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Modal demand: A user perception model
Tran.cpn Res.
Vol. 6, pp. 293-308. Pergamon Press 1972. Printed in Great Britain
MODAL
DEMAND:
A USER PERCEPTION
MODEL
MICHAEL J. DEMETSKY University of Virginia and LESTER A. HOEL Carnegie-Mellon (Received
5 May
University, Pittsburgh
1971; in revised form
21 April 1972)
INTRODUCTION IN CONTRAST with prior approaches which, as a rule, relied on aggregated data bases, increased attention is currently being directed toward the analysis of individual and household travel behavior. The resulting mathematical models indicating the modal choice These recent studies indicate decision have accordingly been described as “behavioral”. two fundamental approaches: econometric models (Lisco, 1967; Lave, 1969) which are based upon data from home-interview, origin-destination surveys, and attitudinal studies (Ackoff, 1965; Bock, 1968) which determine by interview those characteristics influencing the mode choice decision. A review of the capabilities and shortcomings of the two approaches for analyzing the mechanism of modal choice with respect to forecasting within the transportation planning process indicates that a more significant modal split methodology may result from a synthesis of the two approaches. Such a strategy, utilizing both origin-destination data and attitudinal survey information in the development of a behavioral modal split model, has been investigated and is introduced in this paper. These findings are derived from a study of areawide behavioral modal split models (Hoe1 and Demetsky, 1970; Demetsky, 1970) which investigated the selection of explanatory variables, the mathematical form of the model (linear vs. S-shape), the level of transport sensitivity required for such models and the potential of these models for studying the impact of new transit technology and policy. The analysis techniques used to accomplish this research included stepwise linear regression, dummy variable techniques, a model derived from probit analysis which uses the logistic function, a dichotomous dependent variable and concepts of utility theory. In specifying the transportation system characteristics in the behavioral model, three distinct methods are evaluated: socioeconomic models based on trip and tripmaker attributes, trip time models which consider the effects of adding a variable which denotes the relative trip times between auto and transit and modal preference models that employ a measure of user perceptions of the modal attributes. MODEL DEVELOPMENT The basic unit in this model is the individual tripmaker. During calibration the dependent variable is designated as an event which indicates a trip either occurring or not occurring on a particular mode. Accordingly, the observed mode choice decision is formulated as one of binary choice in which the dependent variable is dichotomous and a function of 293 13
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MICHAEL J. DEMETSKYand LESTER A. HOEL
the explanatory variables, such that 1, if the event (Tk) occurs
Wk) i = 0, otherwise
(1)
where Tk indicates the event of a specified trip occurring on mode k and i indicates the ith observation. The most convenient approach to the binary choice problem is the linear regression model (Goldberger, 1964). Once this model is calibrated for P(T,) on several explanatory variables, (X = x1, x2, . . ., x,,,), a value of P(T,) is calculated from the equation. The predicted values of the dependent variable for any specified X are interpreted as an estimate of the conditional probability of Tk, given X (Johnston, 1963). The linear model, however, exhibits potential shortcomings. First, predicted P(T,) values are not necessarily confined to the appropriate interval and may fall either below zero or above one in some cases. This fact is contrary to the definition of a probability function and hence a transformation of the estimates to realistic values is required. The second problem attributed to the linear model is the shape of the curve, as noted by Lisco (1969): “Multiple linear regression analysis is the wrong tool to apply to modal split analysis. The relation between modal choice and the parameters that determine it is not linear, but S-shaped.” Some solutions to the above problem have been demonstrated (Warner, 1962; Lisco, 1967; Lave, 1969) where the basic technique derives from the probit analysis model (Finney, 1952). The model used here follows the development given by Goldberger (1964), but substitutes the logistic function for the standard normal cumulative distribution which typifies the probit model. Ik is defined as a linear function of the regressors: Ik = X’b” and is related to P(T,) as follows: (2) p(T,) = F(zk) where P(T,) = the probability of a specified trip being accomplished via mode k; Ik = a linear function of the independent regression, X’bk = b,k + blk x1 + . . . + bnLkx,. The probit model then assumes
s X’bk
F(I,) = (27r-* _-m e-u’/sdu
(3)
In place of the standard normal function indicated above, the logistic function is employed here (4) The logistic transformation maintains the identity of P(T,) as a function of the bk coefficients which are estimated in a iterative fashion by the maximum likelihood technique (Warner, 1962). The forecast probability, P(Tk), of a specified trip occurring on mode k is thus obtained by substituting equation (4) into the right-hand side of equation (2) (5)
Modal demand: TABLE
Variable X,, r = 1,2, . . . . 16
a user perception
~.INDEPENDENTVARIABLESSELECTED
Value
_____
295
model FORSTUDY
Comments
Description
Xl
1 0
If No. in household Otherwise
= 1,2
X2
1 0
If No. in household Otherwise
= 3
Xl, x2
0
If No. in household24
x3
1 0
If income level 1 Otherwise
rt < $7000
X4
1 0
If income level 2 Otherwise
$7OOOz5Y5 $15,000
x3, x4
0
Income level 3
$15,000< Y
X5
1 0
If work-school Otherwise
X6
I
Auto availability index
X7
1 0
If household Otherwise
X*
1 0
Education Otherwise
level l$
High school or less
X9
1 0
Education Otherwise
level 2
Some college
X,ll
1 0
Education Otherwise
level 3
College degree
x*9 x9, Xl,
0
Education
level 4
Graduate
Xl,
A
Age of tripmaker
Xl,
1
If rush hour trip
trip I _ No. of autos available No. of licensed drivers
head is white
school
7.30 a.m.-9.00 a.m. 4.30 p.m.-6.00 p.m.
0
Otherwise
Xl3
1 0
If non-rush Otherwise
hour day
4% x13
0
If non-rush
hour evening
Xl,
1 0
If trip length level 1 Otherwise
L§j 0.25 miles
x15
1 0
If trip length level 2 Otherwise
0.25
x14, Xl5
0
If trip length level 3
L > 0.75 miles
-L1
Relative travel time
Xi,’ = T,--7-z; T,Pzll
XN2
Average perceived modal attributes
x,,* = w,
XlB3
Trip-sensitive modal attributes
X1tr3=
t Y is defined as the gross annual income per household. $ Education level refers to household head. 5 L indicates airline distance between origin and destination I( Tr = time via auto; r, = time via transit. 7 k indicates the kth mode; i indicates the ith observation.
9.00 a.m.-4.30 p.m. 6.00 p.m.-7.30 a.m.
zonal centroids.
