20 2nd Internatonal Conference on Envronmental Scence and Development IPCBEE vol.4 (20) (20) IACSIT Press, Sngapore Analyzng the Mcroeconomc Determnants of Travel Frequency usng the Com- Posson Regresson model R. Sultan Dept. of Economcs and Statstcs Faculty of Socal Studes and Humantes Unversty of Maurtus Redut,Maurtus r.sultan@uom.ac.mu N. Mamode Khan Dept. of Economcs and Statstcs Faculty of Socal Studes and Humantes Unversty of Maurtus Redut,Maurtus n.mamodekhan@uom.ac.mu Abstract The paper provdes nsght on modellng the mcroeconomc determnants of ndvdual travel behavour usng the Com-Posson regresson model. The level of trps towards a partcular destnaton s used as a count varable. The model was appled to Maurtus, a small sland state, where sze s a constrant to travel demand. A survey was undertaken and the fndngs mply that age, sex, ncome, qualfcaton, ownershp of car and number of chldren are sgnfcant factors affectng travel behavour. The Com-Posson regresson model s a promsng technque to model travel behavour whch accounts for the non-negatve nteger value characterstc of travel frequency and future research on ndvdual travel behavour and moblty usng ths technque s proposed. Keywords-trps, travel behavour, Com-Posson I. INTRODUCTION Modellng travel demand behavour has always been a challenge to analysts. Understandng the hstorc evoluton of travel patterns and the response to changes n crcumstances and economc factors s a necessary component n projectng future travel demand and assessng the nfluence of polcy measures. Indvdual households travel patterns change over the lfe cycle, are dfferent for dfferent generatons and are nfluenced by spatal and socoeconomc characterstcs []. Transportaton scence has evolved consderably over tme snce the begnnng of transportaton as a feld of scentfc nqury n terms of the theoretcal and emprcal determnants of travel behavour, the measurement of travellng and the methods used to analyse data. Intally, the actvty-based approach to model travellng demand had a profound mplcaton on transportaton research. The approach defnes the motves for travellng to be lnked to the actvtes whch take place at the destnatons and people confound utlty for such actvtes and ts relaton to the actvtes whch are conducted whle travellng. Accordng to ths approach, travel has been taken as a derved demand, at least n an absolute term, but as Mokhtaran and Salomon [2] argue, a recent nnovaton has been to model travel demand as an end n tself - people enjoy undrected travel (a sense of speed, moton, control, enjoyment of beauty). Ths may motvate people to undertake excess travellng behavour towards a partcular destnaton. If the sze of the country s a constrant to rsng demand, then the frequency of travellng rses. Ths leads Anas [3] to conclude that formulatng the travel problem n terms of trps undertaken help to treat the complementarness and substtuton between consumpton and travel. Measurng transport behavour poses yet another challenge to analysts. Schafer [4] revews such measurement and varous ndcators whch have been used n the lterature such as the travel tme budget - defned as the tme devoted to travellng - or the travel expendture budget whch s the money spent on travellng. However, over the years, ndcators such as number of trps and the purpose of trps have been used to examne ndvdual transport behavour. One example s the operatve traffc model for Copenhagen, called the Orestad traffc model (OTM), whch conssts of analysng the decson to partcpate n trps [5]. Ye et al. [6] also suggest that analysng the trps of ndvdual provdes a better understandng of travellng behavour. The frequency of trps has receved lttle attenton n emprcal lterature. Ths paper attempts to make three contrbutons: frst, we model travellng behavour through the number of trps whch an ndvdual has undertaken over a perod of tme towards a partcular destnaton. The basc unt for measurng transportaton actvtes s a trp, generally defned as a one-way move from an orgn to a destnaton, motvated by a man purpose, and nvolvng a publc nfrastructure [4]. Hence, as the number trps for one actvty falls, trps for undrected travel demand may rse f travel demand s a seen a normal product. Second, we model the number of trps as a count