MEASURING LAND USE DIVERSITY AND
CORRELATING ITS RELATIONSHIP WITH VMT
Britt Fugitt
B.S., University of California, Davis, 2003
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
CIVIL ENGINEERING
(Transportation Engineering)
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2009
MEASURING LAND USE DIVERSITY AND
CORRELATING ITS RELATIONSHIP WITH VMT
A Project
by
Britt Fugitt
Approved by:
__________________________________, Committee Chair
Dr. Kevan Shafizadeh
__________________________________, Second Reader
Mike Mauch
__________________________________, Third Reader
Bruce Griesenbeck
____________________________
Date
ii
Student: Britt Fugitt
I certify that this student has met the requirements for format contained in the University
format manual, and that this project is suitable for shelving in the Library and credit is to be
awarded for the project.
__________________________, Graduate Coordinator
Dr. Cyrus Aryani
Department of Civil Engineering
iii
___________________
Date
Abstract
of
MEASURING LAND USE DIVERSITY AND
CORRELATING ITS RELATIONSHIP WITH VMT
by
Britt Fugitt
This research effort expands the research and development of SACOG’s mixed-use index (or “mix
index”) originally developed in 2007 to better understand the relationship between land use
diversity with vehicle-miles of travel (VMT).
While it is not well documented how the current
SACOG mixed-index was developed in 2007, this research effort combines parcel-level land use
data with household survey data from the entire six-county SACOG region. This project improves
on the existing mixed index by modeling VMT as a function of surrounding land use diversity then
comparing its effectiveness with SACOG’s current model by testing how well both correlate with
household VMT from travel survey data. The proposed model is applied with the SACSIM
regional travel demand model to illustrate that households with a higher mixed index generate less
VMT. As a result, this research not only confirms that jurisdictions within the SACOG region
would produce less VMT with greater land use diversity policies, it also provides a tool to quantify
or measure the mix of land use at the household or parcel level.
______________________, Committee Chair
Dr. Kevan Shafizadeh
______________________
Date
iv
ACKNOWLEDGMENTS
I extend my gratitude to Bruce Griesenbeck and SACOG staff for the data sets and the initial
research. Also special thanks to Professor Kevan Shafizadeh and Mike Mauch for all their
help and guidance. Lastly, thanks to my supportive family.
v
TABLE OF CONTENTS
Page
Acknowledgments.......................................................................................................................... v
List of Tables ............................................................................................................................... vii
List of Figures ............................................................................................................................. viii
Chapter
1.
INTRODUCTION................................................................................................................. 1
Project Description ................................................................................................................. 2
2.
BACKGROUND OF THE STUDY ..................................................................................... 4
SACOG’s Research................................................................................................................ 4
Other Research........................................................................................................................ 6
3.
METHODOLOGY .............................................................................................................. 10
Base Data ............................................................................................................................... 10
Data Development ................................................................................................................ 12
Model Development............................................................................................................. 14
Model VMT Estimation ...................................................................................................... 20
4.
APPLICATION................................................................................................................... 26
5.
CONCLUSION ................................................................................................................... 28
References .................................................................................................................................... 29
vi
LIST OF TABLES
Page
1.
Land Use Categories ....................................................................................................... 11
2.
Data Description Table ................................................................................................... 14
3.
Variable Test of Significance using the Correlation Coefficient .................................... 17
4.
T-Test for Equality of Means for MIXINDEX_SACOG ............................................... 23
5.
T-Test for Equality of Means for MIXINDEX_G .......................................................... 23
6.
T-Test for Equality of Means for MIXINDEX_H .......................................................... 24
vii
LIST OF FIGURES
Page
1.
The Relationship Between Average Vehicle-Miles of Travel per Household and the