0.75 miles
WtiB
296
MICHAEL J. DEMETSKYand LESTER A. HOEL
Selection of variables
In estimating the models, the stepwise linear regression technique was first employed to select the significant variables and to provide initial values for the bk which were then recalculated by the maximum likelihood technique for the logistic function given in equation (5). A liberal criterion was established for the selection of variables for the model as the minimum reduction in the proportion of the residual sum of squares required for a variable to enter the regression was OWI. The basic array of hypothesized independent variables, of which each particular model represents a subset, are given in Table 1. This set includes 15 primary variables which designate the tripmaker and trip characteristics. Continuous variables are used to specify auto availability and the age of the tripmaker, and dummy variables are employed to indicate classes of the following tripmaker and trip characteristics: household size, income level, educational level of the household head, time of the day and trip length. The underlying assumption in this specification of input variables is that tripmakers behave similarly within specific socioeconomic classes with respect to certain trip types. Another important quality of a model using dummy variables is that the linearity assumption, critical in the stepwise regression phase of the analysis, is relaxed. This is due to the fact the data have more freedom to determine the shape of the relationship between the explanatory variables and the dependent variable, i.e. the slope of the line changes with different cases in a dummy variable class (Morgan, 1964). System attributes are input via Xrec as either trip time measures or the modal preference function (to be discussed later). The data
The trip data used in this study were obtained from the 1967 Home Interview Survey completed by the Southwestern Regional Planning Commission (SPRPC). The information of that survey relevant to a behavioral analysis of mode choice was processed onto a tape, along with travel time information from the SPRPC traffic assignment program. The trip sample consisted of home-based trips which indicated both origin and terminus in Allegheny County, the county consisting of Pittsburgh and the immediate vicinity. The total observations numbered 36,908 interzonal trips since travel times were not available for intrazonal trips. The five mode split
The modal choice models were initially developed with respect to a five mode split, i.e. each model was calibrated five times, with each case characterized by a different dependent variable designation for one of the following modes: (1) auto driver, (2) auto passenger, (3) railroad, (4) transit or (5) taxi. The purpose of this approach was to determine whether a closer differentiation between modes other than the customary auto-transit split can be formulated from origin-destination data. The results were inconclusive in this respect for the following reasons. The railroad and taxi trip proportions of the sample data were very small compared with the other modes (each less than 1 per cent) and gave meaningless models. The auto-passenger models exhibited much lower R2 statistics than did the auto driver and transit models. This observation is attributed to the data base in that no distinct class of auto-passenger types is indicated for the study area and there was little correlation between the explanatory variables and auto-passenger trips. The models are, therefore, presented in the usual form, a dichotomy between automobile and transit trips. SOCIOECONOMIC
MODELS
Modelsreferred to as socioeconomic models are based purely on user and trip characteristics without considering any measure of the transportation alternatives. A model consisting
Modal demand:
a user perception
model
297
of nine independent variables was obtained as shown in Table 2 and can be interpreted to show the sensitivity of transit choice to the significant tripmaker and trip measures. This sensitivity analysis if facilitated by defining two typical cases of travel sitautions in terms of specific values for the explanatory variables.? Case A: Rush-hour, work trips (X5 = 1, X,, = 1, X,, = 0). The remaining primary variables are : X,=0,&= 1, a household size of 3 X,=0,X,= 1, a medium income level x,= 1, automobile availability index of 1 x,= 1, white household X, = 0, X, = 1, X,,, = 0, some college for household head 38-year-old tripmaker X,, = 38, X14=o,X15= 1, a medium trip length Case B: Evening, non-w,ork trips (X5 = 0, A’,, = 0, X,, = 0). The other variables are specified as in case A. The forecasted values of the probability of transit usage, P(T), given by the model shown in Table 2 for the variable values describing the typical travel cases A and B are given in Table 3 as 0.146 and 0.023 respectively. Table 3 then indicates how changes in each of the TABLE 2. LOGIT-SOCIOECONOMIC MODEL P(T,) = er’/l + e’I
where Tt indicates the transit mode and I, =-2~62702+0~86050X,+1~16002X,-1~16136X,-1~02719X, +0.42545X, +0~89312X,,+0~98226XI,+0~64989X,,+0~93769X,, i? = 0.138 The Xi are as defined in Table 1. The corrected coefficient of determination R2 in the above and subsequent models is derived similar to the corresponding statistic in multiple
regression analysis (Goldberger, 1964; Lave, 1969). significant variables affect the socioeconomic model’s prediction of transit choice. If a tripmaker were chosen at random, the probability of his using the transit mode would correspond to the proportion of the sample using transit, O-141. Table 3, therefore, gives an explicit example of how the behavioral model accounts for the variance of expected transit usage over a wide range of travel situations by various socioeconomic groups. TRIP
TIME
MODELS
The two models shown in Table 4 utilize time difference and time ratio measures respectively to indicate the characteristics of the auto and transit modes. The response of the socioeconomic model toward various user and trip types has already been shown; thus, similar sensitivity is assumed for the trip time models. Relationships between transit choice and intermodal travel time comparisons are shown in Figures 1 and 2 where all tripmaker and trip characteristics are held constant (per the typical case defined earlier) and only X181, the trip time measure varies. The lower points on all curves in Figs. 1 and 2 correspond closely to the socioeconomic model’s predictions, implying a poor competitive state for the transit service offered in the t All of the original variables from Table 1 are included in these specifications of the typical cases even though some have not entered this particular socioeconomic model. Such a generalization is warranted in order to provide a basis to which all models in this paper can be associated.
MICHAEL J. DEMETSKY and LESTERA. HOEL
298
study area. The trip time models do, however, indicate a more favorable response to transit as its trip time approaches that of the automobile. The R2 statistics for the trip models are TABLE 3. SENSITIVITYOF TRANSIT CHOICETO TRIPMAKERAND TRIP MEASURES Rush-hour,
Variable change
f’U’,)t
Medium to low income Auto-availability index I to 0.5 1 to 2.0 Race: white to non-white Some college to low education Medium to short trip Medium to long trip Typical case
level
work trips
Evening, non-work
WTJS
PU’d
APU’,)
0.247
+0.101
0.056
+0,033
0.232 0.053 0.323 0.197 0.118 0.064 0.146
+ 0.086 - 0.093 +0.177 +o~osl - 0.028 - 0.082 -
0.040 0007 0.062 0.033 0.009 0.023 0.023
+0.017 -0.016 + 0.038 +0.010 -0.014 0.00 -
trips
t P(T,) refers to the probability of transit choice for the case defined by the change denoted in column 1 and the typical case specification for the remaining variables. $ AP(T,) indicates the variation of predicted transit choice for the “typical case” resulting from the variable change noted in column 1. TABLE 4. TRIP TIME MODELS
Time difference
model
P(T,) = e’l/l + ezl where Tt indicates the transit mode and Zt = -1*21793+0~14279X,+1~02724X,+0~25418X,+1*12037X, -1~06503X,-0~92507X,+0~50218X,+0~19846X,+4~55603X,, -17~O485OX~,+O~82228X,~+O~936l3X~~~O~59O85X~~+3~43l99X~~1 i? = 0.182 Time ratio model P(TJ = e’l/l + e’J where I, =-3~13110+0~15439X,+1~01320X,+0~20605X,+1~07326X, -1~11197X,-0~98602X,+0~45316X~+0~18998X,f6~17131X,, - 13~31660X,,+O~81747X,9+O~92337X,3+O~87762X,, + 1.O2658X,8 + 0.87438 X,,’ i?e = 0.147 The Xi are as defined in Table 1.
better than the corresponding value for the socioeconomic model (i.e. O-182 and 0.147 VS. 0.138). This indicates that by introducing a measure of the characteristics of the competing modes, a better “fit” of the data is obtained. Lave (1969) discussed the problem of using time differences vs. ratios and concluded that the former approach appeared more valid by the nature of his R2 statistics. The results obtained here support that conclusion and, accordingly, the time difference model can be recommended. The real problem encountered is that we do not know how tripmakers perceive the relative times of competing modes and make value judgements. The concept of the modal preference function is aimed at coping with this question and is discussed subsequently. QUANTIFICATION
perceived
OF PERCEIVFD
MODAL
ATTRIBUTES
of utility theory (Samuelson, 1961; Fishburn, 1967) are employed to represent modal characteristics in this model. The modal preference rating is defined as
Concepts
Modal demand:
an index mode on ideal and assuming
299
model
which specifies the tripmaker’s perception of the service rendered by any particular a zero to one continuum, where zero denotes characteristics farthest from the one relates to an ideal. The modal preference rating (MPR) is formulated by additivity, i.e. first estimate a comparative value (between zero and one) for each
__----_--
I -41;
I.
_--
_---
__----
I -30 Time
FIG.
a user perception
I -20 difference
! ai) (auto
‘; time-
transit
I 10
I c 20
time)
Time difference models. (Note: The horizontal prediction
lines denote the socioeconomic for each typical case.)
model’s
I
FIG.
2. Time ratio models.
(Note: The horizontal lines denote prediction for each typical case.)