varable and apply the Com-Posson regresson as a novel approach to modellng travel behavour wthn a soco-demographc framework. The model accounts for the nteger value characterstc of the travel frequency varable. The dstrbuton of the frequency varable s rght skewed because t comprses a large proporton of zeros and ths mples that conventonal OLS estmaton technques are napproprate [7]. In ths context, count data models are a natural startng pont for estmatng the frequency of travel. The regresson analyses the determnants of the frequency of travel takng nto account the fact that t s a dscrete varable that can only take nonnegatve nteger values. The model s proposed as a 240
supplement to the OTM whch s on based a bnary logstc model. Ths novel approach may be compared to the lmted dependent regresson whch s usually used to model transport behavour, followng the work of McFadden [8]. Thrdly, the study s conducted for a small sland state lke Maurtus. An understandng of the travel behavour for Maurtus s even more challengng snce over the last twenty years or so, the small, solated, densely populated, developng Indan Ocean sland of Maurtus has undergone and contnues to undergo a revoluton n the way ts socety lves and works. Maurtus conssts of a relatvely small man sland (58 km north to south by 47 km east to west), and varous other scattered atolls. The man sland has a hgh populaton densty of 624 people per square klometre and ths s set to rse further by a steadly growng populaton. From a transport perspectve, the case of Maurtus s nterestng because t exhbts many of the transport problems facng other countres wth land constrant, such as worsenng congeston, ar polluton and traffc accdents wth lmted sze [9]. A major problem facng the sland s the traffc congeston especally towards the cty of Port-Lous and ths has a negatve mpact on qualty of lfe and on any economy and the socety becomes stressful. Traffc congeston causes loss n productvty and tme. The steady rse n nternal road traffc has become a major problem wth ts mpact also on land use, polluton and njury. Congeston s ncreasng the costs of dong busness, as productve hours are wasted n traffc (and hence wasted fuel) and producton schedules are dsrupted. Congeston s ultmately resultng n a less productve economy and reduced qualty of lfe. The purpose of ths paper s to obtan a better nsght nto the relatve nfluence of soco-economc and demographc varables on travel behavour by modellng the number of trps whch ndvdual undertakes towards the cty of Port- Lous as shown n fgure. Source: Enocks (2003) Fgure. The Map of Maurtus One factor further motvates our study. The transport sector s among the man sectors whch represent the fastest growng source of Greenhouse Gases (GHGs) - a major source for global warmng. A the same tme, demand for travellng s expected to grow at a pace of economc growth whch wll eventually leads to rsng GHGs. Ether the dstance travel ncreases wth hgher standard of lvng and/or the number of trps s expected to rse. In a small sland such as Maurtus, the sze of sland lmts the ncrease n dstance travel and hence, people have a tendency to compensate the demand for travellng through hgher trps towards a partcular destnaton. Understandng the behavoural dynamcs of travel frequency s therefore an mportant contrbuton towards land transportaton plannng. The paper s organzed as follows: In secton II, a bref revew of lterature on modellng travel behavour s provded; Secton III deals wth the methodology and data modellng; Fndngs and dscussons are presented n secton IV; and Secton V concludes. II. MODELLING TRAVEL BEHAVIOUR - A BRIEF REVIEW OF LITERATURE Modellng travel demand, wthn transportaton scence, has a rch lterature on both the theoretcal dmenson as well as on the emprcal dmenson. The theoretcal dmenson was formulated as a response to a major crtcsm of the neoclasscal theory of consumer behavour whch gnores the spatal nature of consumpton and fals to account for a fact that most consumpton cannot be realzed wthout ncurrng travel or communcaton costs [3]. Becker s theory of allocaton of tme assumes that travel s ntmately related to both consumpton and the allocaton of tme among dscretonary actvtes, but overlooked explct treatment of travel tself as an