Dynamic Properties Underlying Shopping Travel Behavior on Non-Workdays : a Panel Data Analysis 利用統計を見る

Original Paper

       ＼

DYNAMIC PROPERTIES UNDERLYING SHOPPING TRAVEL

BEHAVIOR ON NON-WORKDAYS : A PANEL DATA ANALYSIS

（Received on 31， August 1991）

KazuoNISHII

      Abstract     This paper aims to analyze a panel data of shopping travel behaviors focusing on their dynamic properties． While an activity−based panel survey has been conducted once each year for three years since 1989， the panel data sets obtained are composed of the three wave data sets including refreshments in each wave as well as ful1−stayers in the pane1． After the outline of this panel survey is introduced， a panel attrition analysis is introduced from the viewpoint of factors significantly determining participation in the panel survey． Also the causal structure underlying the panel attrition is examined by using a log−linear model． Basic properties related to “dynamics”of travel and activity linkages over time are also examined． The results show that， occupation， car−ownership， and life−cycle stage are classified into a strongly associated group and that there exists in irreversibility in the state transition over time among some of the factors affecting on the shoPPing travel patterns．

1．INTRODUCTION

  Travel behavior analysis has been developing since the 1970’s for the purpose of the better under− standing of various properties underlying travel behavior． The ultimate applications of this analysis include more accurate forecasting of travel demand and effective evaluation of transport policies．   Some researchers have already tried to review previous results in this field obtained prior to the first half of the 1980’s． Their efforts have contribut− ed to the development of the conceptual framework of travel behavior analysis known as the activity− based approach．（See Hanson（1979）， Jones（1983）， Kitamura（1988）， and Kondo（1988）．）   Recently， a dynamic−based approach has been regarded as one of the most exciting new streams of travel behavior analysis． It has been especially in

the spotlight since the Oxford Conference on

“Travel Demand Analysis：activity・based and other new approaches”of 1988． Pas（1990）， as a keynote speaker at this conference， has pointed out that the present stage in travel behavior analysis can be characterized by methodological diversification． He has also suggested that analysts are challenged to make a more productive effort in such a research environment than the expected one in the previous era． It is quite evident in this situation that they have to assess their developed methodologies for both effectiveness in representing Properties of travel behavior and practical apPlicability．   In general the dynamic−based approach is based ＊Department of Civil and Environmental Engineering Yamanashi University Kofu，400， Japan．

一60一

December 1992 on the activity−based approach with the latter foll− owed by the former． The question arises as to why adynamic approach has been developed relating to an activity−based one．   While the previous activity−based approach has been useful for the better understanding of human activity sequences， it has been criticized mainely for its lack of practical apPlicability to transportation policy evaluation． It is required that the activity− based approach should be improved to accurately forecast travel demand as well as to describe travel behavior in detai1． This has motivated analysts to attempt to represent dynamics of travel behavior over time， by incorporating a time dimension into their activity−based models． The dynamic−based approach emphasizes the role of the time・axis， which is needed to identify the decision structure of dynamic travel behavior． This feature therefore allows us to apply those activity−and dynamic−based models to practical issues．   We shall here present the intentions of the panel analysis． While this analysis usually requires the panel data sets defined as those comprising repeated observation of the same individuals or households over time， it is designed to explore travel behavior “dynamics”． It allows us to explicitly analyze dynamic changes in an individual’s travel behavior in relation to those in his／her attributes．   The validity of panel analysis has been addressed through recent projects in the United States and European countries．（See Golob（1990）， Meurs（1989）， and Kitamura（1989）．）Apanel analysis is regarded as a useful tool for identifying dynamic characteris− tics of travel behavior． It is also apPlicable to quantify impacts of socio−demographic changes on trip generation and travel patterns． For example， the effects of an aged society， decreasing household size， and women’s participation in the labor force can be examined． In addition， the economic effects

of transportation facility improvements and

transport−related innovation， such as tele−shoPPing and tele・communication， on travel demand can be evaluated through an empirical application．   In Japan， the use of a panel survey and analysis has rarely been seen． On the other hand， the sequen− tial travel forecasting surveys called person trip surveys have been conducted in several metropoli− tan areas in Japan every ten years since the 1970’s． For instance， the Kei−Han−Shin Person Trip Survey in the Kyoto−Osaka−Kobe metropolitan area was conducted in 1970， 1980， and 1990， respectively． According to the technical reports in this survey， the third of 1990， covering a population of about 16 million in the area， had approximately， a 2．3％ sampling rate， that is about 360，000 individuals were selected． Such a large−scale transport survey is intended for use in the development of comprehen− sive traffic network planning including highways （inter−city freeways）， urban expreessways， and arte− rial in the area． The person trip survey therefore has an advantage in forecasting future travel demand in an aggregate zone level， while it has difficulty in incorporating travel behavioral aspects in a disag− gregate level into the analytical framework．   Compared with the person trip survey， a panel survey may not cover a broader area， yet it requires ahigher sampling rate because it has to take panel attrition and panel bias into consideration． It is also clear that the higher the number of the samples selected， the more detailed the cross multiple− variables included in the panel data that can be examined． There is， however， at least one important problem， that is， how we should determine a reason− able sample size and the time−interval between waves in a panel survey． This is partly influenced by the survey cost and is also related to the purpose of the panel analysis． The usefulness of this type of survey may be therefore guaranteed by satisfying the condition that the spatial and temporal area covered by the panel survey be consistent with the intentions and ultimate goals of the panel analysis and also that the panel respondents be regarded as representatives of the population．