the socioeconomic
model’s
influential modal characteristic and then weight them in view of their relative importance. Finally, the values of each factor for a given mode are combined using the additive model to give a total utility index. A modal preference function (MPF) is then specified to express a tripmaker’s attitude toward competing modes in such a way that a forecast of usage for
300
MICHAEL J. DEMETSKYand
LESTERA. HOEL
any mode will be based on the user’s subjective judgements of the mode in question and all other competing modes. The measurement of individual preference ratings for modes of transportation is similar to the psychophysical problem which is concerned with the association between a stimulus series and the discriminal processes with which an individual differentiates the stimuli (Thurstone, 1959). Psychological scaling methods are the basic procedure of measurement of attributes wherein each attribute corresponds to an axis of an n-dimensional space and, accordingly, the value judgements of all attributes define a point in that space compatible with our definition of the MPR in the additive utility sense. Scaling techniques, therefore, afford a method by which an MPR can be derived from attitude surveys which relate the tripmaker’s perceptions of a mode’s characteristic to a real number scale. Respondents with similar socioeconomic backgrounds can be presented with the various descriptive factors of each mode competing for a specified trip type and asked to rank each factor for every mode. At this early stage of investigation and use of the MPR, a detailed analysis via scaling techniques is not feasible. An implicit alternative approach based on the independence assumption and the theory of additve utility obtains a measure of the MPR directly without considering each characteristic component of the MPR separately. For example, in recent information secured by attitude surveys such as the “National Survey of Transportation Attitudes and Behavior” (NCHRP, 1968) respondents were asked to consider an ideal method of transportation for work, shopping and social trips, rating each mode on a 9 point scale (with 9 representing the most ideal mode). The results of this survey are used with the modification that a 10 point scale is employed for work and non-work trips. Average values are shown in Table 5. The survey data used to calibrate the model include a different array of modes from those indicated in Table 5. Consequently, the above values have been taken as a basis for developing base preference ratings (BPR) for the new array of modes as shown in Table 6. TABLE 5. PREFERENCERATINGSDERIVEDFROM “NATIONAL SURVEY OF TRANSPORTATION ATTITUDESAND BEHAVIOR” Ratings Mode Automobile BUS Subway Railroad
Work trips
Other trips
94 4.5 4.3 4.3
9.6 4.0 3.3 2.8
TABLE 6. BASE PREFERENCERATINGS Mode Auto driver Auto passenger Railrdad _ Mass-transit Taxi
Work trips 9.4 8.0 4.3 4.4 6.0
(BPR) Other trips 9.6 8.2 2.8 3.7 6.5
These preference ratings are formulated to reflect average values for each mode irrespective of the conditions surrounding any particular trip. The next step in the development of the MPR is, therefore, a demonstration of a trip-sensitive preference rating scheme. This trip-sensitive preference rating derives certain information from the trip survey, the
Modal demand:
a user perception
model
301
average ratings shown in Table 6, and measures of the sensitivity of travelers to various modal attributes reported by the University of Pennsylvania (Ackoff, 1965) which are given in Table 7. For purposes of this study the MPR is assumed to be composed to the tripmaker’s perceptions of the following trip related modal characteristics: time, cost, convenience, comfort and others. Using the information in Table 7 the base ratings can be TABLE
~.RELATIVESENSITIVITIESOFTHEMODALPREFERENCE TO VARIOUS MODAL ATTRIBUTES?
Factor
RATING
Work trips
Other trips
0.300 0.136 0,136 0.210 0.217
0.106 0.097 0.201 0,325 0.272
Time cost Convenience Comfort Other
(MPR)
t Obtained from Ackoff (1965).
broken down into the five component parts. The travel survey contains information that is used to imply surrogate measures for the time, cost and convenience portions of the MPR. The time component is represented by either the highway travel time (Tl) or transit travel time which includes access, waiting and transfer time in addition to the period of vehicular travel time (T2); the hourly parking fee measures the automobile cost (CP) while its counterport is the transit fare (TF); and finally convenience (BW) is described by the sum of the blocks walked at the origin (BO) and destination (BD) ends of all trips. Mean values for these time, cost and convenience measures are calculated from the trip file for a stratification of three trip length levels, three trip time classes and two trip purposes. The differences between the mean attribute values and the values for a particular trip serve to modify the MPR. The following example for work trips by transit passengers typifies the strategy by which the MPR of any mode can be adjusted according to the particular information at hand. Table 6 gives the base preference rating (BPR) for mass-transit work trips as 4.4, which can be decomposed proportionally into the component values shown in Table 8. TABLE
8.
DECOMPOSITION OF MPR FOR MASS-TRANSIT WORK INTOCOMPONENTVALUES
Component
Value
Time cost Convenience Comfort Others Total
1.32 0.60 0.60 0.93 0.95 4.40
Scanning the travel data, average values for the modal attributes for the first three components of the preference rating are obtained: time : (E)l,l,p, cost: (rn]l$$, -convenience : (BO + BD),,, where the above are stratified according categories (I) and two trip purposes (p>.
TRIPS
indicating
measures
average travel time average fare average blocks walked
= @ml,,,p, to three trip length
levels (I), three time of day
302
MICHAEL J. DEMETSKY and LESTERA. HOEL
Using the additive utility model, convenience components as follows:
the preference
rating
u transit,I,l,~ = al,I,l,p V,,l$,p + %U,t,p v2J,f,p +
derives
a3,Z,f,p VU,@
from
time,
+ c
cost and
(6)
where u trannit,l,f.p = base preference ai,l~,~ = weighting
rating for transit
factor for characteristic
V.3UP = value of characteristic
trips i
j
C = constant value, accounting for comfort and other components of the MPR The BPR or average preference rating for any sample population is defined to be equivalent to the respective modal value given in Table 6 (e.g. UtransitJJ,r = 4.4). It follows that this base preference rating is composed of average components values, i.e.
is equal to the jth component’s value as given in Table 8. In order for the preceding to be possible, it follows that in the base preference rating l$u,l, must correspond to the respective average modal characteristics of the transportation system as follows :
The weighting factors must now be defined so that the base preference rating will correspond to the above criteria for any data set. This is accomplished with the following specification of weighting factors : al,lc,p = 1.32/(%,p a2,i~,p = O.W7%,~,,
a 3,1,4p =
@WB
(8)
-1 W,,,
After the weighting factors are obtained, the MPR associated with any transit trip can be estimated from the characteristics of that particular journey. This is accomplished by now defining the dynamic preference rating (DYPR) as u transit,l,l,p - ~ttransit.l,l,p - AUtransit.l&p or for transit
(9)
work trips u transitJ#,l = 4.4 + %,Z,Ll(m-
7-2,) + a,,,,@%
WJ + a,,&VL
SWi)
(10)
where i indicates the ith observation. Now, a variable, W,, is introduced and is designated as the modal preference function (MPF). This variable expresses the tripmaker’s perception of preferences toward alternative transport modes so that the forecast of modal choice is based on the public’s attitude toward the mode in question as well as the competing modes. Since there was no priority
Modal demand:
a user perception
for assigning the mathematical form of the MPF, tested, a multiplicative-ratio and an additive ratio:
w, = u,
303
model
two elementary
models
I
were initially
(11)
f=l i#k
(12) where U, refers to the mode of interest and Uj refers to the competing modes. Both models gave similar forecasts; however, the R2 statistic was slightly higher for the model using the multiplicative-ratio form of the MPF. Thus, for the purposes of this study, the subsequent discussion describes models which include the MPF form as given by equation (11). Table 9 indicates values for this MPF using the BPR values given in Table 6. TABLE 9. MODAL PREFERENCE FUNCTION USING THE BASEPREFERENCERATINGS
Mode
Work trips
Auto driver Auto passenger Railroad Transit Taxi
Non-work
0.01035 0.00750 0.00216 0.00227 0.00422
PREFERENCE
VALUES
trips
0.01789 0.01268 0.00148 0.00258 oGI797 MODELS
The concepts of decision theory described in the previous section are derived from prescriptive theories which hold that the tripmaker makes his travel choices in a descending however, order from the most preferred down. A household is somewhat constrained, by its resources (automobile(s), income, time, etc.) for an “optimal” allocation to each trip. In this study, therefore, information on perceptions of modal characteristics is derived by way of the concepts of prescriptive decision theory in the form of the modal preference rating and then a modal preference function is utilized to combine the preference ratings into a single index. Two sets of models are examined that employ the concept of the modal preference function. The first utilizes the base preference rating (BPR) which indicates similar values for all trips on each mode and are equivalent to the assumed population averages given in Table 6. For example, all transit work trips signify a MPR value of 4.4 (Table 6) or an MPF value of 0.00227 (Table 9). The latter strategy exhibits the trip sensitivity developed in equations (9) and (10) and is referred to as the dynamic preference rating (DYPR). The resulting two types of preference models are shown in Table 10. As in the discussion of the trip time models, the socioeconomic and trip measures are held constant for typical cases and the values of the preference function are altered. Because the MPF values in the BPR models are similar for all trips on a given mode for a designated purpose, there is an exceptionally high correlation between the dependent variable and the independent variable expressing the MPF. This fact is shown by the R2 values for the preference models in Table 10. Thus, the BPR model is somewhat unrealistic due to the unnatural measure of user perceptions. On the other hand, the DYPR models exhibit less statistical significance than the BPR model but relate closer to each particular trip. The BPR model is actually similar to models which reflect degrees of a variable by a set of increasing integer values.