actvty [0]. Locaton theory and urban economcs dd not help to provde a formulaton of the demand for travel. For nstance, the conventonal locaton theory, assumes that the consumer travels to the nearest store or destnaton whle n urban economcs, t s standard to assume that the consumer commutes a rather non-standard manner such that the consumer wll not travel n any other way. The emprcal dmenson of travel demand has developed ndependently of standard mcroeconomc theory, manly due to the contrbuton of McFadden s econometrc formulaton of the problem [8]. Most of travel demand analyss has, thus, ts roots n appled econometrc technques and especally n dscrete choce models. An mportant component n emprcal analyss s the measurement of travel behavour. Gordon and Rchardson [], for nstance, use the number of trps as an ndcator for travellng and conclude that for the perod 969 to 995, the average commutng tme n the US fell but the total vehcle mles have ncreased durng the same perod. Some of the hgher vehcle mles may have come about because people travelled longer dstances at hgher speeds on ther commutes, but most of t s lkely to have come from a larger number of dscretonary trps. Anas [3] further adds that the travel demand problem can be and should be defned more 24
generally by how many trps and what knd of trps to make over a perod of tme and to whch destnatons. Theoretcal foundaton of trps as ndcator of travel behavour may be found n Bacon [2] whch constructs a utlty-maxmzng model of the optmum frequency of shoppng at a gven centre. The number of trps s a major component of transport research especally for polcy makng. The operatve traffc model for Copenhagen, called the Orestad traffc model (OTM), s a state-of-practce for modellng passenger travel demand. The OTM s a trp-based or tour-based modellng approach where a tour s defned n the OTM to be a sequence of only two trps,.e. a trp from home to the destnaton and a return trp from the destnaton to home, wthout ntermedate stops. Schafer s cross country analyss provdes ample evdence of changng behavour assocated wth trps [4]. The survey shows that at low moblty levels, one trp n a day s dedcated to a combnaton of work (short term survval) and educaton (longer term well-beng), and about half a trp on average s dedcated largely to personal busness (essentally, shoppng at local markets). Over tme, decentralsaton of work n many countres leads to lower trps beng undertaken for work related purpose but trps for non-work dscretonary purposes rse. The reasons for the prolferaton of non-work dscretonary trps are easy to conjecture. Frst of all, jobs and resdences have decentralzed, reducng the average dstance between homes and employment concentratons to whch non-work trps are made. Incomes have ncreased and as ncomes ncrease the demand for product varety grows and consumers seek a larger dversty of opportuntes to shop, purchase servces and engage n recreaton or lesure-related actvtes. As ncomes ncrease, car ownershp also ncreases and the avalablty of multple prvate vehcles or of more persons wth access to a prvate vehcle stmulates more travel and dscretonary moblty [3]. To close the gap between the theoretcal dmenson and emprcal dmenson of demand travel, formulatng of the travel problem n terms f trps undertaken help to treat the complementarness and substtuton between consumpton and travel. Whle recognsng that travel s necessary for consumpton, t also competes wth consumpton for ncome and tme, that there are many alternatve shoppng destnatons avalable to modern consumers, that such destnatons are substtutes and that the degree of substtutablty vares. Over the past years, there has been consderable research on people s trp patterns. Recent development ncludes the analyss of trp channg patterns [5]. III. METHODOLOGY AND DATA MODELLING The determnants of travel behavour may be classfed nto three dmensons: () the spatal dmenson, () the soco-economc dmenson, and () the personalty dmenson. The spatal dmenson s an mportant part n the actvty system approach n whch daly actvty and travel can be analyzed. Lvng, workng, shoppng, and recreaton are spatally separated actvtes, nducng the need to travel. Consequently, travel demand does not derve ts utlty from the trp