2．OUTLINE OF THE PANEL SURVEY

  It has been a recent trend that the number of large−scale， compound consumer facilities are increasing in the suburbs of metropolitan areas and medium−sized rural cities． As visitors to these facil− ities usually combine their shopping together with other activities， such facilities may be called shop− ping complexes or shopping centers， denoted here as

“SC”．    These shopping facilities can play an important  role in not only daily shoPPing activities but also the travel and activity patterns on non−workdays in medium−sized rural cities in Japan． ln those cities， as mobility in an individual’s travel behavior is often determined by the level of car ownership， an SC is preferable to a central downtown shopping area； the SC having sufficient parking area is easily accessible by car， whereas， traffic congestion cre− ates parking difficulties downtown．   The area under study is Kofu city， a typical mid−sized rural city in Japan． The population in this city is approximately two hundred thousand as of 1990and it is located within the area forming a 130 km circle around the Tokyo metropolitan area． The「 SC surveyed is located in a suburb of this city， that is， a few kilometers from the downtown area． It is composed of a large supermarket， fifty speciality stores selling grourmet groceries， necessities， and clothes， fast food shops， restaurants and a parking area with a capacity of 1000 vehicles． The SC has tended to compete with the department stores and shops in the downtown since it was opened in February of 1989． This occurs despite the fact that difficulty in parking and traffic congestion in the central area has made shop there less attractive． This seems to indicate that there may still be advan− tages in shopping downtown， such as the level of quality and quantity of goods， and the convenience of linking shopping with other activities． It is there− fore an interesting subject for transportation plan− ning in that city to explore ’how visitors to the SC have decided to change their shopPing destination over time．   An activity−based panel survey was begun in the autumn of 1989． The 1，500 questionnaires were distributed to individuals who visited the SC on the survey day． So that the sampling rate per hour could be kept the same rate， the number of distributed questionnaires per hour was assumed to account for about 60％of the total number of vehicles going out of their parking space in the SC in the correspond− ing hour． The sarnpling rate per hour was estimated from the results of a preliminary survey on the SC visitors’departure time distribution． Some basic results from the first and second wave in this panel

surveys have been summarized in the previous

papers．（For example， see Nishii＆Iwamoto（1990） and Nishii（1991）．）    Next， the fundamental procedure of thiS panel survey is here introduced． The survey has been conducted once each year for three years． As it was begun in the autumn of 1989， three waves has been completed by 1991． The first wave in 1989 corre− sponds to the survey in which the questionnaires were distributed only to visitors to the SC as mentioned before． The individuals selected in the

second wave in 1990 include refreshments and

stayers；in this wave， the questionnaires were dis・ tributed as before to individuals who visited the SC in 1990， called refreshments， and mailed to the respondents who had successfully participated in the first wave， called stayers． The third wave in

1991therefore includes refreshments from this

wave， partial−stayers between the second and the third， and full−stayers throughout all three waves． It is therefore noted that this panel survey consists of choice−based sampled individuals， that is， new visi・ tors to the SC in each wave， and partial and full stayer among the surveyed waves．   The items in this panel survey can be divided into two groups：The first comprises the questions com・ mon throughout all waves， such as individual and household attributes， travel and activity patterns on the surveyed day， and shoPPing activity patterns on workdays． The other corresponds to those which can not always be common in these three waves because of differences in the objectives of analysis． For example， questions concerning the effects of the location of the SC and shoPPers’reaction to the SC were asked just in the first wave． Stated preference questions were used in the second wave， and revealed preference questions in the third wave．   As shown in Figure 1， in．the first wave of our panel survey， the number of questionnaires returned totaled 653 for a response rate of 43．5％． In 1990， the second wave of this panel survey was carried out for the respondents in 1989 and we received the answer sheets from 221 individuals． The response rate was thus about 37％． This second wave also included the refreshments of visitors to the SC in 1990． The

