A multivariate analysis of urban travel behavior in Chicago

Transpn Res. Vol. 3, pp. 345-363. Pergamon Press 1969. Printed in Great Britain

A M U L T I V A R I A T E ANALYSIS OF U R B A N T R A V E L B E H A V I O R

IN C H I C A G O t

S. T. WONO

Simon Fraser University, Burnaby, B.C., Canada

(Received 7 February 1969)

1. STATEMENT OF PROBLEM " . . . Understanding of the characteristics of travel is as essential to the planning of a transportation system as is a knowledge of electricity in designing an electrical circuit or of fluids in designing a hydraulic network" (CATS, 1962).

IN A PRELIMINARY analysis of urban travel behavior (Oi and Shuldiner, 1962), it was shown that trip generation, as measured by trips per occupied dwelling unit, was significantly correlated with the following variables: average car ownership, average household size and three social area indices, viz. social rank index, urbanization index and segregation index.

Two models were presented by Oi and Shuldiner to evaluate the effects which these variables have on the variations associated with trip generation.

The first model related trip generation, Y, as a function of the three social area indices: social rank, X 1, urbanization index, X s, and segregation index, X 3 (Shevky and Bell, 1955). The resultant multiple linear regression equation, estimated by least squares is as follows:

Y = 8.47+O.O172Xl-O.O744X2-O.OO23X ~ (R* = 0.8381) (la)

(0.0041) (0.0048) (0.0054)

The second model related trip generation as a linear function of four explanatory variables: average car ownership, A, average household size, H, social rank index, X1, and urbanization index, X2. The final equation in symbolic expression is as follows:

Y = 2.18+3.404A+O.516H+O.Ol19Xl-O.O343X ~ (R 2 = 0.9597) (It))

(0.290) (0.141) (0.0031) (0.0042)

The results of the two multiple-regression equations, on the whole, are striking. In the first model, three explanatory social area variables together account for 84 per cent of the total variation among 57 CATS analysis zones in trip generation, while in the second model four independent variables explain as much as 96 per cent of the total variance in the dependent variable.

Although the R~'s of the two multiple-regression equations are impressive, the investiga- tions undertaken by Oi and Shuldiner (1962) are not completely satisfactory from an analytical point of view.

In model (la), among the three social area indices only social rank and urbanization index have a significant impact on trip generation. This is reflected by the significance level

t This study had its inception while the author was affiliated with the Chicago Area Transportation Study.

345

346 S.T. WoNc

of the standard errors of estimate (number in parentheses) of the regression coefficients of the first and second independent variables. The third independent variable, namely, segregation index, does not appear to have a significant impact on trip generation. Omission of the latter variable in the regression equation perhaps might increase the power efficiency of the final estimation equation.

In model (lb), the estimation equation could have been improved by the deletion of the household size variable since it has an intercorrelation of -0 .572 with the urbanization index. The latter variable is interrelated with car ownership with a simple r of -0.713. Thus inherent in the second model, i.e. (Ib), on trip generation is the presence of some coUinearity. Although the problem of collinearity is not particularly severe, nevertheless some of its effects can be eliminated by dropping out the variables suggested above.

Both Oi and Shuldiner assume the conditions of linearity and normality for their models and ignore non-linearity effects knowing well the "the association revealed by individual household data exhibits a definite non-linearity" (Oi and Shuldiner, 1962).

The use of social area indices in estimating trip generation is imaginative as they reflect the importance which socio-economic variables play in determining the pattern of urban travel demand. However, the consideration of three social area indices alone is not sufficient to warrant their determinancy of trip generation. There are other factors which influence urban travel behavior as well. These are: car ownership, the choice of mode, trip purpose, land use, residential density, age of trip-maker and distance from the center of the city. Although Oi and Shuldiner were aware of some of these variables, they did not, however, treat them in a multi-dimensional framework.t

2. OBJECTIVE OF STUDY AND HYPOTHESIS The purpose of this study is to extend the work of Oi and Shuldiner by adding more

variables to the original study and by examining what underlying patterns are associated with trip generation, and to develop an alternative model for predicting trip generation by testing a number of variables which are postulated to have an influence in accounting for trip generation among 57 analysis zones in Chicago.

It is hypothesized that trip generations varies with car ownership, choice of mode, nature of trip purpose, type of land use, residential density, age of trip-maker and distance from the center of the city.

3. DATA Twenty-eight variables which characterize the selected 57 analysis zones in the city of

Chicago are computed from the CATS, 1956, Home Interview Inventory.§ The statistical unit used is the analysis zone, and the area covered is the city of Chicago.

The 28 variables were selected on the basis of experience and knowledge of travel behavior within the fimitation of available data. (For a list of the variables used, see Table 1.)

The reasons for using the 57 analysis zones are as follows. First, some initial work has already been done in these 57 analysis zones and certain indices characterizing them are

t Oi and Shuldiner tried to consider a wider range of trip generation measures and explanatory variables in Appendix C, pp. 231-243. They considered three measures of trip generation for each analysis zone and related them to five explanatory variables, viz. car ownership, residential density Central Business Dxstrict (CBD) distance, median tract income and household size. They also correlated trips per occupied dwelling unit expressed as a linear function of various combinations of the five explanatory variables.

+* Trip generation is measured in "total" daily residential trips per occupied dwelling unit. § It is recognized that the data are over a decade old, but the conceptualization and methodology of

this study should prove useful to urban transportation planning. Incidentally, this was the source of data which Oi and Shuldiner used for their study.

A multivariate analysis of u rban travel behavior in Chicago 347

available. Second, these 57 analysis zones are ideal as they are within the city limits of Chicago, where urban travel is most intensely concentrated. Third, these 57 analysis zones are quite uniformly distributed in the Chicago area. They constitute about 9 per cent of the CATS Cordon Area.-~ Figure 1 shows the geographic location and the areal pattern of the 57 analysis zones.