tself, but rather from the need to reach locatons where actvtes take place. For that reason, the confguraton of actvtes,.e., the land use pattern, characterzed by densty, dversty, and desgn among others s lkely to nfluence travel behavour. The spatal component s our analyss s accounted for by modellng the number of trps towards one reference destnaton whch s the cty of Maurtus, Port-Lous. The focus of the study s on ndvduals and ther characterstcs. Age, gender, household sze, ncome, level of educaton, employment status, and moblty constrants are commonly used varables []. Evdence on the effect of age on travel behavour suggests that car ownershp s lower among young and older people. Thus, older people walk more often and publc transport usage s greater. Moreover, f older persons travel by car, they travel shorter dstances. However, travel tself may have socalzng opportuntes for older people. Thus, non-work trps have, therefore, been found to be hghest among older people. Therefore, the mpact of age s ambguous and demands emprcal evdence. As n many developng countres, car use s generally found to be lower among Maurtan women than men. Women travel more often by publc transport, or on foot. As women are more relant on slow modes, they cannot travel such long dstances as ther male counterparts. Ths dfference may be explaned by, among others, ther lower wages and the fact that women obtan dfferent types of jobs to man. The cultural aspect also plays an mportant role n determnng travel behavour of women. Travel tends to be less n conservatve relgous settng. However, because women reman responsble for most household mantenance tasks, non-work trps may be hgher. Household sze s postvely assocated wth car ownershp. Because of ntra-household decsons related to the actvtes of several household members, t may be approprate to own more cars. Consequently, car use s hgher, and use of publc transport and walkng are lower wthn large households As these households are more car dependent, they wsh to travel longer dstances. But f sze s a constrant, then, the number of trps wll ncrease. We test the effect of household sze through the number of chldren n the household. A postve relatonshp s expected. Educatonal level, employment status, and ncome may be nterwoven. Hghly educated workers are more nvolved n jobs wth a hgher occupatonal status, whch results n hgher ncomes. Consequently, studes of the effects of educatonal level, employment status or ncome on travel behavour can result n comparable fndngs. For example, hgher car use, longer travel dstances and travel tmes can be found across hghly educated people, employed people, and hgh ncome groups These people often obtan jobs wth a hgh occupaton status that are concentrated n hgh-densty offce parks. As a result, hghly-educated people and hghncome groups are more nvolved n hgher number trps. Our emprcal analyss takes nto account only educaton level to avod any smultanety bas. Car ownershp can be analyzed as an endogenous varable whch s explaned by varous soco-economc varables. Hghly educated people are found to own more cars. Due to relatonshps between educaton and ncome, car 242
ownershp s hgher across hgh-ncome groups as well. On the other hand, car ownershp can be consdered as an exogenous varable, explanng travel behavour. Ownershp of car may be lead to hgher number of trps. Based on the above theoretcal explanatory varables, a survey of 000 respondents was undertaken where respondents n the person sample were asked to report the number of trps undertaken durng the partcular reference week. The destnaton was the cty of Port-Lous and the orgn nvolves varous ponts around the sland. Maurtus s dvded nto nne dstrcts and the sample has been stratfed accordng to the populaton of the dstrcts, excludng Port- Lous. The ponts were chosen at random usng the random street approach and nvolves equal number of male and female. TABLE. Varables VARIABLES DESCRIPTIONS Characterstcs Age Contnuous Sex Bnary: Male =; Female =0 Income Bnary: Hgh=; Low=0 Model of Transport Bnary: Car = ; Bus=0 Number of chldren less Contnuous than 8 Qualfcaton Prmary =; secondary = 2; and tertary =3 From the data collected, we note that the mean of the response varable s greater than the varance. Ths