一62一

No．43 Table 1． Profile of The Panel Data Sets by Year Surve ear 1989 1990 1991 The total number of individuals 653 323 357 Sex _離le 161 24．7％ 71  22．2％   109  32．8％        22  7．2 Age   Less than 20     20 −30     30 ・40     40 −50     0ver 50 years old  years old  years old  years old   ears old  5 125 249 154 115 0．8％ 72．2％ 61．8％ 19．3％    68  21．3％    70  2L1％ 38．4％   103  32．2％   101  30．496 23、8％    91  28．4％    74  22．396 17．7％    51  15．9％    81  24．4％ ”3 ample 艀2 mple Occupation ‡°鵠。 Life cycle stage G⑩up l Th稔head of the houschokl． Ies5廿1畠n     45yc町301d畠nd■ingtc Group 2  The hロd of‘ho hou3巴hoM・less由■n     45y臼口01d⑰d m訂7ied， no childrcn Gmup 3 M町ied． wth childTen tes・山町t     4yc“01d Gro叩4 G⑩叩5 Gm叩6 Group 7 Grou 8 Ma㎡α1， w“h childm bclw㎝ 5■nd 18yo釦r301d MUTiCt⑪，wid1 childreri ovcr 18 ye“01d τhe h白d of the h‘，useholdρ紺45 ye亀「801d．mo「ri◎d． n㏄hild「稔n Wre h臼d of山e h《川記hold， over 4s ycatS old， and single O伽er8 437  67．6％   200  63．1％    230  70．3％       2 7 10 39 154 254 103 43  7 21 L6％    7   2．2弓6 6．2％    24    7．6％ 24．4％    71  225％ 403％   118   373％ 163％    32   10、1％ 6．8％   20   6．3％ 輻1％    5    1．6％ 33％    39   12．4％ 9  2．7％ 31  9．1％ 61 18．0％ 89 26．2％ 78 23．0％ 19  5．6％ 6  L8％ 46 13．6％ 一3 mple Purchasing Patterns Groceries Groceries＋Others Others 222 340 91 34．0％ 52．4％ 13．9％ 102    31．5％      94   27．7％ 175  54．2％   185  54．6％ 46   14．3％    60  17．7％ Activities ShOPPing Only      368 at SC ShePping＋Window・shopPing I 36 Shopplng＋Eating         50 0ユher      81 58．O％ 21．3％ 7．9％ 12．8％ 167  57．6弓筋   185  53，2％ 82  285％    86  24．7％ 23   8．O％    19   5．4％ 17   5．9％    58  16．7％ 653 wavel 1989  544 wave2 1990  660 wave3 1991 Figure 1． Panel Flow Among Three Waves number of questionnaires returned was 323 so that the response rate is about 20％． In the third wave in 1991，0f 221 questionnaires mailed，153 were retur− ned． This leads to a response rate of 69％and the sample is regarded as a full−stayer’s data set． Also， of the 323 individuals in the refreshments of l990， 150 questionnaires were retufned for a response rate of 46％． The third wave also included 357 individ− uals as the refreshment sample in 1991 which means aresponse rate of 20％．   Table l shows the profiles of the refreshment data sets collected in 1989，1990， and 1991． This table indicates that the profiles of the three wave samples are nearly stable over time；the ratio of women to men remain approximately 3 to 1． Individuals in their 30’s and 40’s comprise about 60％of the shop− pers in the SC， with the remainder either in their 20’ sor over 50 years old． The visitors whose life cycle stages range from the third group to七he fifth group account for 80％in 1989 and about 70％in both 1990 and 1991． The distributions of purchasing patterns and activities at the SC indicate that visitors tend to purchase one or two kinds of goods． Groceries・are regarded as a principal good even to purchasers of multiple． It is also clear from the distribution of activities in the SC that shopping is the predominant activity and a few the secondary activities such as window−shopping， eating， and attendance at the recreational events tend to be linked with this shop− ping aCtiVity．

3．PANEL ATTRITION ANAI．YSIS

While Figure l represents a panel data flow among three waves， it is quite evident that this survey includes panel attrition， which means that individuals dropped out of the panel stream；the attrition rate is 63％between the first and second wave， though it is 31％between the second and third one Also， this rate for refreshments in 1990 corre・ sponds to 54％between the second and third wave． It is noted that this panel survey has a significantly high attrition rate．   There are two questions on panel attrition to be addressed in general． What is the causal structure related to an individual’s participation in or refusal of the following wave survey， and how does such

panel attrition influence sample composition

between waves and biases in the parameter esti− mates of a proposed model ？ While the first question will be herein discussed， to， the latter will be out of the scope of this paper．   SupPose a hypothetical causal structure under一

Latent Factors 11ndi∼6dual ahd 織H6usehold1   『雛面bu飴 oSex oAge eC）ccupation oHou鳴ehold size Psychological refusal tcrparticipate in the sumey （；onvenience． artachrnent to SC Spat韮血condition Mob丑ity】巳vel o】Life cycle stage OAnnual Income 一〇SC・Downtown Distance   e Car Ownership −［   o Number of Drivers   o MOde for a viSit to the SC