Mixed-Index for Dataset A ............................................................................................. 20
2.
Comparison of The Relationship Between Average Vehicle-Miles of Travel per
Household and the Mixed-Index for Dataset A and B .................................................... 22
3.
VMT per Household for Each Mixed-Use Class for the Sacramento County General
Plan Update ..................................................................................................................... 27
viii
1
Chapter 1
INTRODUCTION
The Sacramento Area Council of Governments (SACOG) is interested reducing the average
vehicle-miles of travel (VMT) per capita for both existing and new development. The Blueprint
Scenario is the adopted visionary plan to guide the region how to grow over the next 50 years.
The preferred alternative moderates travel demand through changes in the built environment by
favoring development with a greater range of housing choices, reinvestment in already
developed areas, and closer integration of jobs and housing (SACOG, 2007). Designing housing
projects, small shopping centers, entertainment, office and light industrial uses near each other
create active neighborhoods where trips tend to interact more with each other (SACOG, 2007).
As a part of the Blueprint Scenario, combining mixed-use development along with other smart
growth principles such as improvements to transit stops, sidewalks, landscaping, and street-side
aesthetics contribute to the attractiveness of walking or bicycling. Although most trips would
still be made by personal automobile, use of Blueprint growth concepts will encourage other
modes of travel and reduce the average auto trip length.
An analysis of the Blueprint Scenario shows that mixed land use patterns could achieve
significant benefits to the region’s transportation system (SACOG, 2007). To study the benefits
of mixed-use development, SACOG staff has developed a variable mathematical model called
the mixed-use index, which indexes the balance of land use types near a household. SACOG
also hopes to use the mixed-use index model to assist in evaluating land use mix to reduce VMT.
The advantage to the mixed-index method is its simplicity. The inputs are land use type and
2
location at the parcel level for a study area. The mixed-index method does not account for
factors such as building size, population demographics, parking, and location to transit. These
are key factors that do affect travel behavior but are difficult to forecast. Whereas the mixedindex method inputs (zoning maps and/or land use maps) are often finalized in advance at the
planning stage in an environmental impact report (EIR) providing a strong level of confidence in
forecast. Hence the mixed-index model can be applied at local project level or regional level.
The mixed-index method will also be used to estimate the benefits in VMT reduction due to
mixed-use for travel demand models. Four-step travel demand models may capture reductions
in VMT due to mixed-use, but it is often masked because of the lack of detail and design. The
mixed-index method will provide accurate VMT reductions and because of the simplicity it can
be built into the travel demand model.
Project Description
This paper discusses the expanded research and development of SACOG’s mixed-index project.
This project consists of analyzing land use data within a fixed distance of a household with
household travel surveys to correlate a relationship between the diversity of surrounding land use
and VMT per household. Land use totals are computed by land use type (households, education
jobs, retail jobs, service jobs, total jobs) for seven fixed areas for each parcel in the SACOG
region and used to develop the mixed-index model. The main goal of the project is to improve on
SACOG’s mixed-index model. Improvements are defined and determined on two performance
areas:
3
1. The statistical strength in the correlation between household VMT and surrounding land
use. This project redefines SACOG’s mixed-index model to maximize the relationship
between mixed-use and household VMT.
2. The primary use of the mixed-index project is to measure the mix of land use and
estimate household VMT. Improvements focus on the accuracy in estimating VMT
using the mixed-index method.
The improved mixed-index model is applied with the SACSIM regional travel demand model to
illustrate that households with a higher mixed index generate less VMT.
4
Chapter 2
BACKGROUND OF THE STUDY
SACOG’s Research
The starting point of this research effort is based on work completed by SACOG staff. They
developed a methodology for analyzing the diversity of land use and how it relates to travel
behavior. Hossack, in his 2007 paper “Data Measuring and Visualizing the Diversity of Land
Use and Its Relationship with Travel Behavior”, discussed SACOG’s work and described the
technique used for calculating land use diversity (Hossack, 2007). SACOG’s methods calculate
mixed-use for a fixed area focusing on the diversity of land use within a half-mile radius of
households at the parcel level. Unique to other methods of calculating diversity, this approach is
independent of density. The measurement, called MIXINDEX, computes the level of land use
diversity on a scale of 0.0 to 1.0 (Hossack, 2007).
As the MIXINDEX for a household
approaches unity, it implies the jobs-to-housing ratio and schools-to-housing ratio for that
household is approaching the regional ratios and indicates a well-balanced mix of land uses
within a half-mile radius. For each household, the MIXINDEX is calculated using equation 1.
MIXINDEX_ SACOG 

