Value hhsize 2.20 2.16 0.52 0.60 employed 1.27 1.39 −2.27 0.023 income (1,000s) 74.8 83.0 −2.96 0.003 vehicles 1.79 1.93 −2.19 0.029 actden (1,000s) 6.81 6.40 3.90 <0.001 vmt 24.7 29.0 −2.54 0.011 wtrips 2.14 1.36 3.78 <0.001 btrips 0.12 0.20 −1.40 0.16 ttrips 0.86 0.45 4.31 <0.001 atrips 7.65 8.33 −1.64 0.10 trips 11.10 10.51 1.20 0.23 adist 5.72 6.29 −1.39 0.17 n (varies but max) 502 489 Table 29. Westside LRT corridor vs. SW Pacific Highway corridor in 2011.

94 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component Date 1994 2011 T-Ratio P-Value hhsize 2.28 2.20 −0.75 0.45 employed 1.25 1.27 0.38 0.70 income (1000s) 60.2 74.8 5.54 <0.001 vehicles 1.86 1.79 −0.95 0.34 actden (1000s) 5.29 6.81 8.93 <0.001 vmt 23.1 24.7 0.85 0.39 wtrips 0.83 2.14 6.41 <0.001 btrips 0.08 0.12 0.60 0.55 ttrips 0.16 0.86 7.63 <0.001 atrips 8.12 7.65 −0.80 0.42 trips 9.78 11.10 2.06 0.041 adist 4.87 5.72 2.47 0.014 n (varies but max) 194 502 Table 30. Westside LRT corridor in 1994 vs. 2011. In absolute terms, the walk rate actually increased more than the transit rate (1.31 vs. 0.70 trips), suggesting that the indirect effect of transit investment through increased walking may be as large or larger than the ridership effect through increased transit use. Of course, it depends on the length of automobile trips that these two modes are replacing. Generalizing from these three tables, household VMT increased in both corridors between 1994 and 2011, but much less so in the Westside LRT corridor than in the control highway cor- ridor or the region as a whole. VMT increases across the region are probably related to rising incomes and increasing sprawl. The fact that VMT in the transit corridor did not rise as fast appears to be largely due to mode shifts from the automobile to transit and walking. But many variables were at play. These kinds of comparisons naturally suggest a multivariate analysis, as many variables contribute to household VMT, as seen in the next section. Statistical Modeling To predict the ridership and land use effects of the Westside LRT line on household VMT, the research team first estimated a linear regression model using Portland data for the entire region in 2011. The model was estimated for 2011 because the team wanted to know how changes in the LRT corridor between 1994 (pre-LRT) and 2011 (post-LRT) likely affected household VMT in 2011. Excluding households with missing values of one or more variables, there was a sample of 3,665 households. The natural log of household VMT was taken to make the distribution of the dependent vari- able more normally distributed. The log transformation costs households with no VMT, about 9% of the sample. As these are the households most likely affected by the availability of LRT, the effect of LRT on VMT was necessarily underestimated. The natural logs of other variables, specifically household size and household income, were taken to account for nonlinear relationships to VMT. This costs a few additional cases but improved the model fit. The study had three buffer widths to choose from (1⁄4, 1⁄2, and 1 mile); all three were tested. The research team opted for the smallest buffer to capture the most localized conditions and still

Statistical Models in Depth 95 achieve a good model fit. A measure of regional accessibility—percentage of regional jobs acces- sible within 30 minutes by automobile—was used to control for regional location (as opposed to local conditions). Previous studies have found that regional accessibility is the most important determinant of VMT, more important than the local “D” variables (Ewing and Cervero 2001, Ewing and Cervero 2010). The best-fit model is presented in Table 31. As expected, sociodemographic and built environ- mental control variables proved highly significant. The two variables of ultimate interest were also significant. The number of transit trips made by the household has the expected negative sign and is significant at the 0.001 level or beyond. Households that use transit drive less. Activity density also has a negative sign and is significant at the 0.001 level or beyond. Households living at higher densities drive less, independent of their transit use. Effect of Transit on VMT Next, the regression model was used to compute the ridership effect of greater transit use on household VMT in the transit corridor and the land use effect of greater activity density on household VMT in the transit corridor. Consistent with the quasi-experimental methodology, the team assumed a counterfactual, that in the absence of LRT, transit use and activity density in the transit corridor would have changed to just the same extent as in the highway corridor. Between 1994 and 2011, the average number of transit trips per household in the LRT cor- ridor rose from 0.16 to 0.86, an increase of 0.7 daily transit trips. During the same period, due to expanded transit service regionally, the average number of transit trips per household in the highway corridor rose from 0.27 to 0.44, an increase of 0.18 transit trips. Assuming transit use would have increased by this same amount in the absence of LRT, the net increase in the transit corridor attributable to LRT is 0.70–0.18 or 0.52 transit trips per household. Likewise, between 1994 and 2011, the average activity density in the LRT corridor rose from 5.29 to 6.81 persons per square mile, expressed in 1,000s, for an increase of 1.25 persons per square mile, again in 1,000s. During the same period, due to general urbanization of the west side of Portland, the average activity density in the highway corridor rose from 6.26 to 6.40 persons per square mile (in 1,000s), for an increase of 0.14 thousand persons per square mile. Assum- ing activity density would have increased by this same amount in the absence of LRT, the net increase in the activity density attributable to LRT is 1.25–0.14, or 1.11 thousand persons per square mile. Coefficient Standard Error T-Statistic P-Value constant 1.20 0.25 4.75 < 0.001 lnhhsize 0.586 0.033 17.8 < 0.001 employed 0.132 0.022 5.90 < 0.001 lnincome 0.155 0.023 6.63 < 0.001 emp30a −0.0023 0.0008 −2.91 0.004 intden −0.00044 0.00015 −3.04 0.002 int4way −0.0026 0.0007 −3.99 < 0.001 ttrips −0.154 0.013 −11.8 < 0.001 actden −0.022 0.006 −4.05 < 0.001 N = 3,665 R2 = 0.238 Table 31. Natural log of household VMT as a function of transit trips, activity density, and control variables.

96 Quantifying Transit’s Impact on GHG Emissions and Energy Use—The Land Use Component N Mean Standard Deviation lnvmt 458 2.84 1.05 lnhhsize 502 0.63 0.56 employed 539 1.27 0.85 lnincome 506 11.00 0.76 emp30a (1,000s) 539 66.5 17.8 inten 539 212.0 100.4 int4way 537 22.8 19.3 ttrips 502 0.86 1.81 actden (1,000s) 539 5.81 2.29 Table 32. Descriptive statistics for variables in the household VMT model. The net change in the average transit trip rate was then substituted into the VMT model to determine the ridership effect of the LRT line on VMT. Because household VMT was logged in the model, the effect of an increase in transit trips on household VMT depends on other variables in the VMT model. The average values of all other variables for the households in the LRT cor- ridor were substituted into the VMT equation to see what the average effect on household VMT would be. Average variable values are listed in Table 32. A 0.52 increase in the number of transit trips reduces the predicted average VMT from 17.7 to 16.3 vehicle miles per household per day, a reduction of 1.4 VMT. A 1.1 thousand increase in activity density reduces the predicted average VMT from 17.7 to 17.3 vehicle miles per household per day, a reduction of 0.4 VMT.