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FZC. 1. Geographic location and the areal pat tern of the 57 analysis zones in Chicago.

4. M E T H O D O F A N A L Y S I S

Two statistical techniques are employed in this study. Principal axes factor analysis (Seal, 1964) is first applied to determine what underlying patterns are associated with trip generation among the 28 variables and 57 analysis zones in Chicago. Based on the results of the factor analytic solution, surrogate variables for each of the extracted factors are then tested by means of multiple-regression analysis to ascertain which among the combination of independent variables in car ownership, modal choice, trip purpose, land use, residential density, age of trip-maker and distance from the center of the city have the greatest impact in accounting for variations associated with trip generation.

5. F A C T O R A N A L Y S I S O F T R I P G E N E R A T I O N

The factor analysis is proceeded as follows: 1. A 28 × 28 correlation matrix among every pair of variables is first computed. 2. A principal axes factor analysis of the correlation matrix to produce a 28 x r matrix

t This was the Study Area that was arbitrarily set by a cordon line which covers an area of 1236 square miles and contains about 5.2 million persons in 1956.

348 S.T. WONa

TABLE 1. M A T R I X OF CORRELATION COEFFICIENTS AMONG

Variables 1 2 3 4 5 6 7 8 9 10 11 12

1. Trips per occupied dwel- hng umt 1'000

2. Average car ownership 0 800 1 000 3. Average household size 0.407 0 271 1 000 4. Social rank index 0-208 0-347 --0 493 1-000 5, Urbanizat ion index --0.729 --0.663 --0 534 --0.031 1.000 6, Segregation index --0 335 --0.494 0.090 --0-395 0 364 1'000 7. Per cent auto driver 0'595 0.777 0 287 0.089 --0'548 --0.420 I 000 8. Per cent auto driver plus

passenger 0.548 0.537 0 136 0 226 --0.506 --0 414 0.637 1-000 9. Per cent mass transit --0.649 --0.588 --0.369 --0.074 0-542 0.337 --0 791 --0.715 1.000

10. Percentbusands t ree t -car --0.600 --0 565 --0.146 --0 310 0-482 0417 --0.727 --0 723 0.937 1.000 11. Per cent residential o f

developedland --0 073 0 250 - 0 139 0 339 0 130 --0201 0 269 0'225 --0-173 --0"234 1 000 12. Per cent manufaeturmg of

developed land --0'100 - -0265 0 259 --0 591 0 164 0255 --0 041 - 0 198 0082 0'223 --0'504 1 000 13. Per cent commercml o f

developedland --0.580 --0 584 --0 307 --0 172 0 759 0 344 --0 397 --0.397 0277 0-249 0036 0.231 14. Per cent public buildings

o f developed land --0-335 - -0308 - -0447 0207 0251 0 148 --0-411 --0.358 0525 0424 --0 173 - -0202 15. Population per 1000 ft 2 of

resldentlalland --0.793 --0.915 --0-278 --0 308 0 749 0 520 --0 762 --0.609 0 640 0 599 --0-202 0.293 16. Distance from CBD 0 746 0 632 0.193 0-421 --0 657 --0.382 0 548 0-628 --0.666 --0,680 0.071 --0.286 17 Per cent 16 years and over

with driving permits 0 611 0.790 - -0092 0.671 - -0473 --0 499 0 571 0-517 --0.476 --0 568 0.424 --0-446 18. Per cent trips 5 years and

0'530 0407 - -0417 0425 --0"248 - -0294 0 155 0205 - -0069 --0'186 --0 156 --0-127 over 19. Person trips per 1000 ft 2

o f floor area 0'759 0 635 0.297 0 197 --0 592 - -0228 0 501 0 596 --0-646 - -0553 --0.034 - -0202 20. Per cent person trips

home - -0022 --0.081 0052 0.026 - -0043 --0011 --0 110 0032 0047 --0021 0407 - -0239 21. Per cent person trips on

personalbusmess 0140 0185 --0,112 0226 - -0023 0018 0076 0080 - -0117 - -0116 0040 - -0355 22. Per cent person trips to

shop --0"002 0 106 0004 0077 --0 130 --0281 0-180 0 357 - -0280 - -0288 0546 --0 319 23. Per cent person trips for

socaal recreatmn 0 165 0 163 --0-057 0 202 0 004 - -0288 0 407 0 455 --0 583 --0 591 0.397 --0 122 24. Per cent person trips to

work --0 355 - -0292 --0091 - -0286 0313 0259 --0.264 - -0512 0.564 0598 - -0414 0573 23. Per cent person trips for

other purposes --0 151 0 006 --0 274 0'305 0 208 0 029 --0 094 0 J54 ] 0 122 0 023 0'461 --0-298 )-6. Per cent person trips for

school - -0116 0058 - -0078 0163 0150 0016 - -0025 - -0104 0047 0022 0'334 --0'264 )-7. Per cent person trips for

a ride 0'055 0 203 --0 395 0 279 0 265 --0"135 0 096 0'026 0 081 0'042 0 260 --0 050 )-9. Per cent person trips to

eat a meal --0.071 0 304 --0.377 0 455 i 0.098 --0 179 0 077 0 003 0.243 0.115 0 532 --0.361

which shows the correlations of each of the original ("factor loadings") correlations of each of the r underlying patterns of variations ("factors") and a 57 × r matrix which provides the scores of the zones on each of the new factors is then performed.

3. An analysis of the factor scores allows the 57 analysis zones to be differentiated by two relatively uniform factors to obtain a socio-eeonomic classification of the travel analysis zones.