 min( hh

halfmile *  edu , eduhalfmile)
 


  WGTedu
 max(hhhalfmile *  edu , eduhalfmile)

 min( hhhalfmile *  ret , rethalfmile) 
 

  WGTret
 max(hh
halfmile *  ret , rethalfmile)


 min( hhhalfmile *  srv , srv halfmile) 

 

  WGTsrv
 max(hhhalfmile *  srv , srv halfmile)
 

 min( hhhalfmile *  tot , tothalfmile)   WGT
tot

 
 max(hhhalfmile *  tot , tothalfmile)














(1)
5
where:
hhhalfmile
= households within a half-mile of parcel
βedu
= regional ratio of K-12 enrollment per household
eduhalfmile
= K-12 enrollment within a half-mile of parcel
WGTedu
= weight factor for education
βret
= regional ratio of retail jobs per household
rethalfmile
= retail jobs within a half-mile of parcel
WGTret
= weight factor for retail employment
βsrv
= regional ratio of service jobs per household
srvhalfmile
= service jobs within a half-mile of parcel
WGTsrv
= weight factor for service employment
βtot
= regional ratio of total jobs per household
tothalfmile
= total jobs within a half-mile of parcel
WGTtot
= weight factor for total employment
The minimum value function denoted by min(number1, number2,…) returns the minimum value
in the set. The maximum value function denoted by max(number1, number2,…) returns the
maximum value in the set.
The regional ratios are a good indication of well-balanced mix of land uses, because a high
percent of all trips are internal to the region. Likewise as the MIXINDEX for a household
approaches zero, it indicates a poor-balanced mix of land uses within a half-mile with respect to
the regional mix. Weights factors are applied to each land use ratio to set the upper and lower
bounds as unity and zero respectively; and also the weights allow for more or less emphasis to be
6
placed on a land use. The weight factors are 0.3, 0.3, 0.3, and 0.1 for education, retail, service,
and total jobs respectively (Hossack, 2007). Total jobs were weighted lower to 0.1 because most
people in the SACOG region work beyond a half-mile of their home (Hossack, 2007).
SACOG’s MIXINDEX research shows a good balance of households, schools, shopping and
jobs reduces automobile trip lengths (Hossack 2007). Households with a MIXINDEX of less
than 0.15 generated over 50 vehicle-miles of travel (VMT) per house on an average day.
Households with a MIXINDEX greater than 0.40 produced more non-vehicle trips (walk, bike,
and transit) and reduced VMT per household by about 40 percent. As a result, land use diversity,
as represented by the mix index, is important to metropolitan planning organizations such as
SACOG that are trying to reduce VMT by critically evaluating land use patterns to meet regional
VMT goals as well as proposed greenhouse gas emission goals set forth by California State
Assembly Bill 375 in 2008.
Other Research
Another practical method for quantifying land-use mix is the entropy method derived by Cervero
(Cervero, 1989) as shown in equation 2.
Ent r opy (1) * 
P j * l n(P j )
j
l n(J)
(2)
where Pj is the proportion of developed land in the jth use type.