304
MICHAELJ. DEMETSKYand LESTERA. HOEL
In other words, the BPR as used here is a type of dummy variable. The BPR models are incorporated to establish a basis for the DYPR model with which the latter can be compared to indicate the effects of the trip sensitivity. TABLE 10. PREFERENCEMODELS Base perference
rating (BPR) model P(T,)
= e”/l +ert
where Tt indicates the transit mode I, = 22.9844 - 2.56711 X, - 2,04208X, + 1.59309X,, - 1.9425 1XI, -l~94714X,,+1~40565XI,+1~26818X~~-5412~76X~s3 RZ = 0.997 Dynamic preference
rating (D YPR) modeI P(T,)
= tit/l +el’
where It = 0~49234+0~97347X,+0~50846X,-0~30610X,-0~60194X, -O~63019X,+044506X,+24~3936X,,+O~57614XI, +0.53420X1,+0.47721 XI,+0.64432X,,-312*922X,,3 R2 = 0.628 The Xi are as defined in Table 1.
Evening,
non -work
trips
.t e t >r C
0.6-
05
-
a 0.3-
0.2-
O.I----0.001
Preference FIG.
3.
Base
preference
I_ 0.01
O-005
function
values
(BPR) models for the typical cases. (Note: The horizontal socioeconomic model’s prediction for each typical case.)
lines denote the
Figures 3 and 4 are plots of the BPR and DYPR models respectively for typical cases of the auto-transit split along with the corresponding socioeconomic model predictions. The DYPR model appears the more sensitive to wider ranges of MPF values and indicates a significantly higher R2 than the trip time models. Statistical verification of the model, however, is not in itself a sufficient criterion for determining its validity as a forecasting
Modal demand:
a user perception
modal
305
tool. It is also necessary to examine these preference models in view of the apriori theoretical base. A major assumption underlying the development of the modal preference function was that increasing modal patronage corresponds with increasing values of the MPF, ceteris paribus. The preference models dispute such reasoning as they maintain negative
Preference
function
“olues
FIG. 4. Dynamic
preference (DYPR) models for the typical cases. (Note: The horizontal the socioeconomic model’s prediction for each typical case.)
FIG. 5. Dynamic
preference (DYPR) model for auto driver trips. (Note: The horizontal the socioeconomic model’s prediction for each typical case.)
Preference
function
lines denote
values
lines denote
sloping curves. This problem of an inconsistency within the preference model is similar to that encountered in application of the “Abstract Mode Model” (Quandt and Baumol, 1966). In this case the introduction of a new mode, under certain circumstances, led to an increase in travel on some existing modes. Such problems may be inherent in all models which attempt to abstractly quantify modal characteristics. Fundamentally, these modals perform as the data direct and it is, therefore, necessary to closely examine the phenomena being represented and reinterpret the resulting models. For a closer analysis, the MPF formulation of perceived modal attributes allows ease in isolating the measures of the transportation system from the other variables.
306
MICHAELJ. DEMETSKYand LESTERA. HOEL
Similar models which denoted the auto driver mode in the dependent variable are shown in Fig. 5. These curves are consistent with the theoretical development of the MPR and MPF and are utilized to aid in evaluating the preference model. A THEORY
OF
MODAL
CHOICE
BEHAVIOR
If the MPR is designated as a measure of tripmakers’ minimum standards for choosing the transit mode, then, as an individual’s standards for acceptable transit service increase, a higher probability of his selecting the automobile mode over existing transit is a reasonable assumption. Under such circumstances, the negatively sloping curves would correspond to theory. Simultaneously, the positively sloping curves for the automobile mode also uphold the theory since at present there is no better alternative for those who can afford this mode. The preference models have thus given the basis for a theory of modal choice behavior which renders a single model applicable to any number of urban areas. Another important need in the modal split methodology is providing a potential for investigation of the impact of new transit technology (e.g. dial-a-bus, dual-mode vehicles, etc.) on travel demand. The theory of minimum standards for public transportation also satisfies this requirement as is implied in the subsequent interpretation.
Change
1, FIG. 6. General public transportation
Minimum
standards
supply-demand
I”
probablhfv
of
Index
relationships
derived from preference
models.
A series of models, based on home-interview, origin-destination data and an accompanying attitude survey from different urban areas, provide a family of curves, each similar to those shown in Fig. 4. Holding other variables constant, the difference in the probabilities for patronage of public transportation in any two areas is attributed to the variation in the levels of service provided in each case. Accordingly, each curve implies the demand for a given supply of public transportation which can be directly measured via parameters such as connectivity, average travel times, frequency of service, etc. (Morlok, 1968). Figure 6 shows a hypothetical family of curves, corresponding to this approach, where the tradeoff between the expected use of public transportation and changes in levels of service (Si> is explicitly given for a specific tripmaker-trip category and a minimum standards
Modal demand:
a user perception
model
307
index, Ii. These curves can be used directly or extrapolated to predict changes in modal demand resulting from improvements in public transportation. Direct mathematical expressions which are stratified for various tripmaker-trip situations may also be derived from the following functional relationship :
where P,(I,, Sj) = the probability that the tripmaker-trip category Z uses public transportation when a minimum standard’s index, Ii, is indicated and a level of service, Si, defines the supply of public transportation. In addition to providing a generalization for the modal split process, the strategy presented in the prior discussion furnishes a forecasting methodology for areas which have no public transportation today. Thus, if such cities are considering mass transportation for the future, demand analysis can be accomplished by using the models from other urban centers. CONCLUSIONS
The results presented in this paper are significant in the development of a theoretical basis for mathematical representations of the modal choice process. The use of selected socioeconomic tripmaker descriptors and trip type indicators in modal split analysis, whatever level of data aggregation is employed, is relatively clear when compared with the problem of structuring a meaningful representation of the transportation system characteristics. This analysis of various methods for representing modal characteristics in the model with respect to the sensitivity of the forecast, indicates an apparent improvement when measures of user perceptions are utilized. Consequently, a practical supply-demand representation of the modal choice process has evolved which indicates a strategy wherein models calibrated in one urban area may be readily applied to others. Further research is required to ascertain whether the theories derived here do, in fact, eliminate many of the limitations of previous modal split models. REFERENCES ACKOFF R. L. (1965). Individual Preferences of Various Means of Transportation. Interim Report to Highway Research Board on Contract No. HR-8-3, Management Science Center, University of Pennsylvania, Philadelphia, Pennsylvania. BOCK B. C. (1968). Factors influencing modal trip assignment, National Cooperative Highway Research Program Report, No. 57, Highway Research Board, Washington, D.C. DEMETSKYM. J. (1970). An Investigation of the Application of Behavioral Concepts in the Formulation of Areawide Modal Demand Analysis Models. Unpublished Ph.D. Thesis, Department of Civil Engineering, Carnegie-Mellon University. FINNEY D. J. (1952). Probit Analysis. Cambridge University Press, Cambridge. FISHBURNP. C. (1967). Methods of estimating additive utilities. Mgmt Sci. 13, 425-453. GOLDBERGERA. S. (1964). Econometric Theory, pp. 248-252. John Wiley, New York. HOEL L. A. and DEMETSKYM. J. (1970). Behavioral Considerations in Modal Split Analysis, Paper presented at the 37th National Meeting, Operations Research Society of America, Washington, D.C. JOHNSTONJ. (1963). Econometric Methods, p. 224. McGraw-Hill, New York. LAVE C. A. (1969). A behavioral approach to modal split forecasting. Tramp Res. 3, 463-480. LISCO T. E. (1967). The Value of Commuters’ Travel Time-A Study of Urban Transportation. Unpublished. Docioral Dissertation, Department of Economics, University of Chicago. Lrsco T. E. (1969). Northwest Chicago Corridor Modal Solit Project. Proiect _ Statement . Chicago Area Transpoitation Study, Chicago, Illinois. MORGANJ. N. (1964). A Note on the Interpretation of Multiple Regression Using Dummy Variables. Survey Research Center, Institute for Social Research, University of Michigan. MORLOK E. K. (1968). The comparison of transport technologies. Highway Res. Rec. 238, Highway Research Board, Washington, D.C.
308
MICHAELJ. DEMETSKYand LESTER A. HOEL
National Cooperatiue Highway Research Program (1968). National Survey of Transportation Attitudes and Behavior, Phase 1 Summary Report, Report No. 49, Highway Research Board, Washington, D.C., pp. 12-15. QUANDT R. E. and BAUMOLW. (1966). The abstract mode model: theory and measurement, J. Reg. Sci. 13-26. SAMUEL~ONP. A. (1961). Foundations of Economic Analysis. Harvard University Press, Cambridge, Massachusetts. THUR~TONEL. L. (1959). The Measurement of Values. University of Chicago Press, Chicago, Illinois. WARNER S. L. (1962). Stochastic Choice of Mode in Urban Travel: A Study in Binary Choice. Northwestern University Press, Evanston, Illinois.