Table 1 shows the correlation matrix of the 28 variables.t Examination of the correlation matrix indicates that about 21 per cent of the correlation coefficients are significant at the 0.05 level (i.e. 156 out of 764 possible correlation coefficients). The overall level of correlation is low. The range in correlation coefficients varies from 0"000 to 0.937, and the average absolute correlation coefficient is 0.25. The reason for the low correlation coefficients perhaps is due to the heterogeneity of the data and the variability in sizes of the analysis z o n e s .

The correlation matrix (Table 1), which had its factors isolated by the principal axes method, yielded a 28 × r matrix. The latter is then subjected to varimax rotation (Kaiser, 1958) to approximate a simple structure solution (Thurstone, 1947).

t All the variables are transformed to common logs in order to fulfill the conditions of normality and homoscadestlcity.

A multivariate analysis of urban travel behavior in Chicago

2 8 VARIABLES ASSOCIATED W I T H TRIP GENERATION

13 14 15 16 17 18 19 20 21 22 23 24

349

25 26 27 28

1-000

0.228 1'000

0 659 0-265 1-000 - 0 . 6 1 9 - -0258 --0-760 1 000

--0 524 --0.143 --0.747 0 694 1 000

--0-368 0-058 --0.371 0.434 0.480 1 000

--0.397 --0 262 - -0713 0 726 0.522 0.340

- -0237 --0 323 0-089 0.062 0.044 0 021

0 134 0.350 --0.172 0.143 0 134 0-107

--0 087 - -0284 --0 190 0.212 0.120 --0.037

--0.055 --0.321 --0 315 0478 0 311 --0.001

0298 0.247 0411 --0 609 --0-430 --0.055

0 176 --0.013 0.040 --0.095 0 151 0 046

0257 0.141 --0-041 --0.083 0 124 --0 175

0.280 0.087 - -0098 --0 094 0228 0.337

--0-028 0.313 --0.177 - -0081 0 503 0 136

25

1 "000

--0 216 1 000

0.458 --0 458 1 000

0139 - -0367 - -0009 1000

0-276 0 141 - -0048 0,419 1'000

- -0480 --0.446 --0'119 - -0509 - -0620

- -0079 0 198 - -0006 0-457 - -0028

0 002 --0 260 0-202 0081 0'062

0'000 --0"155 0'067 --0.039 0'087

--0-150 --0 106 0063 - -0017 --0 126

1000

--0 077 1 000

- 0 0 2 8 0309 1'000

0'139 0238 0'103

0 125 0'427 0418

1 "000

0'404 1 000

Table 2 gives the results of the rotated factor matrix and its rotated factors. Out of 28 variables, 7 common factors have been extracted. Together they account for 81"5 per cent of the common variance. This means that the covariance among the 28 variables can be attributable to 7 common factors which are the underlying patterns differentiating trip generation among the 57 analysis zones in the city of Chicago.

Table 3 presents the results of the principal axes factor analysis of the 57 x r matrix, indicating the factor scores for each of the 57 analysis zones in terms of the 7 common factors.

6. INTERPRETATION OF THE FACTORS Factor I: General size

Factor I is clearly an expression of the size differences among the 57 analysis zones. It has the highest factor loading in average car ownership and might be designated as a car ownership factor. But this identification would be misleading since car ownership is only one among several of the determinants affecting trip generation. A general size factor would seem to be a more appropriate designation than a car ownership dimension because trip generation as measured by trips per occupied dwelling unit, increases with average car ownership, household size, per cent auto driver, per cent auto driver plus passengers, distance from CBD, per cent 16 years over with driving permit and person trips per 1000 ft 2.

350 S . T . WONO

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A mul t iva r i a t e analys is o f u r b a n travel behav io r in Ch icago 351

TABLE 3. FACXOR SCORES Or SEVEN rACXORS

Ana lys i s zone No . I II III IV V VI VII

6 1 --1"98 0"58 - -1 .18 0 '42 1"28 1'32 - 0 " 1 2 10 2 --2"09 0"22 --0"82 0"24 0-80 0"50 0"57 25 3 --1"59 0"16 --0"04 - 0 " 1 7 2.19 2"85 - 0 " 8 6 28 4 -- 1"94 0.16 - 0"53 0"20 0.22 0"41 0"50 34 5 --1"47 0"77 --1-81 1"30 1"30 - 0 ' 0 9 - -0 ,57 41 6 -- 1"63 0"47 - 0"80 0 '58 0 '96 0"30 0.59 57 7 -- 1"35 -- 0 '59 0.26 0"87 0"77 1"40 0.34 58 8 - 1"44 - 0"41 0.92 0"53 1"00 - 0"05 0.67 60 9 - 0 . 5 7 - 0 " 2 2 0"16 0"89 1-20 1"28 0.73 61 10 - 1 " 1 5 - 0 " 4 0 0.47 - 0 " 1 1 0"75 1"24 1.38 65 11 - 1 " 9 3 - 0 " 1 4 0.50 0"44 - 0 " 2 0 1"34 1.71 67 12 - 1"39 1"15 - 1"16 0"85 0"78 - 1"00 0"20 73 13 - 1 " 0 9 - 0 " 4 1 - 0 " 3 0 - 0 " 4 6 1"06 - 0 - 4 2 0-31 74 14 - 1 " 2 2 0"28 - 0 . 6 2 1"33 0"89 1.01 - 1 . 6 1 79 15 - 1 " 1 6 0'05 - 0 " 6 4 0"49 2"01 2"79 0 '29 81 16 - 1'48 - 0 " 3 3 - 0 " 4 9 0"57 0 '60 - 0 ' 4 1 0"12 84 17 - 2 " 3 3 - 0 " 4 3 1"51 0"85 0"97 - 0 " 9 5 - 1"12 88 18 - 1 " 8 5 0"10 1-02 0"86 - 1 " 8 3 - 0 " 3 9 - 1 . 3 2 97 19 -- 2"50 - 0"99 3"40 - 0"49 0"69 0 '42 0.03