Similar to SACOG’s method, the entropy method produces an index between zero and one,
where a value of one implies a balanced mix of land uses. As noted by Kockelman, all uses are
7
viewed equally important in the entropy calculation (Kockelman, 1996). For example, if four
use types (commercial, office, schools, and residential) are being analyzed in a district, then an
entropy value of one implies that each land use type occupies one quarter of the developed land.
Having a uniform mix of land uses in a district is not necessarily desired from an urban planner’s
perspective. Kockelman suggested the entropy method of balance would be improved if weights
were applied for each “j” use type (Kockelman, 1996). An advantage to the entropy method is it
can be applied to nonresidential areas measuring the mix of employment only. SACOG’s
method however is based on an areas employment mix and balance of jobs to housing.
Research by Frank and Pivo applied the entropy method to travel surveys and demographics in
the Puget Sound Regional Council (PSRC) area (Frank and Pivo, 1994). The developed entropy
index described the uniformity of distribution among seven land-use categories for each census
tract (Frank and Pivo, 1994). Unlike SACOG’s MIXINDEX calculation, Frank and Pivo’s
methodology is based on a large fixed boundary indexing each census tract as a whole area.
Because census tracts are so large, a well-mixed tract only showed benefits to work-based trips.
Which are typically longer than shopping-based trips (Frank and Pivo, 1994).
Greenwald’s (2006) research in the Portland Metro area applied the entropy method to
understand the relationship between land use balance and trip internalization at the traffic
analysis zone (TAZ) level. He noted that internal trips are not necessarily shorter in distance to
external trips; an individual living on the edge of a TAZ may make a shorter trip traveling to a
neighboring TAZ (Greenwald, 2006). Greenwald’s analysis point’s out a primary issue with a
fixed boundary analysis for measuring an area’s land use balance. In the Portland Metro region
the average size of a TAZ area is large, about 2.99 square miles. The TAZ’s land use balance is
8
only an accurate measure for households located near the center of the TAZ. Households along
the border of a TAZ could have a different land use balance.
Both Kockelman (1996) and Levine (2000) in their research attempted to fix this issue of fixed
boundaries by defining and creating fixed area “neighborhoods”. Kockelman’s analysis applied
the entropy method to the neighborhood level by averaging the indices of all developed hectares
within each census tract. A neighborhood is defined as all developed area within one-half mile
of each active hectare (Kockelman, 1996). Levine used a similar approach by defining several
neighborhood variables of which mix-use is calculated using surrounding quarter-mile and twomile grid cells, and then is averaged over each TAZ (Levine, 2000). Although both methods
compute an index for a smaller fixed area, the relationship to trip behavior is still based on the
average of neighborhood indexes within a large area.
Levine’s method proved to be more
accurate for estimating travel behavior compared to the tract-bounded entropy measure
(Kockelman, 1996). As will be shown, the research presented here investigates the correlation
of varying sizes of parcel-level, radial boundaries to determine which distance best fits the
relationship with VMT.
Zhang (2005) diagnoses the modifiable areal unit problem (MAUP) of averaging land use
indicators over a spatial aggregation like TAZs or fixed distance grids for travel analysis in the
Boston region. Zhang’s research compares aggregation of land use balance for five sized grid
areas (1/16 mi, ¼ mi, ½ mi, 1 mi, and 2 mi) and at the TAZ and block level (Zhang, 2005). The
entropy measure of land use balance proved to be important to explain travel mode choice when
calculated at a grid size of ½ mi or larger (Zhang, 2005). No statistical relationship was shown
for land use balance at the TAZ or block level (Zhang, 2005). Like Zhang’s research, the
9
research in this paper too calculates land use mix based different sized grid areas; however grid
size can differ based on the land use type. In addition, this paper takes a different approach of
calculating land use mix.
SACOG’s Sacramento Regional Travel Simulation Model (SACSIM) uses parcel level land use
data rather than aggregating into TAZs in order to better capture the relationships between land
use and travel behavior (Griesenbeck, 2006). Similar to the mixed-index model, SACSIM also
uses a buffering process to summarize land use totals by type within a quarter-mile and a halfmile of each parcel. Like TAZs, the buffering aggregates land use for a given area. Unlike
TAZs, the buffering varies by parcel, where as TAZ land use totals are fixed for every parcel
within the same TAZ. In other words, the buffering process for a given parcel is likely to be
different from its immediate neighbor even if both parcels are in the same TAZ (Griesenbeck,
2009).
10
Chapter 3
METHODOLOGY
The first step of this project is to redefine SACOG’s MIXINDEX equation such that the
correlation between mixed-use and household VMT is maximized. SACOG’s method only
accounted for land uses within a half-mile of a household and applied weights to each land use.
This project tests the half-mile assumption and determines if larger distance area would
strengthen the relationship between mixed-use and household VMT without the use of weights.
By not using weights all variables are viewed equally important and emphasis is placed on the
fixed distance.
Base Data
The study area for this project is the entire six-county SACOG region: El Dorado, Placer,
Sacramento, Sutter, Yolo and Yuba counties. SACOG provided the SACSIM (SACOG’s
activity-based travel demand model) parcel level land use database for the region containing
approximately 550,000 parcels based on the best available assessors records in 2004 (SACOG
MTP 2007). From GIS parcel point files, the database includes the parcel location represented
by a point in X and Y coordinates which is approximately located at the geographic center of the
parcel (SACOG MTP 2007).
Each parcel in the database also includes the number of units for
each land use in the parcel. See Table 1 for the types land uses included in the parcel database.
Note a land use has a sector use category and project use category; this project’s analysis is
based on the project use category.
11
Table 1: Land Use Categories
Sector Use
Unit
Project Use
Households
Dwelling Units
Households
K-12 Education
Student Enrollment
K-12 Education
College Education
Student Enrollment
College Education
Education Employment
Employees
Education Employment
Food Employment
Employees
Retail Employment
Government Employment
Employees
Other Employment
Office Employment
Employees
Other Employment
Other Employment
Employees
Other Employment
Retail Employment
Employees
Retail Employment
Services Employment
Employees
Service Employment
Medical Employment
Employees
Other Employment
Industrial Employment
Employees
Other Employment
In addition to the parcel database, SACOG made available travel data from its year 2000
household surveys. The survey was conducted in spring of 2000 and had 3,942 respondents that
completed 24-hour place-based travel diaries (Hossack, 2007). Of the 3,942 respondents, 710 of
them did not provide trip data implicating that the households made no trips. These 710 surveys
were discarded from the analysis for two reasons. First because it seems unreasonable to
suggested that eighteen percent of households do not make trips for an average day. And
second, the intent of this research is to focus on the relationship of land use mix and households
that make trips.
12
SACOG with the help of outside consultants went through great efforts to compute household
daily trips and vehicle-miles-traveled (VMT) for each survey respondent. Of the respondents, a
total of 29,636 trips were tallied and classified by household and mode of travel.
Data Development
Using the parcel point X and Y coordinates from the parcel database, a program was developed
in Matlab to calculate the total number of specific jobs and households within a fixed distance of
a household for each individual household in the regional database.
Land use totals were
calculated for seven different fixed area types: half-mile radius, one-mile radius, two-mile
radius, three-mile radius, four-mile radius, five-mile radius, and 15-mile radius. The large region
dataset was then reduced to contain land use totals for only households where travel surveys
were conducted.
Land use totals were aggregated into five categories for all seven fixed area types: households,
education jobs, retail jobs, service jobs, and total jobs. Land use totals were normalized to a
value between zero and one using a minimum-to-maximum method developed by SACOG. The
minimum-to-maximum method computes a jobs-to-household ratio for each of four job
categories and four of the seven fixed areas as shown in equation 3.
13
 min( hh
 