・識藩瓢・｛

hopPing Activity        LeV o Parkng Convenience o ShopPing・Activity Convenience oShopPing frequency oShopPing at the SC on non・workdays       per a month ODuration in the SC        eParchase expense Figure．2Hypothetical Causal・Structure underlying Panel        Attrition Behavior lying panel attrition behavior as shown in Figure 2． It is here assumed that the causal structure in which individuals make a decision on either participation ln or refusal of the panel can be explained by the degree of two latent factors；psychological refusal to the panel survey， and the attachment to the SC． This psychological factor is mainly characterized by individual and household attributes， on the other hand， the latter is determined by various viewpoints such as spatial and temporal constraints， mobility， activity contents and evaluation of the SC concern− ing Parking and shoPPing activity conveniences． The parking convenience is here evaluated by the viewpoints comprising waiting time and fee in park・ ing， accessibility to the parking area， and traffic congestion． The shopping activity convenience is on the other hand concerned with variety and amount of goods， price of goods， sales information， attractiveness for compound activities， and possibil・ ity that customers can purchase goods at one place．   Assuming the causal structure in this figure， let us Table．2Testing for independence in individual attributes        between participation and non−participation in the        following wave survey        SC visitors in 1989（653sample）SC visitors in 1990（323sample） 1・di・id・・1・tUib・tes X2 d．f α  Z2 d，f α Sex Age Occupation Household size Life cycle stage Annual income SC ・・ DOwntown      distance Car ownership Number of drivers 0。00 1．46 2．53 11．28＊＊ 7，63 6．63 6．89＊ L24 L28 Mode f6ravisi“o SC1．49 Tオamc convenience ShopPing’Aαivhy       く）n  nlen   Shopping f比quency  per nonworkdays 4．62      in a month

瓢瓢灘6、長83

 inamo爪h Duration in the SC  4．51 PUI℃hase expense   8．48 1 3 2 5 6 5 3 3 3 2 O．OOO O．002 0．004 0．046 0．013 0．013 0．013 0．002 0．002 0．002 6 6 5 8 0．008 O，009 0．007 0．Ol4 0，78 3．54  1．01 4．00 13．28＊＊ 9、80＊ 5．74 156 1．12 1．07 12．49‘−

_{_}

15．92＊＊ 11．50＊ 9．25 3．75 4．66 1 3 2 5 6 5 3 3 3 2 9 9 6 6 5 8 0．002 0．011 0．003 0．012 0．048 0．037 0．020 0．004 0．004 0．004 0．046 0．058 0、038 0．031 0．012 0．015 ＊10％ significant ＊＊5％ significant

一64一

test for independence in those variables between participation in and refusal of the following wave using the X2 values． Table 2 shows the result of testing for independence in 16 variables for visitors to the SC in 1989 and those in 1990． The test statistic X2 is usually apPlied to testing for independence when the number of sample， n， is large：   Consider general measures of association for r× ccontingency tables． The value of x2 is defined as     c  r X2＝ΣΣ｛nlj−riCj／n｝2／（riCj／n）．     i＝ll＝1 where nij；observed frequency in the cell（i， j），   ri， cj；marginal frequency in the row（i）and the column 6）， respectively． As the value of X2 will possess approximately a chi−square distribution， the rejection region for this tasting will be x 2＞x2αwithα％significant level．   This table indicates that the null hypothesis that two direCtions of data classification， that is， to participate in and to refuse at the following wave of the panel， are independent is rejected in some of individual attributes for two kinds of the data sets： In the case of the individuals who visited the SC in 1989（wave 1）， two variables， that mean the house− hold size and the SC−downtown distance be rejected for independence testing． On the other hand， the SC visitors in 1990， that is，323 refreshments sample （wave 2）， has three significant variables；life cycle stage， annual income， shoPPing activity conve− nience， and shopping frequency per non−workdays in

amonth．

  Figure 3 shows the distribution of participation and non−participation by category of those individ− ual attributes． With relation to the household size and life cycle stage， it can be found that， in wave 1， as the number of household size increases， the ratio of participation increases， too and that， in wave 2， the individuals who are classified into the young and aged single households（group l and group 7）tend not to stay in the panel． It is noted that the longer distance between the SC and home， the ratio of participation tend to decrease in the second wave and that， as the shoPPing frequency per non− workdays in a month increases， the participation ratio increases in the second wave． Also， a large difference exists in the participation ratio depend− ing on the evaluation score on shoPPing activity convenience which individual answered their prefer− ences for the SC comparing with those for the downtown shopping area in the second wave questi・ onnalre．   The log−linear model of cross classification tables is apPlied to identifying the causal structure under・ lying a panel attrition behavior． While this model has been introduced in the text of in Fienberg（1980） and Goodman（1973）in detai1， it aims to obtain a description of the causal relationships among cate− gorical factors with the cross classification tables by forming a model for the data or by testing and ordering the importance of the interactions between factors．   The table used for the causal analysis is defined in terms of the following five categorical variables：   Participation（P），   Life cycle stage（L），   Shopping frequency（F），   Transportation convenience（T），   ShoPPing activity convenience（A）， where the letters in the parenthesis will be used t refer to the variables． In selecting these variables in the causal model， the result from testing for in− dependence mentioned before was taken into consid− eration． The categories of these variables shown in Table 3 are developed by examining the cell fre− quencies of the five way table and its marginal tables， to avoid cells with extremely small number of observations．   Causal relationships among these variables are examined by applying alternative models represent・ ing different causal structure underlying panel attri− tion behavior． The types of models used here corre− spond to the three−tier， four−tier， and five tier types： The three−tier model has two hierarchical structure of interactions between variables， the four tier model does three hierarchies， and the five tier hav− ing four hierarchies corresponds to a linear models． Each． type of causal models is created by、the combi− nation of the primordial， intermediate and final variables． As the life cycle stage（L）is here regarded as a primordial variable in the causal structure and the participation（P）as a final choice， the three