102 20 0"92 2"09 2"13 - 0 " 7 3 - 2 " 7 7 3"11 - 2 . 3 5 104 21 -- 1"44 - -0-56 0"57 1"29 0"48 0"50 - 0"21 106 22 - 0 " 8 6 - 0 " 8 8 0-13 1-55 1"55 1"97 - 0 " 4 8 108 23 - 1"10 - 1"11 1"50 1"70 - 0 " 3 0 1"84 0.83 110 24 - 0 " 4 4 - 0 . 5 1 0"42 1"14 0"65 - 0 " 2 6 0.35 113 25 - 0 " 7 7 - 0 ' 3 0 0.31 1"11 - 0 " 0 1 1"07 2.62 119 26 - 0 " 6 7 - 1.23 0.81 0"23 1"05 0"65 0.07 122 27 - 1 " 1 3 - 1 . 3 7 1.06 1"05 1'03 0 '10 - 0 . 7 8 125 28 - 1"40 - 0"64 1-17 1-36 0"05 0.30 0.27 146 29 - 0 " 2 4 - 0 " 0 1 - 0 " 6 6 0"84 1"14 0.10 0.07 153 30 --1"11 - 0 . 2 2 0"43 1"26 - 0 " 3 3 0"21 0.63 155 31 - 0 ' 8 1 - 1"13 0-18 0"56 0"57 0"57 1.55 156 32 - 1 " 0 2 - 0 . 4 0 0"59 0"62 1-12 - 0 " 5 4 0.16 158 33 - 0 ' 5 8 - 0 ' 5 1 0"03 0"65 0"26 0'45 0.18 159 34 0"58 0"08 - 0 . 6 4 1'35 1"60 0"80 - 0 " 3 7 161 35 - 0 " 4 6 - 0 - 8 7 1"27 0"41 0 '67 0"66 0.83 166 36 --1"64 1"05 - 0 " 1 5 0 '79 - 1 " 2 4 - 0 ' 7 8 0.37 167 37 - 1"30 - 1"41 2-30 0"44 0"37 0"01 0.15 169 38 --1-05 - 0 . 5 2 0.06 - 0 " 1 9 0"42 - 0 " 8 3 0.04 171 39 --1"12 - 1 " 3 6 1"65 - 0 " 4 8 2"71 1"06 - 0 " 4 6 173 40 - -0 '45 - 1 ' 1 5 0.51 0'61 0"72 1"70 1-57 175 41 - 0 " 3 3 - 0 " 1 1 0"70 1"04 1'19 0"78 --0"42 203 42 0"14 - -0-34 0"08 1"66 1"91 1.27 0.11 205 43 0"84 - 0 " 1 1 0"45 2"24 0"53 1'49 1.82 249 44 - 0 " 4 7 - -1 .62 1.15 0"35 1.35 0"49 - 0 . 6 7 255 45 0.11 - 1.48 1.40 1"98 0-36 1"30 0"60 260 46 0"54 - 0 " 8 9 0-35 0'73 1-46 - 0 " 1 3 1"68 262 47 1"16 --0"88 0 '56 2"32 1"38 0-48 - 0 . 6 0 275 48 0 '36 - 1.27 0.46 0"31 1"19 1"85 0.44 282 49 0"77 0.04 0"56 0"37 2"47 0"41 0"55 280 50 0"40 -- 1.35 0.22 0,07 0"65 - 0"03 - 0"54 278 51 --0-63 - -2 .34 0.10 1.57 0"50 1"84 - 1.75 352 52 - 0 " 0 5 --0"36 --0"06 1.73 - 0 " 8 6 - 0 - 7 2 0.81 380 53 0-58 --0"59 0"18 1.63 1"14 --0"90 -- 1.02 382 54 0"22 0.76 0.34 - 4 " 5 3 1"24 0"36 0'81 385 55 --0"68 - 1"08 0 '69 0.67 - 0 ' 9 7 2.32 2"98 391 56 - 0 " 1 5 - 1 " 0 6 - 0 " 2 2 0.25 - 0 " 2 6 - 0 . 3 6 0-92 393 57 - 0 " 9 2 --5"29 - -2 .89 - -1 .27 --1"46 1"10 - 0 - 8 6

352 S.T. WONO

Conversely trips per occupied dwelling unit decrease as degree of urbanization and segregation is found to be significantly associated with a low proportion in mass transit, bus and street-car, low commercial land development and low net residential density. These relations are consistent with the theory of urban land use as has been suggested by urban economists and urban geographers (Isard, 1956; Berry, 1965). The negative simple correlation coefficient between distance from the CBD and net residential density (Table 1) suggests the distance-density effect. This relationship agrees well with the signs of the factor loadings of these two variables in Table 2. It implies that as distance from the CBD increases, general size increases as well and the lower is the net residential density. Several reasons may be attributable to this phenomenon. First, families further away from the city tend to be larger in size, and hence the higher is the frequency of trip-making. Second, as income increases people are likely to live further away from the center of the city, as they would rather substitute transportation cost for rent than vice versa. Furthermore, a low net residential density allows greater flexibility of trip-making (being devoid of congestion in non-residential land) than a high net residential density area.

Factor II: Modal choice

Factor II seems to be a factor having to do with the choice of mode or, in short, modal choice. It covaries with Factor I and is affected by land use and trip purpose. The proportion of people who choose mass transit, bus and street-car is associated with the proportion of people going to work and the proportion of public buildings (offices downtown), while the proportion that is auto driver and auto driver plus passenger is correlated with those going to shop or for social recreation. The latter tends to come from the outskirts of the city in residential communities characterized by a low segregation index. This finding agrees with Nancy Leathers's results of the Skokie Swift Study (Leathers, 1967).