Vol. 6, pp. 293-308. Pergamon Press 1972. Printed in Great Britain
MODAL
DEMAND:
A USER PERCEPTION
MODEL
MICHAEL J. DEMETSKY University of Virginia and LESTER A. HOEL Carnegie-Mellon (Received
5 May
University, Pittsburgh
1971; in revised form
21 April 1972)
INTRODUCTION IN CONTRAST with prior approaches which, as a rule, relied on aggregated data bases, increased attention is currently being directed toward the analysis of individual and household travel behavior. The resulting mathematical models indicating the modal choice These recent studies indicate decision have accordingly been described as “behavioral”. two fundamental approaches: econometric models (Lisco, 1967; Lave, 1969) which are based upon data from home-interview, origin-destination surveys, and attitudinal studies (Ackoff, 1965; Bock, 1968) which determine by interview those characteristics influencing the mode choice decision. A review of the capabilities and shortcomings of the two approaches for analyzing the mechanism of modal choice with respect to forecasting within the transportation planning process indicates that a more significant modal split methodology may result from a synthesis of the two approaches. Such a strategy, utilizing both origin-destination data and attitudinal survey information in the development of a behavioral modal split model, has been investigated and is introduced in this paper. These findings are derived from a study of areawide behavioral modal split models (Hoe1 and Demetsky, 1970; Demetsky, 1970) which investigated the selection of explanatory variables, the mathematical form of the model (linear vs. S-shape), the level of transport sensitivity required for such models and the potential of these models for studying the impact of new transit technology and policy. The analysis techniques used to accomplish this research included stepwise linear regression, dummy variable techniques, a model derived from probit analysis which uses the logistic function, a dichotomous dependent variable and concepts of utility theory. In specifying the transportation system characteristics in the behavioral model, three distinct methods are evaluated: socioeconomic models based on trip and tripmaker attributes, trip time models which consider the effects of adding a variable which denotes the relative trip times between auto and transit and modal preference models that employ a measure of user perceptions of the modal attributes. MODEL DEVELOPMENT The basic unit in this model is the individual tripmaker. During calibration the dependent variable is designated as an event which indicates a trip either occurring or not occurring on a particular mode. Accordingly, the observed mode choice decision is formulated as one of binary choice in which the dependent variable is dichotomous and a function of 293 13
294
MICHAEL J. DEMETSKYand LESTER A. HOEL
the explanatory variables, such that 1, if the event (Tk) occurs
Wk) i = 0, otherwise
(1)
where Tk indicates the event of a specified trip occurring on mode k and i indicates the ith observation. The most convenient approach to the binary choice problem is the linear regression model (Goldberger, 1964). Once this model is calibrated for P(T,) on several explanatory variables, (X = x1, x2, . . ., x,,,), a value of P(T,) is calculated from the equation. The predicted values of the dependent variable for any specified X are interpreted as an estimate of the conditional probability of Tk, given X (Johnston, 1963). The linear model, however, exhibits potential shortcomings. First, predicted P(T,) values are not necessarily confined to the appropriate interval and may fall either below zero or above one in some cases. This fact is contrary to the definition of a probability function and hence a transformation of the estimates to realistic values is required. The second problem attributed to the linear model is the shape of the curve, as noted by Lisco (1969): “Multiple linear regression analysis is the wrong tool to apply to modal split analysis. The relation between modal choice and the parameters that determine it is not linear, but S-shaped.” Some solutions to the above problem have been demonstrated (Warner, 1962; Lisco, 1967; Lave, 1969) where the basic technique derives from the probit analysis model (Finney, 1952). The model used here follows the development given by Goldberger (1964), but substitutes the logistic function for the standard normal cumulative distribution which typifies the probit model. Ik is defined as a linear function of the regressors: Ik = X’b” and is related to P(T,) as follows: (2) p(T,) = F(zk) where P(T,) = the probability of a specified trip being accomplished via mode k; Ik = a linear function of the independent regression, X’bk = b,k + blk x1 + . . . + bnLkx,. The probit model then assumes
s X’bk
F(I,) = (27r-* _-m e-u’/sdu
(3)
In place of the standard normal function indicated above, the logistic function is employed here (4) The logistic transformation maintains the identity of P(T,) as a function of the bk coefficients which are estimated in a iterative fashion by the maximum likelihood technique (Warner, 1962). The forecast probability, P(Tk), of a specified trip occurring on mode k is thus obtained by substituting equation (4) into the right-hand side of equation (2) (5)
Modal demand: TABLE
Variable X,, r = 1,2, . . . . 16
a user perception
~.INDEPENDENTVARIABLESSELECTED
Value
_____
295
model FORSTUDY
Comments
Description
Xl
1 0
If No. in household Otherwise
= 1,2
X2
1 0
If No. in household Otherwise
= 3
Xl, x2
0
If No. in household24
x3
1 0
If income level 1 Otherwise
rt < $7000
X4
1 0
If income level 2 Otherwise
$7OOOz5Y5 $15,000
x3, x4
0
Income level 3
$15,000< Y
X5
1 0
If work-school Otherwise
X6
I
Auto availability index
X7
1 0
If household Otherwise
X*
1 0
Education Otherwise
level l$
High school or less
X9
1 0
Education Otherwise
level 2
Some college
X,ll
1 0
Education Otherwise
level 3
College degree
x*9 x9, Xl,
0
Education
level 4
Graduate
Xl,
A
Age of tripmaker
Xl,
1
If rush hour trip
trip I _ No. of autos available No. of licensed drivers
head is white
school
7.30 a.m.-9.00 a.m. 4.30 p.m.-6.00 p.m.
0
Otherwise
Xl3
1 0
If non-rush Otherwise
hour day
4% x13
0
If non-rush
hour evening
Xl,
1 0
If trip length level 1 Otherwise
L§j 0.25 miles
x15
1 0
If trip length level 2 Otherwise
0.25
x14, Xl5
0
If trip length level 3
L > 0.75 miles
-L1
Relative travel time
Xi,’ = T,--7-z; T,Pzll
XN2
Average perceived modal attributes
x,,* = w,
XlB3
Trip-sensitive modal attributes
X1tr3=
t Y is defined as the gross annual income per household. $ Education level refers to household head. 5 L indicates airline distance between origin and destination I( Tr = time via auto; r, = time via transit. 7 k indicates the kth mode; i indicates the ith observation.
9.00 a.m.-4.30 p.m. 6.00 p.m.-7.30 a.m.
zonal centroids.