0

    wave1 20  40  60  80  1000     wave2   （％） 20  40  60  80  100 Sex       male @      飴male ⑪       1 1 1 Age      Less than 30 years old @         30−40years old @         40−50years old @         over 50 years old ‘       ‘ ‘       1

Occupation Sala亘ed workers

@      Workers who own @       and run busines @      Non−workers ‘       I h       l Household size（person） @      1ess than 2 @       3 @       4 @       5 @       0ver 6 8       9 Life cycle stage Group 1

Gro叩2

Group 3

Gro叩4

Group 5 Group 6 Group 7 The head of the household， less than 45 years old and single The head of血e household，1ess tban 45years old md ma㎡ed， no children Ma㎡ed， with children ！ess th紐 4ye釦rs old Ma㎡ed， with children between sand l 8 years old M釦㎡ed， with children over 18 yeals old The head of dle household，over 45 years old， marTied， no children The head of the kousehold， over 45 years old， and sh191e 1 1 I l         I       I

一圏圏圏vazzzzzza

        ‘       ‖

團圏圏團ZZZIz團國誌國唖

1 1 麗闘Participation

囮Non panicipation

Figure 3a． The ratio of participation in the刷owing wave o価e

      panel survey by category of individual attributes 一 66一

No．43       wave 1

0 20 40 60

111．ll l

80 1000

111

   wave2    （％） 20  40  60  80  100 Annual income（million yen）       less than 4 4−6 6−8 8・10 over 10 1 ‘ 1 ‘ ‘       ：          l

SNIItzzzzz

         I          1 SC−home （listance（㎞） 1‘ 1 ‖ 1 ‘ 1ess血an O．5 0．5・1．5 1．5・3．O over 3．0 Car ownership in a h皿sehold 1ess than 1

2

3

over 4 t 1 ‖ 1          ：

sptlZZZZZZ

         l

ISPtezzzzzzi

         ‘ Number of drivers in a household less than 1       2       3   0ver 4 l l I ‘ l I

囲Participation

i：：1 Non participation

Figure 3b． The ratio of participation in therfollowing wave of the

         survey by category of individual attributes

wave1

20 40 60

80 1000

wave2

20 40 60

80 100

虚票鼎㌫6五‘5智瓢臨）

      1ess than 1 1 1 ‘

2

3

4

5

   6 0ver 7

NsPtmPlll

Frequency of SC shoPPing （per non−workdays in a mon血）

0

1

2

3

4

5 ‖       I

xgptpmzzzz

over 6 Duration in the SC（min．）       less than 30       30∼60

60∼90

1       I

E−ptZmp

EPtkgpmzzz

90∼120

over 120 Pur℃hase expense   less than 2，000 Yen     2，000∼4，000Yen     4，000∼ 6，000Yen

ESPtuapm

1       1

IIPtNEIZZIIl

 6，000∼8，000 Yen 8，000−10，000 Yen lO，OOO∼12，000 Yen   over 12，000 Yen

EPtPtltlZZIIIl

（％）

圃Participation

田Non pa】宜cipation

Figure 3c． The ratio of participation in the fbllowing wave of the

      survey by category of individual attributes

一68一

December 1992 Rerative evaluation between SC and Downtown

wave2

Parking

 COnVenlenCe

   score

Shopping

 −Activity

Convenience

   score

60

100（％） Note）These mean the relative evaluation−scores・on parking and shopping conveniences fbr the S C compared with the downtown        囲Participation        囮Non pa㎡cipation

Figure 3d． The ratio of participation in the following wave of the

      survey by category of lndividual attriblltes No．43

Tablle 3． The variables used in log・linear models

Item

Intention for  panel survey   （P） Life cyqle   stage  （L） Shopping frequency   per nonworkdays      ㎞amonth      （F） TranspO血tion ShopPing−Activity and par㎞9 convenlence   （T） convenience （A）

Category

1．panicipation   1．with children  1．≦4．43 1．≦．3．15poillt 1．≦0．44 point 2．non participation 2．without children 2．＞4．43 2．＞3．15 point 2．＞0．44 p6int