Factor III: Social status

Factor III is perhaps best designated as a social status factor since the underlying pattern identifies itself clearly with family size and social rank. A high inverse correlation is found between family size and social rank. Large family size is found to be associated with low social rank, high degree of segregation and living in commercial developed land. Because of the low social status, there are few public buildings. In these areas there are very few people who possess driving permits or who can afford the luxury of taking trips to eat a meal or for a ride.

Factor IV: General trip purpose

Factor IV can be interpreted as a general trip purpose factor. Trips to shop, home and for other purposes are determined primarily by per cent developed residential land, while trips to work are associated with per cent manufacturing of developed land.

Factor V: School Factor V seems to be an extension of Factor IV. Since the highest loading here is the

variable "trips to school", it may be designated as a factor concerning education. It says that trips to school and to eat a meal are attracted to residential developed land, and they vary inversely with the proportion of people 5 years and over. The latter relationship is in accord with Sato's conclusion that school trips can be estimated from school age of population (Sato, 1965).

Factor VI: Ride Factor VI can be interpreted as a factor concerned with trips for a ride. It covaries with

Factors IlI, IV and V. It says that trips for a ride increase with degree of urbanization,

A multivariate analysis of urban travel behavior m Chicago 353

proportion of commercial developed land, proportion of people 5 years and over, and diminish with family size. It also shows that trips for a ride are interrelated with trips to work, trips for other purposes and trips to eat a meal.

Factor VII: Personal business Factor VII finally picks up a factor of personal business. It covaries with Factors II,

III, IV and V. It expresses that personal business trips increase with non-residential density and the proportion of public buildings of developed land. This is not unexpected since the area of study is focused within the city of Chicago. It also increases with person trips to school but decreases as trips home increase.

Principal axes factor analysis simplified considerably the pattern of urban travel behavior among 28 variables which characterize the 57 analysis zones in Chicago. The factor analytic solution has shown that a substantial proportion of the common variance can be explained by 7 factors. Among them 34 per cent of the common variance is accounted for by the first factor alone, while about 14 and 11 per cent are contributed by choice of mode and social status respectively. Trip purpose, which explains 7 per cent of the common variance and which has been isolated and identified as the fourth factor, is highly diversified. This is reflected by the low factor loadings which have been recognized to be associated with it and their covariations with Factors V, VI and VII. The latter factors are extensions of Factor IV. Their identities in separate factors suggest the lack of interrelatedness iti trip purpose. Each of these three factors contributes an average of about 4 per cent to the total common variance as revealed by the 7 factors.

Principal axes factor analysis has also shown that there is some systematic regularity which underlies the 28 variables among the 57 analysis zones in Chicago. The emergence of the 7 discernible factors is an indication of such orderliness.

Interesting contrasts too are revealed by the factor analytic solution. While the variables that are associated with choice of mode and social status are quite homogeneous, those that are correlated with trip purpose and land use tend to be diversified.

7. ANALYSIS OF THE FACTOR SCORES Factor scores of the 57 analysis zones on the 7 factors permit these zones to be analyzed

with respect to the contribution of each factor to their character. This gives a gross charac- terization of the 57 analysis zones with respect to the 7 factors.

In Table 4 the observations with standard scores that fall outside the range of _+ 0.70 are tabulated. (The choice of 0.70 as the lower limit is an arbitrary division.) Factor scores are arrayed by rank order form high positive to high negative.

The first factor is identified with general size structure and accounts for 33.9 per cent of the common variance. It varies directly with variables 1, 2, 3, 4, 7, 8, 16, 17, 18 and 19, and inversely with variables 5, 6, 10, 13 and 15 (see Table 2). Therefore, analysis zones that rank high positive on this factor are those that have high frequency of trips, high car ownership, high per cent auto driver, further distance from the CBD and high frequency trips per 1000 ft z floor area. These analysis zones tend to have high social rank, large households and high per cent 16 years and over with driving permits. They are generally characterized by a low degree of urbanization, segregation, a low proportion in mass transit, bus and street-car, low commercial land development and a low net residential density. A striking feature among these 57 analysis zones is that those that rank high negative are about eight times greater than those that rank high positive.

Factor II is identified with modal choice. It is positively correlated with per cent mass transit, per cent bus and street-car, per cent public buildings of developed land and per cent

354 S . T . Wo~G

TABLE 4. ANALYSIS ZONES WITH EXTREME FACTOR SCORES

Analys i s H i g h Ana lys i s H i gh zone posi t ive zone negat ive

Fac to r I - - G e n e r a l size

Ana lys i s H i g h Ana lys i s H igh zone posit ive zone negat ive

Fac to r I I I - -Soc i a l s t a tus

262 1-16 102 0-92 205 0-84 282 0.77

97 - 2 . 5 0 84 - 2 . 3 3 10 - 2 . 0 9

6 - 1 . 9 8 28 - 1.94 65 - 1 . 9 3 88 - 1.85

166 - 1-64 41 - 1-63 25 - 1.59 81 - 1 . 4 8 34 - 1 . 4 7 58 - 1.44

104 - 1 . 4 4 125 - 1 . 4 0

67 - 1.39 57 - 1.35

167 - -1 .30 74 - -1 .22 79 - -1 .16 61 - 1.15

122 - 1.13 171 -- 1.12 153 - -1 .11 108 -- 1.10

73 - -1 .09 169 - -1 .08 156 -- 1.02 393 - 0 . 9 2 106 - 0 . 8 8 155 - 0 . 8 1 113 - 0 . 7 7