0.75 miles
WtiB
296
MICHAEL J. DEMETSKYand LESTER A. HOEL
Selection of variables
In estimating the models, the stepwise linear regression technique was first employed to select the significant variables and to provide initial values for the bk which were then recalculated by the maximum likelihood technique for the logistic function given in equation (5). A liberal criterion was established for the selection of variables for the model as the minimum reduction in the proportion of the residual sum of squares required for a variable to enter the regression was OWI. The basic array of hypothesized independent variables, of which each particular model represents a subset, are given in Table 1. This set includes 15 primary variables which designate the tripmaker and trip characteristics. Continuous variables are used to specify auto availability and the age of the tripmaker, and dummy variables are employed to indicate classes of the following tripmaker and trip characteristics: household size, income level, educational level of the household head, time of the day and trip length. The underlying assumption in this specification of input variables is that tripmakers behave similarly within specific socioeconomic classes with respect to certain trip types. Another important quality of a model using dummy variables is that the linearity assumption, critical in the stepwise regression phase of the analysis, is relaxed. This is due to the fact the data have more freedom to determine the shape of the relationship between the explanatory variables and the dependent variable, i.e. the slope of the line changes with different cases in a dummy variable class (Morgan, 1964). System attributes are input via Xrec as either trip time measures or the modal preference function (to be discussed later). The data
The trip data used in this study were obtained from the 1967 Home Interview Survey completed by the Southwestern Regional Planning Commission (SPRPC). The information of that survey relevant to a behavioral analysis of mode choice was processed onto a tape, along with travel time information from the SPRPC traffic assignment program. The trip sample consisted of home-based trips which indicated both origin and terminus in Allegheny County, the county consisting of Pittsburgh and the immediate vicinity. The total observations numbered 36,908 interzonal trips since travel times were not available for intrazonal trips. The five mode split
The modal choice models were initially developed with respect to a five mode split, i.e. each model was calibrated five times, with each case characterized by a different dependent variable designation for one of the following modes: (1) auto driver, (2) auto passenger, (3) railroad, (4) transit or (5) taxi. The purpose of this approach was to determine whether a closer differentiation between modes other than the customary auto-transit split can be formulated from origin-destination data. The results were inconclusive in this respect for the following reasons. The railroad and taxi trip proportions of the sample data were very small compared with the other modes (each less than 1 per cent) and gave meaningless models. The auto-passenger models exhibited much lower R2 statistics than did the auto driver and transit models. This observation is attributed to the data base in that no distinct class of auto-passenger types is indicated for the study area and there was little correlation between the explanatory variables and auto-passenger trips. The models are, therefore, presented in the usual form, a dichotomy between automobile and transit trips. SOCIOECONOMIC
MODELS
Modelsreferred to as socioeconomic models are based purely on user and trip characteristics without considering any measure of the transportation alternatives. A model consisting
Modal demand:
a user perception
model
297
of nine independent variables was obtained as shown in Table 2 and can be interpreted to show the sensitivity of transit choice to the significant tripmaker and trip measures. This sensitivity analysis if facilitated by defining two typical cases of travel sitautions in terms of specific values for the explanatory variables.? Case A: Rush-hour, work trips (X5 = 1, X,, = 1, X,, = 0). The remaining primary variables are : X,=0,&= 1, a household size of 3 X,=0,X,= 1, a medium income level x,= 1, automobile availability index of 1 x,= 1, white household X, = 0, X, = 1, X,,, = 0, some college for household head 38-year-old tripmaker X,, = 38, X14=o,X15= 1, a medium trip length Case B: Evening, non-w,ork trips (X5 = 0, A’,, = 0, X,, = 0). The other variables are specified as in case A. The forecasted values of the probability of transit usage, P(T), given by the model shown in Table 2 for the variable values describing the typical travel cases A and B are given in Table 3 as 0.146 and 0.023 respectively. Table 3 then indicates how changes in each of the TABLE 2. LOGIT-SOCIOECONOMIC MODEL P(T,) = er’/l + e’I
where Tt indicates the transit mode and I, =-2~62702+0~86050X,+1~16002X,-1~16136X,-1~02719X, +0.42545X, +0~89312X,,+0~98226XI,+0~64989X,,+0~93769X,, i? = 0.138 The Xi are as defined in Table 1. The corrected coefficient of determination R2 in the above and subsequent models is derived similar to the corresponding statistic in multiple
regression analysis (Goldberger, 1964; Lave, 1969). significant variables affect the socioeconomic model’s prediction of transit choice. If a tripmaker were chosen at random, the probability of his using the transit mode would correspond to the proportion of the sample using transit, O-141. Table 3, therefore, gives an explicit example of how the behavioral model accounts for the variance of expected transit usage over a wide range of travel situations by various socioeconomic groups. TRIP
TIME
MODELS
The two models shown in Table 4 utilize time difference and time ratio measures respectively to indicate the characteristics of the auto and transit modes. The response of the socioeconomic model toward various user and trip types has already been shown; thus, similar sensitivity is assumed for the trip time models. Relationships between transit choice and intermodal travel time comparisons are shown in Figures 1 and 2 where all tripmaker and trip characteristics are held constant (per the typical case defined earlier) and only X181, the trip time measure varies. The lower points on all curves in Figs. 1 and 2 correspond closely to the socioeconomic model’s predictions, implying a poor competitive state for the transit service offered in the t All of the original variables from Table 1 are included in these specifications of the typical cases even though some have not entered this particular socioeconomic model. Such a generalization is warranted in order to provide a basis to which all models in this paper can be associated.
MICHAEL J. DEMETSKY and LESTERA. HOEL
298
study area. The trip time models do, however, indicate a more favorable response to transit as its trip time approaches that of the automobile. The R2 statistics for the trip models are TABLE 3. SENSITIVITYOF TRANSIT CHOICETO TRIPMAKERAND TRIP MEASURES Rush-hour,
Variable change
f’U’,)t
Medium to low income Auto-availability index I to 0.5 1 to 2.0 Race: white to non-white Some college to low education Medium to short trip Medium to long trip Typical case
level
work trips
Evening, non-work
WTJS
PU’d
APU’,)
0.247
+0.101
0.056
+0,033
0.232 0.053 0.323 0.197 0.118 0.064 0.146
+ 0.086 - 0.093 +0.177 +o~osl - 0.028 - 0.082 -
0.040 0007 0.062 0.033 0.009 0.023 0.023
+0.017 -0.016 + 0.038 +0.010 -0.014 0.00 -
trips
t P(T,) refers to the probability of transit choice for the case defined by the change denoted in column 1 and the typical case specification for the remaining variables. $ AP(T,) indicates the variation of predicted transit choice for the “typical case” resulting from the variable change noted in column 1. TABLE 4. TRIP TIME MODELS
Time difference
model
P(T,) = e’l/l + ezl where Tt indicates the transit mode and Zt = -1*21793+0~14279X,+1~02724X,+0~25418X,+1*12037X, -1~06503X,-0~92507X,+0~50218X,+0~19846X,+4~55603X,, -17~O485OX~,+O~82228X,~+O~936l3X~~~O~59O85X~~+3~43l99X~~1 i? = 0.182 Time ratio model P(TJ = e’l/l + e’J where I, =-3~13110+0~15439X,+1~01320X,+0~20605X,+1~07326X, -1~11197X,-0~98602X,+0~45316X~+0~18998X,f6~17131X,, - 13~31660X,,+O~81747X,9+O~92337X,3+O~87762X,, + 1.O2658X,8 + 0.87438 X,,’ i?e = 0.147 The Xi are as defined in Table 1.
better than the corresponding value for the socioeconomic model (i.e. O-182 and 0.147 VS. 0.138). This indicates that by introducing a measure of the characteristics of the competing modes, a better “fit” of the data is obtained. Lave (1969) discussed the problem of using time differences vs. ratios and concluded that the former approach appeared more valid by the nature of his R2 statistics. The results obtained here support that conclusion and, accordingly, the time difference model can be recommended. The real problem encountered is that we do not know how tripmakers perceive the relative times of competing modes and make value judgements. The concept of the modal preference function is aimed at coping with this question and is discussed subsequently. QUANTIFICATION
perceived
OF PERCEIVFD
MODAL
ATTRIBUTES
of utility theory (Samuelson, 1961; Fishburn, 1967) are employed to represent modal characteristics in this model. The modal preference rating is defined as
Concepts
Modal demand:
an index mode on ideal and assuming
299
model
which specifies the tripmaker’s perception of the service rendered by any particular a zero to one continuum, where zero denotes characteristics farthest from the one relates to an ideal. The modal preference rating (MPR) is formulated by additivity, i.e. first estimate a comparative value (between zero and one) for each
__----_--
I -41;
I.
_--
_---
__----
I -30 Time
FIG.
a user perception
I -20 difference
! ai) (auto
‘; time-
transit
I 10
I c 20
time)
Time difference models. (Note: The horizontal prediction
lines denote the socioeconomic for each typical case.)
model’s
I
FIG.
2. Time ratio models.
(Note: The horizontal lines denote prediction for each typical case.)