The best 3 tier mode1

       A

d．f』23 GZ＝12．86 AIC＝−33．14

kvel 1；L，F，T，A，LF，LT，LA、，FT，TA Leve12；L，F，T，A，P，LF，LT，LA，Fr，TA，       FP，TP，AP，LFrA

’lhe best 4tier model

A

Level1’LFTLF LTFT

     ，   ，  ，  ，    ，        ， Leve12；L，F，T，A，LF，LT，Fr，FA，TA，LFT Level3；L，F，T，A，P，LF，LT，FT，FA，TA，

      AP，LFrA

d．f』24 G㌔8．35 AIC＝−39．65

L

The best 5tier model

A

F

T

P

d．f…＝30 G2」48．95 AIC＝一 1 1．05 Level 1；L，A，LA L嬬ve12；L，A，F，LA，AF

Leve13；L，A，F，T，LA，AF，FT，LAF

Level4；L，A，F，T，P，LA，AF，FT，TP

      LAF，LFrA

Figure 4． Results of log linear models

remained variables rnade alternative structures．  Figure 4 shows the results of the log linear models proposed here with their goodness of fit statistics and degrees of freedom． While likelihood ratio X2 values called G2・values and Akaike’s information criterion（AIC）can express the goodness of fit statis− tics， these indices are defined as follows：       I J K  G2＝2ΣΣΣn耽lo9（n壌／μゼゴh），      i＝1j＝1k＝l  AIC＝G2−2（d．f）， where n融：observed frequency in the cell（i， j， k），  μ∠ゴ々：expected frequency in the cell（i， j， k）， and d．f：degree of freedom．

一70一

  This figure indicates that these three models exhibit substantially better fits than other typed models． In the three tier mode1， it is noted that two qualitative factors such as transportation（T）and

shopping activity convenience（A）and shopping

frequency（F）are put their positions in the same leve1． On the other hand， there are a slight difference in the causal level of shoPPing activity convenience （A）for other two typed models． These similar levels of goodness of fit shown by these three different models may suggest the presence of more than one causal structure underlying Panel attrition behavior．

  4．RELEVANCE AND IRREVERSIBILITY

     AS DYNAMIC PROPERTIES

  Since a panel analysis usually requires the data sets comprising repeated observation of the same individuals or households over time， it intends to explore travel behavior“dynamics”． This analysis can thus deal with longitudinal data concerning both individuals’attributes and their travel behav− ior patterns． This enables us to explicitly analyze dynamic changes in individual’s travel behavior in relation to those in his／her attributes． Those dynamics can be classified into the following types； relevance， regularity， and stability． As they are

concemed with the state−transition patterns

between waves in a panel survey， they may be called the state−dependency among waves．   When focusing on the factors affecting the deci− sion structure underlying travel behavior， a pan宇l analysis can identify the causality among them over time． Thus the analyst may challenge to develop a model for representing dynamic responses on travel

behaviors in accuracy． We can also analyze

dynamic effects in relation to decision−making on travel behavior such as， habitual， learning， lagged， and adjusted effects． As Kitamura＆Hoorn（1987） suggested， it is not true that we can assume the spontaneous correspondence of individual’s travel behavior to his／her travel・environments when there exists in the lagged or habitual responses to an environmental change．   The focus of this section is the study of dynamic properties underlying shoPPing activity and travel linkages will be examined empirically focusing oh the relevance and irreversibility of travel and activ一 lty patterns over tlme．   First， focus on a measure of association with the

summary numbers that describe relationship

between two cross−classified variables． Those vari− ables correspond to individual attributes and the indices representing travel and activity patterns such as， temporal and spatial constraints， prism height， shopping frequency， mode for a visit to the SC， activity contents at the SC， duration and pur− chase expense． The relevance in each of those vari− ables between waves are tested with using X 2 values and the Cramer’s values（Cr）which can be defined as Cr＝ X2／N／min［（r−1），（c−1）］．   Table 4 shows the results of testing for relevance in variables between two waves；the first and sec− ond waves， and the second and third ones． This table indicates that the null hypothesis that the two direc− tions of data classification are independent is reject・ ed in any case of variables in two waves． According to the results of measurement of association by the Cramer’s coefficient， age， occupation， car owner− ship， and life cycle stage are classified to a strongly associated group． On the other hand， variables such as shopping frequency， duration time， purchasing goods and expenses belong to the weakly associated group．   Finally， let us discuss irreversibility as one of dynamic properties underlying shopping travel and activity behaviors． Figure 5 shows the example of dynamic changes in mobility level in relation to the individual’s state transition over time．1

jitamura

and van der Hoorn（1987）denoted such an individ− ual’s response contemporaneous Markov transition： This response pattern is obtained under the condi− tions such as， no time lagged， reversible response， and stationary behavior．   It is important to clarify whether dynamics in the variables determining travel and activity behaviors Can be characterized by the Markovian pattern or not． If there exists in the irreversible response against change in the socio−economic variables over time， it implies that we should require an analytical