Fac to r I I - - M o d a l Choice

102 2"09 67 1-15

166 1"05 34 0"77

382 0 '76

393 --5"29 278 - -2-34 249 - -1 .62 255 -- 1"48 167 --1"41 122 - 1 " 3 7 171 - 1"36 280 --1"35 275 - -1 .27 119 - 1.23 173 -- 1"15 155 -- 1-13 108 -- 1.11 385 -- 1"08 391 - -1 .06

97 --0"99 260 --0"89 106 --0"88 262 - 0 " 8 8 161 --0"87

97 3.40 167 2.30 102 2.13 171 1.65

84 1"51 108 1.50 255 1.40 161 1.27 125 1"17 249 1.15 122 1.06

88 1.02 58 0.92

119 0.81 175 0"70

393 - 2"89 34 - 1.81

6 - 1 " 1 8 67 - 1"16 10 - 0 " 8 2 41 - 0 " 8 0

Fac to r I V - - G e n e r a l t r ip pu rpose

262 205 255 352 108 203 380 278 106 125 159

74 34

104 153 110 175

60 57 88 84 67

146 166 260

2.32 2.24 1.98 1"73 1 "70 1.66 1"63 1.57 1"55 1"36 1"35 1"33 1 "30 1"29 1-26 1"14 1"04 0-89 0"87 0"86 0.85 0-85 0.84 0"79 0.73

382 393 102

- 4 " 5 3 - 1 "27 - 0 " 7 3

Fac to r V - - S c h o o l

171 282

25 79

203 159 106 260 262

2"71 2"47 2"19 2"01 1"91 1 "60 1"55 1 "46 1"38

102 88

393 166 385 352

- 2 . 7 7 -- 1"83 -- 1"46 --1"24 - -0 .97 --0"86


TABLE 4 (cont.)

355

Analysis zone

High Analysis High Analysis High Analysis High positive zone negative zone positive zone negative

Factor V (cont.)

249 1.35 34 1-30 6 1.28

382 1.24 60 1.20

175 1.19 275 1.19 146 1.14 380 1.14 156 1.12 73 1"06

119 1.05 122 1.03 58 1.00 84 0.97 41 0-96 74 0-89 10 0-80 67 0.78 57 0.77 61 0.75

173 0.72

Factor VI--Ride

102 3.11 67 - 1.00 25 2-85 380 -0 .90 79 2"79 169 -0.83

385 2"32 166 -0.78 106 1"97 352 -0"72 275 1"85 108 1"84

Factor VI (cont.)

278 1"84 173 1.70 205 1"49

57 1"40 65 1"34

6 1.32 255 1.30

60 1"28 203 1"27

61 1'24 393 1"10 113 1"07 171 1"06 74 1"01

159 0"80 175 0"78

Factor VII--Personal business

385 2-98 102 -2.35 113 2"62 278 - 1"75 205 1.82 74 -- 1"61

65 1-71 88 -1 .32 260 1'68 84 - 1"12 173 1-57 380 -1"02 155 1'55 25 -0 ' 86 61 1"38 393 -0"86

108 0 83 122 -0 '78 161 0"83 352 0.81

60 0"73

pe rson t r ips to work and inversely re la ted to the segregat ion index, per cent au to driver, pe r cent au to dr iver plus passenger, per cent resident ial o f developed land, dis tance f rom the CBD, per cent t r ips to shop and per cent t r ips for social recreat ion. I t accounts for 14-5 per cent o f c o m m o n var iance. Analys is zones tha t r ank high positive on this fac tor are 102,67, 166, 34 and 382 (see Figs. 2 and 5). They all have high p ropor t i ons o f mass transi t , bus and s t reet -car and person t r ips to work. M o s t of the t r ips made are wi th in the city as reflected by the h igh p r o p o r t i o n o f t r ips to publ ic bui ldings of developed land. Analys is zones r ank ing high negative on this fac tor tend to be fur ther f rom the CBD. They number four t imes higher than those tha t r ank high positive.

The th i rd factor , account ing for 10.6 per cent c o m m o n variance, reflects a social status differentiat ion. Analys is zones tha t r ank high positive on this fac tor general ly have large families and a low social status. They are d is t r ibuted mainly in the indust r ia l ized areas o f the city. Par t icular ly high positive zones are 97, 167 and 102 (see Figs. 3 and 5). In contrast , analysis zones tha t r ank high negative are those which have a low social r ank and where the p r o p o r t i o n t r ips to publ ic bui ldings is low. There are fewer zones tha t r ank high negative t han those tha t r ank high positive.

356 S .T . WO~G

~ ' ' ' ' 1 . . . .

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r . . . . . i . . . . . . . . . . •

Factor Scores ' ~ ~ '

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FI6. 2. Modal choice of analysis zones in Chicago.

• ¢ ST 8T

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107 I'M ~ r

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A multivariate analysis of urban travel behavior in Chicago 357

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FIG. 3. Social status of analysis zones in Chicago.

~ ~ S r s r

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358

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S. T. WONG

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169%~5 T el04 I ,>=u 106e 260e262

39,. Is.s .,~3.~s o280e275 el19

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FACTOR III (SOCIAL STATUS) FIG. 4, Classification of analysis zones in Chicago by modal choice and socml status.


I . . . . . . p'HARE FIELD

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YESTEUX ~elH5$

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r - - " , ' ~ ' - - ~ ~ . . . . . . . ~.~ ' i ~1 , 545 ADOI$O~ ST

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124' 123 I 122 ! 014 , 063 I 0IF , 030 I 01n i 00~ f 008 ~ 6 0 7 . . . . .

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- C i t y b o u n d a r y ~ .

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M Lies i o s,

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FIG. 5. Analyms zone base map (part of Chicago Area Transportation Study map).