the socioeconomic
model’s
influential modal characteristic and then weight them in view of their relative importance. Finally, the values of each factor for a given mode are combined using the additive model to give a total utility index. A modal preference function (MPF) is then specified to express a tripmaker’s attitude toward competing modes in such a way that a forecast of usage for
300
MICHAEL J. DEMETSKYand
LESTERA. HOEL
any mode will be based on the user’s subjective judgements of the mode in question and all other competing modes. The measurement of individual preference ratings for modes of transportation is similar to the psychophysical problem which is concerned with the association between a stimulus series and the discriminal processes with which an individual differentiates the stimuli (Thurstone, 1959). Psychological scaling methods are the basic procedure of measurement of attributes wherein each attribute corresponds to an axis of an n-dimensional space and, accordingly, the value judgements of all attributes define a point in that space compatible with our definition of the MPR in the additive utility sense. Scaling techniques, therefore, afford a method by which an MPR can be derived from attitude surveys which relate the tripmaker’s perceptions of a mode’s characteristic to a real number scale. Respondents with similar socioeconomic backgrounds can be presented with the various descriptive factors of each mode competing for a specified trip type and asked to rank each factor for every mode. At this early stage of investigation and use of the MPR, a detailed analysis via scaling techniques is not feasible. An implicit alternative approach based on the independence assumption and the theory of additve utility obtains a measure of the MPR directly without considering each characteristic component of the MPR separately. For example, in recent information secured by attitude surveys such as the “National Survey of Transportation Attitudes and Behavior” (NCHRP, 1968) respondents were asked to consider an ideal method of transportation for work, shopping and social trips, rating each mode on a 9 point scale (with 9 representing the most ideal mode). The results of this survey are used with the modification that a 10 point scale is employed for work and non-work trips. Average values are shown in Table 5. The survey data used to calibrate the model include a different array of modes from those indicated in Table 5. Consequently, the above values have been taken as a basis for developing base preference ratings (BPR) for the new array of modes as shown in Table 6. TABLE 5. PREFERENCERATINGSDERIVEDFROM “NATIONAL SURVEY OF TRANSPORTATION ATTITUDESAND BEHAVIOR” Ratings Mode Automobile BUS Subway Railroad
Work trips
Other trips
94 4.5 4.3 4.3
9.6 4.0 3.3 2.8
TABLE 6. BASE PREFERENCERATINGS Mode Auto driver Auto passenger Railrdad _ Mass-transit Taxi
Work trips 9.4 8.0 4.3 4.4 6.0
(BPR) Other trips 9.6 8.2 2.8 3.7 6.5
These preference ratings are formulated to reflect average values for each mode irrespective of the conditions surrounding any particular trip. The next step in the development of the MPR is, therefore, a demonstration of a trip-sensitive preference rating scheme. This trip-sensitive preference rating derives certain information from the trip survey, the
Modal demand:
a user perception
model
301
average ratings shown in Table 6, and measures of the sensitivity of travelers to various modal attributes reported by the University of Pennsylvania (Ackoff, 1965) which are given in Table 7. For purposes of this study the MPR is assumed to be composed to the tripmaker’s perceptions of the following trip related modal characteristics: time, cost, convenience, comfort and others. Using the information in Table 7 the base ratings can be TABLE
~.RELATIVESENSITIVITIESOFTHEMODALPREFERENCE TO VARIOUS MODAL ATTRIBUTES?
Factor
RATING
Work trips
Other trips
0.300 0.136 0,136 0.210 0.217
0.106 0.097 0.201 0,325 0.272
Time cost Convenience Comfort Other
(MPR)
t Obtained from Ackoff (1965).
broken down into the five component parts. The travel survey contains information that is used to imply surrogate measures for the time, cost and convenience portions of the MPR. The time component is represented by either the highway travel time (Tl) or transit travel time which includes access, waiting and transfer time in addition to the period of vehicular travel time (T2); the hourly parking fee measures the automobile cost (CP) while its counterport is the transit fare (TF); and finally convenience (BW) is described by the sum of the blocks walked at the origin (BO) and destination (BD) ends of all trips. Mean values for these time, cost and convenience measures are calculated from the trip file for a stratification of three trip length levels, three trip time classes and two trip purposes. The differences between the mean attribute values and the values for a particular trip serve to modify the MPR. The following example for work trips by transit passengers typifies the strategy by which the MPR of any mode can be adjusted according to the particular information at hand. Table 6 gives the base preference rating (BPR) for mass-transit work trips as 4.4, which can be decomposed proportionally into the component values shown in Table 8. TABLE
8.
DECOMPOSITION OF MPR FOR MASS-TRANSIT WORK INTOCOMPONENTVALUES
Component
Value
Time cost Convenience Comfort Others Total
1.32 0.60 0.60 0.93 0.95 4.40
Scanning the travel data, average values for the modal attributes for the first three components of the preference rating are obtained: time : (E)l,l,p, cost: (rn]l$$, -convenience : (BO + BD),,, where the above are stratified according categories (I) and two trip purposes (p>.
TRIPS
indicating
measures
average travel time average fare average blocks walked
= @ml,,,p, to three trip length
levels (I), three time of day
302
MICHAEL J. DEMETSKY and LESTERA. HOEL
Using the additive utility model, convenience components as follows:
the preference
rating
u transit,I,l,~ = al,I,l,p V,,l$,p + %U,t,p v2J,f,p +
derives
a3,Z,f,p VU,@
from
time,
+ c
cost and
(6)
where u trannit,l,f.p = base preference ai,l~,~ = weighting
rating for transit
factor for characteristic
V.3UP = value of characteristic
trips i
j
C = constant value, accounting for comfort and other components of the MPR The BPR or average preference rating for any sample population is defined to be equivalent to the respective modal value given in Table 6 (e.g. UtransitJJ,r = 4.4). It follows that this base preference rating is composed of average components values, i.e.
is equal to the jth component’s value as given in Table 8. In order for the preceding to be possible, it follows that in the base preference rating l$u,l, must correspond to the respective average modal characteristics of the transportation system as follows :
The weighting factors must now be defined so that the base preference rating will correspond to the above criteria for any data set. This is accomplished with the following specification of weighting factors : al,lc,p = 1.32/(%,p a2,i~,p = O.W7%,~,,
a 3,1,4p =
@WB
(8)
-1 W,,,
After the weighting factors are obtained, the MPR associated with any transit trip can be estimated from the characteristics of that particular journey. This is accomplished by now defining the dynamic preference rating (DYPR) as u transit,l,l,p - ~ttransit.l,l,p - AUtransit.l&p or for transit
(9)
work trips u transitJ#,l = 4.4 + %,Z,Ll(m-
7-2,) + a,,,,@%
WJ + a,,&VL
SWi)
(10)
where i indicates the ith observation. Now, a variable, W,, is introduced and is designated as the modal preference function (MPF). This variable expresses the tripmaker’s perception of preferences toward alternative transport modes so that the forecast of modal choice is based on the public’s attitude toward the mode in question as well as the competing modes. Since there was no priority
Modal demand:
a user perception
for assigning the mathematical form of the MPF, tested, a multiplicative-ratio and an additive ratio:
w, = u,
303
model
two elementary
models
I
were initially
(11)
f=l i#k
(12) where U, refers to the mode of interest and Uj refers to the competing modes. Both models gave similar forecasts; however, the R2 statistic was slightly higher for the model using the multiplicative-ratio form of the MPF. Thus, for the purposes of this study, the subsequent discussion describes models which include the MPF form as given by equation (11). Table 9 indicates values for this MPF using the BPR values given in Table 6. TABLE 9. MODAL PREFERENCE FUNCTION USING THE BASEPREFERENCERATINGS
Mode
Work trips
Auto driver Auto passenger Railroad Transit Taxi
Non-work
0.01035 0.00750 0.00216 0.00227 0.00422
PREFERENCE
VALUES
trips
0.01789 0.01268 0.00148 0.00258 oGI797 MODELS
The concepts of decision theory described in the previous section are derived from prescriptive theories which hold that the tripmaker makes his travel choices in a descending however, order from the most preferred down. A household is somewhat constrained, by its resources (automobile(s), income, time, etc.) for an “optimal” allocation to each trip. In this study, therefore, information on perceptions of modal characteristics is derived by way of the concepts of prescriptive decision theory in the form of the modal preference rating and then a modal preference function is utilized to combine the preference ratings into a single index. Two sets of models are examined that employ the concept of the modal preference function. The first utilizes the base preference rating (BPR) which indicates similar values for all trips on each mode and are equivalent to the assumed population averages given in Table 6. For example, all transit work trips signify a MPR value of 4.4 (Table 6) or an MPF value of 0.00227 (Table 9). The latter strategy exhibits the trip sensitivity developed in equations (9) and (10) and is referred to as the dynamic preference rating (DYPR). The resulting two types of preference models are shown in Table 10. As in the discussion of the trip time models, the socioeconomic and trip measures are held constant for typical cases and the values of the preference function are altered. Because the MPF values in the BPR models are similar for all trips on a given mode for a designated purpose, there is an exceptionally high correlation between the dependent variable and the independent variable expressing the MPF. This fact is shown by the R2 values for the preference models in Table 10. Thus, the BPR model is somewhat unrealistic due to the unnatural measure of user perceptions. On the other hand, the DYPR models exhibit less statistical significance than the BPR model but relate closer to each particular trip. The BPR model is actually similar to models which reflect degrees of a variable by a set of increasing integer values.