(a,b,c,d ) *  X _ jobs , X _ jobs(a,b,c,d ) )

Normalization Ratio(a,b,c,d )   

 

 max(hh(a,b,c,d ) *  X _ jobs , X _ jobs(a,b,c,d ) ) 

(3)
where:

hh(a,b,c,d)
= Households within (a, b, c, or d) miles of household
X_jobs(a,b,c,d) = jobs (education, retail, service, or total) within (a, b, c, or d) miles of
household
βX_jobs
= regional ratio of jobs (education, retail, service, or total) per household
a,b,c,d
= half-mile, one-mile, two-miles, three-miles respectively
The only difference between this method and SACOG’s method, is this method is a function of
land uses within four distances of a household: half-mile, one-mile, two-miles, and three-miles.
SACOG’s normalization method only accounted for land uses within a half-mile of a household.
Computing land use within four distances of a household provides four times as many ratios for
a total of sixteen (four-job-categories x four-distances = 16 ratios). Although only four of the
sixteen ratios will be used in the mixed-use model, all will be evaluated to determine which four
contribute to the largest correlation with household VMT.
The sixteen new normalized ratios are combined with the household daily VMT to form an m x n
matrix where m = 3,232 (number of usable surveys) and n = 17. See Table 2 for a description of
each n variable in the data set.
14
Table 2: Data Description Table
n
Name
Description
1
hh_vmt
2
edua
Normalized education jobs within a half mile of household
3
edub
Normalized education jobs within a one mile of household
4
educ
Normalized education jobs within two miles of household
5
edud
Normalized education jobs within three miles of household
6
reta
Normalized retail jobs within a half mile of household
7
retb
Normalized retail jobs within a one mile of household
8
retc
Normalized retail jobs within two miles of household
9
retd
Normalized retail jobs within three miles of household
10
srva
Normalized service jobs within a half mile of household
11
srvb
Normalized service jobs within a one mile of household
12
srvc
Normalized service jobs within two miles of household
13
srvd
Normalized service jobs within three miles of household
14
tota
Normalized total jobs within a half mile of household
15
totb
Normalized total jobs within a one mile of household
16
totc
Normalized total jobs within two miles of household
17
totd
Normalized total jobs within three miles of household
Daily VMT of household
The m x n matrix provides the final data set needed for the mixed-index model development.
Model Development
The model development is based on evaluating each variable in the Table 2 to optimize a
correlation between surrounding land use and household daily VMT. The correlation method
was applied to explore this relationship. The correlation method is a statistical method to
measure the strength of a linear relationship between two variables by computing a coefficient
that explains the proportion of variation between the two variables.
The correlation coefficient
15
ranges from zero to one where zero is a poor fit and one is a perfect fit. The correlation
coefficient is defined in equation 4.
correlation coefficient 
m(r _ jobsi vmti ) (r _ jobs)i  vmti
m(r _ jobs)  ( r _ jobsi )
2
i
2
m vmt  ( vmti )
2
i
2
(4)
where:

r_jobsi
=
edu(a,b,c,d) + ret(a,b,c,d) + svr(a,b,c,d) + tot(a,b,c,d) ; see Table 2
vmti
=
hh_vmt ; see Table 2
i
=
from 1 to m such that m = 3232
The correlation method does a better job at measuring the strength of a linear relationship
between two variables opposed to other common statistical methods because no other factors are
included. For example a linear regression computation includes variable coefficients and a yintercept. Both variable coefficients and the y-intercept skew the relationship test, but will
enhance the model goodness-to-fit.
A linear regression between land use variables and
household VMT could produce negative variable coefficients implying that job use nearby
increases VMT. Also a linear regression could significantly favor or disfavor a variable with a
larger/smaller coefficient. For example, SACOG’s approach to enhance the model was to
logically apply a weight to each variable. The larger the weight the more emphasis is placed on
that variable. This project’s approach focused more on obtaining an optimal linear relationship
between two variables, mixed-use index and household VMT, where mixed-use index is
computed without the use of weights or parameters.
All land use variables are of equal
importance, but the fixed area radius of each land use variable is adjusted to maximize a
16
correlation on VMT. For example, a smaller radius implies there is more of an effect on VMT
when that land use is near the household.
With four job categories and four fixed areas, there exist 256 (44) possible combinations. To
simplify the optimization process, a computer program was written in R that loops through all
possible combinations and outputs the correlation coefficient. The correlation coefficient ranged
from about -0.16 to -0.22; which implies a correlation exists, but there is a lot of noise in the
data. The negative implies an inverse relationship between the two variables. In other words, as
the normalized land use index approaches unity household VMT decreases. Although the
correlation is “small” it may be viewed as high because the simplicity of the inputs. As noted
above, the mixed-index method ignores key factors of household VMT such as building size,
population demographics, parking, and location to transit.
The second step of the R program statistically analyzes the correlated output searching for
patterns in distance from household among the higher correlated combinations. Of the higher
correlated combinations, 68 percent included educational employment within a half-mile, 44
percent included retail employment within one mile, 40 percent included service employment
within two miles, and 64 percent included total employment within a half-mile radius. These
findings are important because they are used to create the mixed-index model. Table 3 shows
the output of the correlation test.
17
Table 3: Variable Test of Significance using the Correlation Coefficient
Distance from
Land Use Employment Type
Household
Education
Retail
Service
Total
Within Half-Mile
68%
4%
8%
64%
Within One-Mile
20%
44%
20%
20%
Within Two-Miles
0%
12%
40%
4%
Within Three-Miles
12%
40%
32%
12%
As stated above, this project’s approach focused more on obtaining an optimal linear relationship
between mixed-use and household VMT based on the results from the correlation test. However,
because total employment captures all types of employment (education, retail, service, office,
government, industrial, etc.), it is reasonable to assume a larger fixed area of two-miles would be
more useful for the mixed-use model. As stated in SACOG’s research, in the SACOG region,
most people’s job is located beyond a half-mile of their home (Hossack, 2007). Because of this
concern, the project tested two fixed areas for total jobs, half-mile radius (MIXINDEX_G) and
two-mile radius (MIXINDEX_H). Equation 5 shows the MIXINDEX_G, which uses a half-mile
radius for total jobs and equation 6 shows MIXINDEX_H, which uses a two-mile radius for total
jobs. Note that G and H are arbitrary identifiers.
The 2009 298 TRB Special report summarizes recent research on travel demand with respect to
density, diversity, design, and regional accessibility. It reports that the reductions in VMT due to
local diversity are small in comparison to the reductions due to regional accessibility (NCR,
2009). Which means dense, mixed-use developments in the middle of nowhere may offer only
18
modest regional travel benefits (NCR, 2009). By using a two-mile radius for total jobs, the
mixed-index is also capturing the benefits due to job accessibility beyond the local level.
MIXINDEX _ G 
 min( hh

halfmile *  edu , eduhalfmile)
 



 max(hhhalfmile *  edu , eduhalfmile)

 min( hhonemile *  ret , retonemile ) 

 
max( hhonemile *  ret , retonemile )

 min( hhtwomile *  srv , srv twomile ) 

 
max( hhtwomile *  srv , srv twomile )

 min( hhhalfmile *  tot , tothalfmile) 

 



 max( hhhalfmile *  tot , tothalfmile)






 (5)







MIXINDEX _ H 
 min( hh

halfmile *  edu , eduhalfmile)
 



 max(hhhalfmile *  edu , eduhalfmile)

 min( hhonemile *  ret , retonemile ) 

 
max(hhonemile *  ret , retonemile )

 min( hhtwomile *  srv , srv twomile ) 

 
max(hhtwomile *  srv , srv twomile )

 min( hhtwomile *  tot , tottwomile ) 

 
 max(hhtwomile *  tot , tottwomile )






 (6)







where:

hhhalf-mile
= households within a half-mile of parcel
βedu
= regional ratio of K-12 educational jobs per household
eduhalf-mile
= K-12 educational jobs within a half-mile of parcel
hhone-mile
= households within one-mile of parcel
βret
= regional ratio of retail jobs per household
retone-mile
= retail jobs within one-mile of parcel
hhtwo-mile
= households within two-miles of parcel
19
βsrv
= regional ratio of service jobs per household
srvtwo-mile
= service jobs within two-miles of parcel
βtot
= regional ratio of total jobs per household
tothalf-mile
= total jobs within a half-mile of parcel
tottwo-fmile
= total jobs within two-miles of a parcel
The final step in model development was to use the surveys to determine the average household
VMT for a given mixed-index. The household survey dataset was randomly split into two
datasets: A and B. Dataset A was used for model development, while dataset B was used for
model testing. Figure 1 shows relationship between average household daily VMT and the
mixed-index for the three MIXINDEX models (SACOG’s MIXINDEX; the mixed-index with a
half-mile radius for total jobs, MIXINDEX_G; and the mixed-index with a two-mile radius for
total jobs, MIXINDEX_H) using dataset A. Average household daily VMT is grouped and
averaged by mixed-index increments of 0.2. All three mix-index calculations show a similar
relationship for mix-indices greater than 0.4; but for mix-indices less than 0.4 calculation G and
H show households produce more daily VMT than SACOG’s calculation.
20
Figure 1: The Relationship Between Average Vehicle-Miles of Travel per Household and the
Mixed-Index for Dataset A
Model VMT Estimation
As stated earlier, the primary use of the mixed-index project is to estimate household VMT.
This section discusses test and results of the accuracy in estimating VMT between the three
MIXINDEX models developed in the above section.
From dataset A, the average household daily VMT has been calculated for five mixed-index
intervals (< 0.2, 0.2 to 0.4, 0.4 to 0.6, 0.6 to 0.8, and >= 0.8). The same calculation was done for
21
dataset B, which served as the testing dataset for estimating the average household VMT. Figure
2 shows the visual comparison of average household daily VMT for both datasets A and B.
Visually dataset B followed the same trend as dataset A for each mixed-index with the exception
of indices greater than 0.8. Both SACOG’s MIXINDEX and the mixed-index with a half-mile
radius for total jobs (MIXINDEX_G) showed sizable changes in VMT for indexes greater than
0.8 when comparing dataset A to dataset B. These important observations imply that SACOG’s
MIXINDEX and the mixed-index with a half-mile radius for total jobs (MIXINDEX_G) do not
accurately estimate household VMT for indexes greater than 0.8. However, the mixed-index
with a two-mile radius for total jobs (MIXINDEX_H) appears to be more stable for indexes
greater than 0.8 implying overall it is a more accurate tool compared to SACOG’s MIXINDEX
and the mixed-index with a half-mile radius for total jobs (MIXINDEX_G).
22
Figure 2: Comparison of The Relationship Between Average Vehicle-Miles of Travel per
Household and the Mixed-Index for Dataset A and B
A two-sample t-test was used to statistically compare the average household VMT between
dataset A and B for each mixed-index interval. The t-test is used to test if there is a statistically
significant difference between the two means within a level of confidence by proving or
disproving the null hypothesis, which states that the two means are the same. This method uses
the mean and variance of each dataset group to calculate a t-value to determine the probability
that the means are significantly different. The t-test was computed using SPSS.
23
The SPSS t-test output for MIXINDEX_SACOG, MIXINDEX_G, and MIXINDEX_H are in
Table 4, Table 5, and Table 6 respectively.
Table 4: T-Test for Equality of Means for MIXINDEX_SACOG
Mixedt
95% C.I.
Sig.
Mean
Std. Error
(2-tailed)
Difference
Difference
Lower
Upper
df
Index
< 0.2
-0.81
629
0.42
-2.32
2.84
-7.90
3.27
0.2 - 0.4
-0.24
932
0.81
-0.48
2.02
-4.45
3.50
0.4 - 0.6
1.00
967
0.32
1.91
1.91
-1.83
5.65
0.6 - 0.8
0.13
626
0.90
0.30
2.31
-4.24
4.84
>= 0.8
-0.63
68
0.53
-4.28
6.85
-17.94
9.39
0.60
-0.05
2.31
-4.58
4.48
Weighted Average
Table 5: T-Test for Equality of Means for MIXINDEX_G
Mixedt
95% C.I.
Sig.
Mean
Std. Error
(2-tailed)
Difference
Difference
Lower
Upper
df
Index
< 0.2
0.14
210
0.89
0.74
5.30
-9.71
11.20
0.2 - 0.4
-0.26
562
0.80
-0.76
2.98
-6.61
5.09
0.4 - 0.6
-0.85
1310
0.39
-1.40
1.64
-4.61
1.82
0.6 - 0.8
1.38
1029
0.17
2.41
1.74
-1.01
5.82
>= 0.8
-1.09
111
0.28
-5.78
5.32
-16.33
4.77
0.42
-0.08
2.27
-4.55
4.38
Weighted Average
24
Table 6: T-Test for Equality of Means for MIXINDEX_H
Mixedt
95% C.I.
Sig.
Mean
Std. Error
(2-tailed)
Difference
Difference
Lower
Upper
df
Index
< 0.2
-0.23
131
0.82
-1.42
6.12
-13.53
10.69
0.2 - 0.4
0.11
428
0.91
0.39
3.47
-6.43
7.22
0.4 - 0.6
-0.21
1134
0.83
-0.39
1.84
-3.99
3.22
0.6 - 0.8
0.20
1358