360 S.T. WONG

The fourth factor, which explains 7 per cent of the common variance, depicts one of general trip purpose. Trips to shop, home and for other purposes vary directly with the proportion of residential development and inversely with the proportion of manufacturing developed land and trips to work. Analysis zones which rank high positive are about eight times higher than those that rank high negative.

Factor V is essentially related to trips to school, trips to eat a meal and the proportions of residential developed land. It varies inversely with the proportion of trips 5 years and over. Analysis zones that rank high positive are about six times more numerous than those that rank high negative.

Factor VI is identified predominantly with trips for a ride. It is correlated directly with per cent trips 5 years and over, trips for other purposes, trips to work, trips to eat a meal, the degree of urbanization and per cent commercial of developed land, and inversely with average household size. Like Factors IV and V, more of the analysis zones rank high positive than high negative. In this factor, those that rank high positive are four times higher than those that rank high negative.

Factor VII represents a dimension of personal business. It expresses that personal trips increase with non-residential density and the proportion of public buildings, and decrease as trips home increase. The number of analysis zones that rank high positive and those that rank high negative is about the same.

8. SOCIO-ECONOMIC CLASSIFICATION OF THE ANALYSIS ZONES Of relevance to the analysis of urban travel behavior are the socio-economic variables--

modal choice (Factor II) and social status (Factor III). If the 57 analysis zones are plotted in a graph with their scores on Factor II located on the ordinate and their scores on Factor III located on the abscissa, one can differentiate the analysis zones in terms of two- dimensional socio-economic space. Such an array of the scores permits similar analysis zones to fall at the same point on the graph and dissimilar analysis zones to be widely separated.

Figure 4 shows how the analysis zones are plotted this way and presents a classification of analysis zones in Chicago by modal choice and social status. Note how the analysis zones which score high negative in Factor II and those that score high positive in Factor lII are related to their positions on the graph. Those that are high in social status tend to show a low modal choice and, conversely, vice versa. With the exception of analysis zones 393 and 102, one might generalize that modal choice tends to vary inversely with social status.

9. SUMMARY Factor analysis reduced the 28 variables to 7 factors which together explain 82 per cent

of the common variance. It made it possible to interpret the factors from the loadings of the 28 variables on them. It also made available the scores for each of the zones on each of the factors. Analysis of the factor scores shows that it is possible to Not the scores of the 57 analysis zones in terms of a two-dimensional socio-economic space which permits one to differentiate spatially which analysis zone is similar or dissimilar among the 57 analysis zones studied.

Based on the results of the foregoing factor analytic solution as a rationale, one may now proceed to develop an alternative model for predicting trip generation in Chicago.

10. MULTIPLE-REGRESSION ANALYSES OF TRIP GENERATION IN CHICAGO

The main reason for developing an alternative model for predicting trip generation in Chicago is the contention that variations in trip generation can be explained by car


ownership, choice of mode, trip purpose, land use, residential density, age of trip-maker and distance from the center of the city, other than the three social area indices used by Oi and Shuldiner.

Whereas the factor analysis in the foregoing section was concerned with interdependencies among the 28 variables, the ensuing discussion will be concerned with the dependence of values which are assumed by certain variables upon the values that are assumed by other variables. The concern now is with variations in the dependent variable as a function of their covariations with one or more simultaneously considered predictor variables. A number of equations are developed to predict values of the former (i.e. trip generation), given values of the latter.

Using trips per occupied dwelling unit as the dependent variable, several combinations of independent or predictor variables (which were surrogates of the 7 factors) are now tested by multiple-regression analysis to ascertain what simultaneous and cumulative effect they might have in determining variations associated with trip generation.

Since the data are transformed to common logs, the resultant multiple regression equation will be expressed in the form:

log10 Tr = a + b loglo X 1 + c lOgl0 J(2 + dlogl0 X 3 +.. . + e log10 X~ (lc)

where Tr stands for the dependent variable trip generation; X1, X2, X3, ... , X~ represent the independent or predictor variables characterizing trip generation, and a, b, c, d and e are the numerical constants of the regression equation.

The results of the combination of variables tested with trip generation are summarized in Table 5. For purposes of comparison, the results of models (la) and (lb) of the Oi and Shuldiner study are presented first in Table 5.

Several observations may be made with regard to variations associated with trip generation. First, the multiple R ~ of equation (2) is much lower than that of equation (lb). This suggests that better fits were yielded without transformation than with transformation. The low multiple R 2 could be attributable to the large standard errors of estimate of the regression coefficients of average household size and social rank in equation (2). Second, the multiple R~'s on the whole, with the exception of equation (2), are fairly strong and encouraging.

Among the other five equations (3-7), various degrees of influences in explaining variations associated with trip generation are reflected by the different combinations of independent variables, t Between equations (3) and (4) by deleting the urbanization index and replacing it with distance from the CBD, a much high multiple R 2 is achieved than vice versa. By dropping distance from the CBD and replacing the latter with household size, the three independent variables in equation (5) yield only a multiple R ~ of 0.862. Although the standard errors of estimate of the regression coefficients in equation (6) are all significant, the cumulative effect which family size, net residential density and age of trip-makers have on trip generation is only 1 per cent higher than the multiple R ~ of equation (6). Of the independent variables tested, those of equation (7) account for the highest proportion of variance associated with trip generation. Since the latter has produced the best results among the various combination of explanatory variables tested, we shall designate this equation as the alternative model for predicting trip generation. It might be noted that all the standard errors of estimate among the regression coefficients of the set of independent variables in equation (9) are significant. The high multiple R 2 and the significant variance- ratio with 51 degrees of freedom are indicative of the power of the model.

t The results in Table 5 of equations (3), (4), (5), (6) and (7) on the whole show better fits than those of the Oi and Shuldiner study that were presented in Table 66 on p. 236.