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MICHAELJ. DEMETSKYand LESTERA. HOEL
In other words, the BPR as used here is a type of dummy variable. The BPR models are incorporated to establish a basis for the DYPR model with which the latter can be compared to indicate the effects of the trip sensitivity. TABLE 10. PREFERENCEMODELS Base perference
rating (BPR) model P(T,)
= e”/l +ert
where Tt indicates the transit mode I, = 22.9844 - 2.56711 X, - 2,04208X, + 1.59309X,, - 1.9425 1XI, -l~94714X,,+1~40565XI,+1~26818X~~-5412~76X~s3 RZ = 0.997 Dynamic preference
rating (D YPR) modeI P(T,)
= tit/l +el’
where It = 0~49234+0~97347X,+0~50846X,-0~30610X,-0~60194X, -O~63019X,+044506X,+24~3936X,,+O~57614XI, +0.53420X1,+0.47721 XI,+0.64432X,,-312*922X,,3 R2 = 0.628 The Xi are as defined in Table 1.
Evening,
non -work
trips
.t e t >r C
0.6-
05
-
a 0.3-
0.2-
O.I----0.001
Preference FIG.
3.
Base
preference
I_ 0.01
O-005
function
values
(BPR) models for the typical cases. (Note: The horizontal socioeconomic model’s prediction for each typical case.)
lines denote the
Figures 3 and 4 are plots of the BPR and DYPR models respectively for typical cases of the auto-transit split along with the corresponding socioeconomic model predictions. The DYPR model appears the more sensitive to wider ranges of MPF values and indicates a significantly higher R2 than the trip time models. Statistical verification of the model, however, is not in itself a sufficient criterion for determining its validity as a forecasting
Modal demand:
a user perception
modal
305
tool. It is also necessary to examine these preference models in view of the apriori theoretical base. A major assumption underlying the development of the modal preference function was that increasing modal patronage corresponds with increasing values of the MPF, ceteris paribus. The preference models dispute such reasoning as they maintain negative
Preference
function
“olues
FIG. 4. Dynamic
preference (DYPR) models for the typical cases. (Note: The horizontal the socioeconomic model’s prediction for each typical case.)
FIG. 5. Dynamic
preference (DYPR) model for auto driver trips. (Note: The horizontal the socioeconomic model’s prediction for each typical case.)
Preference
function
lines denote
values
lines denote
sloping curves. This problem of an inconsistency within the preference model is similar to that encountered in application of the “Abstract Mode Model” (Quandt and Baumol, 1966). In this case the introduction of a new mode, under certain circumstances, led to an increase in travel on some existing modes. Such problems may be inherent in all models which attempt to abstractly quantify modal characteristics. Fundamentally, these modals perform as the data direct and it is, therefore, necessary to closely examine the phenomena being represented and reinterpret the resulting models. For a closer analysis, the MPF formulation of perceived modal attributes allows ease in isolating the measures of the transportation system from the other variables.
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MICHAELJ. DEMETSKYand LESTERA. HOEL
Similar models which denoted the auto driver mode in the dependent variable are shown in Fig. 5. These curves are consistent with the theoretical development of the MPR and MPF and are utilized to aid in evaluating the preference model. A THEORY
OF
MODAL
CHOICE
BEHAVIOR
If the MPR is designated as a measure of tripmakers’ minimum standards for choosing the transit mode, then, as an individual’s standards for acceptable transit service increase, a higher probability of his selecting the automobile mode over existing transit is a reasonable assumption. Under such circumstances, the negatively sloping curves would correspond to theory. Simultaneously, the positively sloping curves for the automobile mode also uphold the theory since at present there is no better alternative for those who can afford this mode. The preference models have thus given the basis for a theory of modal choice behavior which renders a single model applicable to any number of urban areas. Another important need in the modal split methodology is providing a potential for investigation of the impact of new transit technology (e.g. dial-a-bus, dual-mode vehicles, etc.) on travel demand. The theory of minimum standards for public transportation also satisfies this requirement as is implied in the subsequent interpretation.
Change
1, FIG. 6. General public transportation
Minimum
standards
supply-demand
I”
probablhfv
of
Index
relationships
derived from preference
models.
A series of models, based on home-interview, origin-destination data and an accompanying attitude survey from different urban areas, provide a family of curves, each similar to those shown in Fig. 4. Holding other variables constant, the difference in the probabilities for patronage of public transportation in any two areas is attributed to the variation in the levels of service provided in each case. Accordingly, each curve implies the demand for a given supply of public transportation which can be directly measured via parameters such as connectivity, average travel times, frequency of service, etc. (Morlok, 1968). Figure 6 shows a hypothetical family of curves, corresponding to this approach, where the tradeoff between the expected use of public transportation and changes in levels of service (Si> is explicitly given for a specific tripmaker-trip category and a minimum standards
Modal demand:
a user perception
model
307
index, Ii. These curves can be used directly or extrapolated to predict changes in modal demand resulting from improvements in public transportation. Direct mathematical expressions which are stratified for various tripmaker-trip situations may also be derived from the following functional relationship :
where P,(I,, Sj) = the probability that the tripmaker-trip category Z uses public transportation when a minimum standard’s index, Ii, is indicated and a level of service, Si, defines the supply of public transportation. In addition to providing a generalization for the modal split process, the strategy presented in the prior discussion furnishes a forecasting methodology for areas which have no public transportation today. Thus, if such cities are considering mass transportation for the future, demand analysis can be accomplished by using the models from other urban centers. CONCLUSIONS
The results presented in this paper are significant in the development of a theoretical basis for mathematical representations of the modal choice process. The use of selected socioeconomic tripmaker descriptors and trip type indicators in modal split analysis, whatever level of data aggregation is employed, is relatively clear when compared with the problem of structuring a meaningful representation of the transportation system characteristics. This analysis of various methods for representing modal characteristics in the model with respect to the sensitivity of the forecast, indicates an apparent improvement when measures of user perceptions are utilized. Consequently, a practical supply-demand representation of the modal choice process has evolved which indicates a strategy wherein models calibrated in one urban area may be readily applied to others. Further research is required to ascertain whether the theories derived here do, in fact, eliminate many of the limitations of previous modal split models. REFERENCES ACKOFF R. L. (1965). Individual Preferences of Various Means of Transportation. Interim Report to Highway Research Board on Contract No. HR-8-3, Management Science Center, University of Pennsylvania, Philadelphia, Pennsylvania. BOCK B. C. (1968). Factors influencing modal trip assignment, National Cooperative Highway Research Program Report, No. 57, Highway Research Board, Washington, D.C. DEMETSKYM. J. (1970). An Investigation of the Application of Behavioral Concepts in the Formulation of Areawide Modal Demand Analysis Models. Unpublished Ph.D. Thesis, Department of Civil Engineering, Carnegie-Mellon University. FINNEY D. J. (1952). Probit Analysis. Cambridge University Press, Cambridge. FISHBURNP. C. (1967). Methods of estimating additive utilities. Mgmt Sci. 13, 425-453. GOLDBERGERA. S. (1964). Econometric Theory, pp. 248-252. John Wiley, New York. HOEL L. A. and DEMETSKYM. J. (1970). Behavioral Considerations in Modal Split Analysis, Paper presented at the 37th National Meeting, Operations Research Society of America, Washington, D.C. JOHNSTONJ. (1963). Econometric Methods, p. 224. McGraw-Hill, New York. LAVE C. A. (1969). A behavioral approach to modal split forecasting. Tramp Res. 3, 463-480. LISCO T. E. (1967). The Value of Commuters’ Travel Time-A Study of Urban Transportation. Unpublished. Docioral Dissertation, Department of Economics, University of Chicago. Lrsco T. E. (1969). Northwest Chicago Corridor Modal Solit Project. Proiect _ Statement . Chicago Area Transpoitation Study, Chicago, Illinois. MORGANJ. N. (1964). A Note on the Interpretation of Multiple Regression Using Dummy Variables. Survey Research Center, Institute for Social Research, University of Michigan. MORLOK E. K. (1968). The comparison of transport technologies. Highway Res. Rec. 238, Highway Research Board, Washington, D.C.
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National Cooperatiue Highway Research Program (1968). National Survey of Transportation Attitudes and Behavior, Phase 1 Summary Report, Report No. 49, Highway Research Board, Washington, D.C., pp. 12-15. QUANDT R. E. and BAUMOLW. (1966). The abstract mode model: theory and measurement, J. Reg. Sci. 13-26. SAMUEL~ONP. A. (1961). Foundations of Economic Analysis. Harvard University Press, Cambridge, Massachusetts. THUR~TONEL. L. (1959). The Measurement of Values. University of Chicago Press, Chicago, Illinois. WARNER S. L. (1962). Stochastic Choice of Mode in Urban Travel: A Study in Binary Choice. Northwestern University Press, Evanston, Illinois.