0.84
0.32
1.61
-2.83
3.47
>= 0.8
-0.26
171
0.80
-1.11
4.32
-9.64
7.42
0.85
-0.07
2.26
-4.51
4.38
Weighted Average
The probability (sig. 2-tailed) in each table represents the statistical confidence that the null
hypothesis is false. A basic criterion for statistical significance is a "2-tailed significance" less
than 0.05. If the probability is less than 0.05, the difference is statistically significant and the
null hypothesis is rejected.
If the probability is greater than 0.05, the difference is not
statistically significant. In other words the null hypothesis is accepted, the two means are
statistically similar. Data where the means are identical would have a probability of 1.0. From
Table 4, Table 5, and Table 6; all three mixed-index calculations for all five intervals had a
probability greater than 0.05. Hence all three models produced meaningful results. SACOG’s
MIXINDEX ranged from a probability of 0.42 to 0.90 with an average of 0.60. The mixed-index
with a half-mile radius for total jobs (MIXINDEX_G) ranged from a probability of 0.17 to 0.89
with an average of 0.42. The mixed-index with a two-mile radius for total jobs (MIXINDEX_H)
ranged from a probability of 0.80 to 0.91 with an average of 0.85. Overall the t-test results for
the mixed-index with a two-mile radius for total jobs (MIXINDEX_H) showed the highest
25
probability that the means are similar. The result implies the mixed-index with a two-mile radius
for total jobs (MIXINDEX_H) is statistically a better model at estimating household daily VMT
compared to SACOG’s MIXINDEX and the mixed-index with a half-mile radius for total jobs
(MIXINDEX_G).
26
Chapter 4
APPLICATION
The mixed-index with a two-mile radius for total jobs (MIXINDEX_H) was applied in
conjunction with the SACOG’s Sacramento Regional Travel Simulation Model (SACSIM) for
the 2009 Sacramento County General Plan Update to estimate the benefits in VMT reduction due
to the proposed land use plan. The proposed land use plan contains land use and transportation
strategies, goals, and policies related to smart growth in an effort to reduce the average
household daily generated VMT (DERA, 2009). A key factor used in the evaluation was
analyzing the location of various types of land use in a close proximity at a parcel level. The
mixed-index with a two-mile radius for total jobs (MIXINDEX_H) was used in the analysis to
quantify and then stratify the entire unincorporated Sacramento County by a parcel level mixused index. SACSIM was used as the travel-forecasting tool to estimated VMT per household
for the Smart Growth section.
Figure 3 illustrates VMT for each mixed-use class for the Sacramento County General Plan
Update. Areas with better (higher) mixed-use characteristics have substantially lower VMT than
areas of low mixed use. It is estimated that the highest mixed-use category will have 37.6
vehicle-miles of travel per household for the growth areas and planned communities, compared
to 57.6 vehicle-miles of travel per household for the areas of low mixed-use (DERA, 2009).
Figure 3 illustrates VMT for each mixed-use class for the major new growth areas proposed in
Sacramento County General Plan Update.
27
Figure 3: VMT per Household for Each Mixed-Use Class for the Sacramento County General
Plan Update
28
Chapter 5
CONCLUSION
This research effort expands the research and development of SACOG’s mixed-use index to
better understand the relationship between land use diversity and vehicle-miles of travel (VMT).
This study focused on correlating parcel-level land use data with household VMT travel data to
estimate the benefits in VMT reduction due to mixed-use. It improved on SACOG’s existing
mixed-index by modeling VMT as a function of surrounding land use diversity then comparing
its effectiveness with SACOG’s current model by testing how well both correlate with household
VMT from travel survey data. Overall, the project develops a simple method for quantifying
diversity of land use at the parcel level, which proved to be statistically stronger than SACOG's
original model at estimating household VMT.
The proposed model (MIXINDEX_H) developed from this research effort was applied in
conjunction with the SACOG’s Sacramento Regional Travel Simulation Model (SACSIM) for
the 2009 Sacramento County General Plan Update to estimate the benefits in VMT reduction due
to the proposed land use plan. It has been shown that areas with better (higher) mixed-use
characteristics have substantially lower VMT than areas of low mixed-use. The results in the
2009 Sacramento County General Plan Update confirm that jurisdictions within the SACOG
region would produce less VMT with greater land use diversity policies. The results in the 2009
Sacramento County General Plan Update also illustrated the practical value of this research
providing the county with a tool to quantify or measure the mix of land use and estimate the
benefits in VMT reduction due to mixed-use.
29
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