362 S.T. WONG

TABLE 5. MULTIPLE REGRESSIONS OF TRIP

Dependent variable

and equationt

Independent

A N X~ X2 X~ X, X~ X~

(la)~ - - - - 0.0172 -0.0744 -0.0023 - - - - - - (0"0041) (0"0048) (0"0054)

(lb)~ 3"404 0"516 0'0119 -0'0343 . . . . (0.290) (0.141) (0.0031) (0.0042)

(2) 0.5371 0.1481 0.0856 -0-2914 . . . . (0.1107) (0.1106) (0.1030) (0.1128)

(3) 0.5632 - - - - --0.2544 - - - - 0.7012 m (0.1013) (0.0951) (0.0884)

(4) 0.5959 . . . . . 0.6209 0.3621 (0.0675) (0.0736) (0.0682)

(5) 0.4172 0.5374 . . . . 0.5840 (0.0659) (0.0662) (0.0698)

(6) - - 0-5389 . . . . 0.4210 0.5979 (0.0635) (0.0622) (0.0657)

(7) 0.5818 . . . . . 0.6444 (0-0647) (0.0611)

t The dependent variable is the trip generation rate as measured in trips per occupied dwelling unit. ++ The variables in equations (1 a) and (1 b) are not transformed, while those in the other equations are

all transformed to common logarithms. Equations (la) and (lb) are the first and second models of Oi and Shuldiner (1962). Equation (2) is (lb) with a common log transformation.

Note: The coefficients within parentheses are the standard errors of estimate of the regression coefficients.

Symbols: A = Average car ownership N = Average household size

X1 = Social rank index X~ = Urbanization index X~ = Segregation index X 4 = Population per 1000 ft 2 of residential land (NRD) X5 = Per cent trips 5 years and over X 6 = Distance from CBD

11. C O N C L U S I O N This s tudy has extended the work o f Oi and Shuldiner by examining a wider range o f

var iables tha t were no t considered by the au thors in a mul t id imens iona l manner . In extending their work, i t was found tha t 7 factors were associa ted with u rban travel behavior in Chicago. Analys is o f the fac tor scores indicates tha t the 57 analysis zones can be differentiated in socio-economic space in terms o f two f a c t o r s - - m o d a l choice and social status.

In compar ing the results o f the a l ternat ive model [i.e. equa t ion (7)] wi th models ( l a ) and ( l b ) o f the Oi and Shuldiner s tudy, several features s tand out. Firs t , the mul t ip le R 2 o f equa t ion (7) is much higher than tha t of mode l ( la ) . Second, a l though the mul t ip le R 2 o f equa t ion (7) is no t as high as tha t o f mode l l (b) , the set o f var iables used reflect a more comprehensive range o f var iables which have a considerable influence in de termining t r ip generat ion. Third , car ownership remains the d o m i n a n t var iable in account ing for t r ip generat ion. Unl ike the Oi and Shuldiner mode l o f l (b) , the mul t ip le R 2 o f equa t ion (7) was no t thwar ted by the inclusion o f such var iables as the age o f t r ip -maker , choice o f mode, non-res ident ia l densi ty and t r ip purpose. Fur ther , the col l inear i ty effects are no t as appa ren t as tha t o f the Oi and Shuldiner study. Final ly , the al ternat ive mode l has given add i t iona l insights in to u rban t ravel behav ior by consider ing o ther var iables which are fundamenta l to the unders tand ing o f t r ip genera t ion analysis.


GENERATION IN CHICAGO FOR 57 ANALYSIS ZONES

363

variables

X7 Xs X9 Xlo Intercept R ~ S.E. F-V

. . . . 8.47 0.8381

. . . . 2.18 0.9597

. . . . 0.951974 0.720

. . . . . 2.152062 0.786

. . . . . 2.412008 0.842

. . . . . 1.994125 0.862

. . . . . 2.055088 0.870

0.1688 0.2402 -0 .1186 0.0978 -2.949845 0.900 (0.0558) (0.0683) (0.0537) (0.0413)

0.058143

0.050344

0.043330

0.040474

0.039278

0.036168

33.48

65.00

93.93

110.23

118.14

71.75

X7 = Per cent auto driver plus passenger X8 = Person trips per 1000 ft ~ floor area X9 = Per cent personal trips to work

Xx0 = Per cent person trips to eat a meal R ~ = Multiple correlation coefficient of determination

S.E. = Standard error of estimate of multiple regression equation F-V = Value or variance-ratio

Acknowledgements--The author wishes to express his thanks to the Research and Data Service Divisions of the Chicago Area Transporta t ion Study for allowing him to use certain categories of the Home Interview Data Inventory. He is grateful to Messrs. Frederick A. Petrick and John J. Howe for providing him with the CATS base maps and their permission to use them for his research purposes. The maps in the original manuscript were made by Mr. Louis Skoda of the Cartography Laboratory of Simon Fraser University. To him, the author is much indebted for his fine draftsmanship.

R E F E R E N C E S

BERRY B. J. L. (1965). Commercial Structure. Northeastern Illinois Planning Commision, Chicago, Illinois.

CHICAGO AREA TRANSPORTATION STUDY (CATS) (1962). Final Report, 3 Vols. Chicago Area Trans- porta t ion Study, Chicago, Illinois.

ISARD W. (1956). Location and Space-Economy. Wiley, New York. KAISER I-I. F. (1958). The varimax criterion for analytic rotat ion in factor analysis. Psychometrica 23,

187-200. LEATttERS N. J. (1967). Residential location and mode of t ransportat ion to work: a model of choice.

Transpn Res. 1, 129-155. OI W. Y. and SHULDINER P. W. (1962). An Analysis of Urban Travel Demands. Northwestern University

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Documents

A multivariate analysis of urban travel behavior in Chicago