framework for representing a dynamic mechanism

Table 4． Testing f（）r independence in variables between waves

wavel∼2

wave2∼3

X2

d．f

Cr

X2

d．f

Cr

Life cycle stage

Household size

588．192＊＊ 482．166＊＊

36

25

0．52424 0．45274 840．309＊＊ 646．006＊＊

36

25

0．58355 0．45018     Age

Occupation

Annual income

Number of

Non−wo】rk days 539．815＊＊ 269．289＊＊ 104．207＊＊ 152．502＊＊

16

4

16

25

0．64264 0．62335 0．15600 0．15886 1170．960＊＊ 352．404＊＊ 269．809＊＊

16

4

25

0．98566 0，62483 0．19135

Car ownership

Number of drivers 555．133＊＊ 301．230＊＊

16

9

0．64550 0．46920 715．949＊＊ 486．234＊＊

16

9

0．60469 0．55317 Starting time in the total available time Ending time in the total availble time   Prism height 15．601 42．001＊ 71．155＊

16

25

49

0．02167 0．04616 0．05711 38．905＊＊ 94．151＊＊ 106．165＊＊

9

25

49

0．04857 0．07026 0．05745

§：：麟瓢蒜555・18＊＊

Mode for a visit to theSC S5．792＊＊   PurPose of activities  8．565＊＊   Duration in the SC   29．893＊   Purchasing patterns l．655＊＊   Purchase expense    37．072

16

1  1

16

 1

25

0．07201 0．36705 0．04199 0．03645 0．00824 0．03965 88．935＊＊ 75．291＊＊ 12．616＊＊ 44．854＊＊ 10．295＊＊ 63．382＊＊

16

4

1

16

1

25

0．07998 0．16227 0．04381 0．03962 0．03664 0．04712 ＊ 5％significant ＊＊’_{P％significant} bO °ξL 合 傷 ℃ む

8

呂 巴 錫 3 2 1 0 −1 −2 −3 Car holding Non car holding Wave 1 Car holding Non car holding Wave 2 Figure 5． Example of dynamic changes in mobility level in       relation to the individua1’s state transition

一72一

December 1992 ＋1． {0． @ 0 ￨0． ￨1． Wave l      Wave2 ＋1．0 ＋0．5 0   Car ownership；   Wave 1！Wave2 −O・ Less than average   ／Less than average −◆−Less than ave了age   ／Greater than average −｛■卜Greater than average   ／Lcss than average −O−Greater than average   ！Greater than average Average Wave11．763      Wave21．805   Car ownership；   Wave2！Wave3 →コトLess than average   ILess than average −●−Less than average   ／Greater than average −｛■−Greater than average   ／Less than average ＜》−Greater than average   ／Greater than average Average Wave21．780      Wave31．812 ＋1． 唱 0 0 む o−0． 一1． 一〇．5 ．1．0        Wave2       Wave3 Figure 6． Irreversibility of changes in shopPing frequency        by transition of car ownership level ゜’一一一’一一一一一一一一一一一．一。 Wavc 1 Wave2  Numbcr of drivers；  Wave 1ハVave2 一仁卜】L∋ss than average   ／Less than average −÷ Less than average   ／Greater than average H■トGrcater than average   刀已∋ss than average ＜》−Greater than average   ／Greatcr than average Average Wavel L944      Wave21．991 ＋1．0 ¥〇5  0 ￨05 ￨LO Wave2       Wave3  Number of drivers；   Wave2！Wave3 一ロトLess than average   lLess than average ◆ Less than average   ／Greate「than average ■個卜Greater than average   ／Lcss than average ■○ Greater than average   ／Greater than average Average Wavc22．047      Wavc32．034 Figure 7． Irreversibility of changes in shopping frequency        by transition of No． of drivers leve1 ＋1． {0． @ 0 ￨0． ￨1． Wave l      Wave2 ＋1．0 ＋O．5 0 ・O．5 一1．0 o”一’一“一一一・一一一一一…一一・一一…−o c｝一一一一一一一一一．． Wave2 Wave3 Non−work days in a month； Wave 1／Wave2 −C｝一 Less than average   ／Less than average −●−Less than average   ／Greater than average −■トGreater than average   ／Less than average −0声Greater than average   ！Greater than average Average Wave15．448      Wave25．703 Non−work days in a month；  ave2／Wave3 −【断Less than average   ／Less than average −● 】しess than average   ／Greater than average −■トGrcater than average   ／Less than average −◎pGreater than average   ／Greater than average Averag9 Wave25．716      Wave36．011 Figure 8． Irreversibility of changes in shoPPing frequency        by transition of No． of Non−work days level of travel behavior．   Figure 6 to Figure 8 show the shopping frequency

on non−workdays in a month by wave against

changes in car ownership， number of drivers， and non−workdays． Figure g also shows the duration time at the SC by wave against changes in shopping frequency． These shopping frequencies and the dura− tion time are normalized in these figures by taking the difference from the sample−wide mean． These figures indicate that the response patterns are by no means close to the idealized Markovian patterns：It is noted that the pattern of dynamic change in the relation between shopping frequency and the num一 ＋10 8＋5 ．H ・8 § △ 0 一5 一10 Wave 1 Wave2  Frequency of shopPing； Wave 1！Wave2 −《コ1−Less than average   ／Les⑨than average −●−Less than average   ／Greater than average −■トGreater than average   ／Less than average −◎−GTeater than average   ／Greatcr than average Average Wave13．693      Wave24．120 冒

o

＋10 8＋5 旦

80

一5 一10 Wave2 Wave3  F爬quency of shoPPing； Wave2！Wave3 −cr Less than average   lLess than average −● Less thatt average   ／Greater than average →■トGreater than average   ！Less than average −o・Greater than average   ／Greater than average Average Wave24．322      Wave34．158 Figure 9． Irreversibility of changes in Duration by transi・        tion of ShoPPing frequency level ber of non−workdays in the period from the second to third wave shown in Figure 8 is exceptionally similar to that in the Markovian transition in Figure 5．On the other hand， it is found from Figure 6 that， the state−transition patterns in car ownership level in both the first to the second and the second to third

wave evolved the different types of dynamic

changes in shopping frequency over time． It is also evident from Figure 7 that this type of irrever− sibility is characterized by the Significantly differ− ent patterns over time；for example， even the house− holds whose the number of drivers changes from the state in“less than the average”in the first wave to

that in ‘‘greater than the average” in the second wave， have a different type of the change in Shop− ping frequency comparing with those in the period from the second to third wave． Hanson， S．（1979）Urban−travel linkages：Review． in Behavioral Travel Mo de ling， edited by Hensher D． A．and P． R． Stopher， Groom Helm， London，81−100．

5．CONCLUSIONS

  In this paper， we introduced some results of the panel survey on shoPPing activity and travel pat・ terns on non−workdays． The analysis focused on fundamental properties on dynamic changes over time in relation to the concept of relevance and irreversibility． The results indicate that， occupation， car ownership， and life cycle stage are classified into a strongly associated group． It is also evident frorn this analysis that there exists in irreversibility in the state transition over time among factors determining shopping travel behaviors． This means that these response patterns are by no means close to the idealized Markovian patterns．   The panel attrition behavior was also analyzed using a contingency table and log−linear models． The analysis indicated that some variables be re− jected for independence testing． It can also be found from the log−linear models that a panel attrition behavior can bee seen on a large scale in the panel data set and that it may comprise more than one causal structure．   It is noted that there remain many subjects to be solved in the future because such a panel study is still regarded as an on−going research in travel behavior analysis． Especially， it is important to develop a dynamic model of travel behavior by incorporating a panel attrition effect into the parameter−estimation procedure．

6。REFERENCIi】S

Fienberg （1980）The analysis of cross＜1assified categorical data． MIT Press， Cambridge， MA． Goodman（1973）Causal analysis of data from panel studies and other kinds of surveys． A merican／bur・ nal ρゾ Sociol（）9ソ， 78，1135−91． Jones， P． M．（1983）The practical application of activity−based apProaches in transport planning：

An assessment． in Recent、4dvances in Travel

l）emand、Analysis， edited by S． Carpenter and P． M． Jones，56−78， Gower， Aldershot， England． Kitamura， R． and Bovy， P． H． L．（1987）Analysis of attrition biases and trip reporting errors forpanel data． TranSportation Research A 21A，287−302． Kitamura， R． and Toon van der Hoorn（1987）Regu・ larity and irreversibility of weekly travel behavior． Tran毎）ortation 14，227−251． Kitamura， R．（1988）Evaluation of activity−based travel analysis． TranSt）ortation，15，9−34． Kitamura， R．（1989）Apanel analysis of household car ownership and mobility． Proceedings of／SCE， No．411．

Kondo， K．（1988） Travel Behavior Analysis．

Shouyou−shobou，（in Japanese）． Meurs， H．（1989）Trip generation models with per− manent unobserved effects． TranSportation Research B，24B， No．2，145−158． Nishii， K and Iwamoto T．（1990）Empirical analysis of travel and activity linkages by visitors to shoP− ping complex． Reports（ゾthe．Facu lty（ゾE㎎・吻θ召γ一 ing Ya〃￠anashi乙lniversily． No．41115−121． Nishii， K．（1991）Destination choice behavior of shopping complex visitors：Stated preference analy− sis． RePorts（’f the」Faczalty（）f Engineering y吻αηα一 shi乙lniversity． N o．4297−104 Golob， T．（1990）The dynamics of household travel time expenditures and car ownership model． Trans− portation Research A，24A，443・463． Pas， E（1990）Is travel demand analysis and model−

ing in the doldrums？in DeveloPments沈Llynamic

α励Activ⑳一」Based鋤伽aches to Travel Aηψs‘s，

一74一

December 1992