ndcates under-dsperson. In statstcal lterature, under-dsperson s handled through varous generalzed forms of the Posson dstrbuton such as the Generalzed Posson dstrbuton [3,4] and the class of weghted Posson dstrbutons [5]. However, modellng of under-dsperson by the Generalzed Posson dstrbuton may not always be effcent [4]. In ths paper, we emphasze on one of the weghted Posson dstrbutons that have become ncreasngly popular n the recent years known as the Conway Maxwell Posson or Com-Posson dstrbuton (CMP) [6]. Ths dstrbuton has elegant statstcal propertes such as ts flexblty to model both over-,equ- and under-dspersed data. Moreover, t forms part of the famly of exponental dsperson models and s a generalzaton of some popular dscrete dstrbutons such as the Geometrc, Posson and Negatve-Bnomal dstrbutons. In fact, Shmuel et al.[6] have shown that CMP yelds fts wth almost equal effcency as the negatvebnomal model and other dscrete dstrbutons. Besdes, ts generalzed lnear model (GLM) has also been establshed. In the regresson set-up, Jowaheer and Mamode Khan [7] has developed the Com-Posson (GLM) and studed ts applcaton to set up a regresson model for analyzng car breakdowns n Maurtus [8]. In ths paper, we use ther Com-Posson GLM to set up a regresson model between the number of trps an ndvdual undertakes to Port-Lous n relaton wth hs age, sex, level of ncome, hs mode of transport, the number of chldren he has and hs qualfcaton level. More specfcally, the covarate sex wll be coded as for Male and 0 for female. Hs level of ncome wll be classfed nto two categores: hgh ncome (> Rs 5,000) coded as and low ncome (< Rs 5,000) coded as 0. Snce the most common mode of transport n Maurtus s car, we categorze ths varable as : car-usage coded as and non-car usage as 0. As for the number of chldren, we focus on school chldren less than 8 years old. Fnally, the level of qualfcaton s splt nto three types: prmary coded as, secondary coded as 2 and tertary coded as 3. To estmate these regresson parameters, we wll refer to the jont quaslkelhood estmaton approach (JQL) developed by Jowaheer and Mamode Khan [7] and Mamode Khan and Jowaheer [8]. In the next secton, we present the Com- Posson regresson model and the JQL approach. A. Com-Posson Regresson model (CPRM) and the quaslkelhood estmaton technque Let y be the number of trps for the th ndvdual ( y > 0, =,2,3,...,000) and x be the 7-dmensonal vector of covarates correspondng to y. Let β be the 7- dmensonal vector of covarates such that β j ( j =,2,3,...,7) s the regresson effect of the covarate on the number of trps. The Com-Posson regresson model s gven by y λ P( Y = y ) = () ( y!) Z( λ, ) where j λ Z( λ, ) =, λ > 0, > 0 (2) j= 0 ( j!) and T ln( λ ) = β (3) x Note that λ < ndcates over-dsperson, λ = ndcates equ-dsperson and λ > ndcates underdsperson. Followng Shmuel et al. [6], equaton (2) can also be approxmated by λ, ) = exp( λ ) ( 2 2 λ (2π ) Z (4) To estmate the parameters β and, we solve the jont quas-lkelhood equaton 000 = T D V ( f μ ) = 0 (5) th j 243
2 where f = ( y, y ) and θ, m ) μ =. Note ( λ 2 θ = E ( Y ) = and m = θ + Var( Y ), 2 where λ Var ( Y ) =. The components of D and are derved followng the approach of Jowaheer and Mamode Khan [7]. The JQL equaton (5) s solved teratvely usng the Newton-Raphson technque,.e, β r r + + V β 000 000 r T T = + D V D D V ( f μ ) = r = (6) IV. FINDINGS AND DISCUSSION In ths secton, we apply the JQL equaton (6) to obtan estmates of the regresson parameters. The followng table shows the regresson estmates for the varous covarates. The covarate of age s negatve and sgnfcant. Ths mples that older people have a tendency to undertake less trps towards Port-Lous. One major reason may be because of the spatal characterstcs of the place n terms of ts hgh temperature and populaton densty, among others. The fndng also mples that the frequency of travellng towards our reference destnaton s hgher for younger people. TABLE 2. Estmates Standard Error Intercept 2.34 (0.3) Age -.29 (0.234) Sex 3.552 (0.88) Income 4.557 (0.372) Mode of transport 7.2 (0.23) Number of -2.0 (0.5) chldren Qualfcaton Level 6.70 (0.38) The postve covarate assocated wth sex mples that gender plays a role n travel behavour. As stated prevously, famly settng, women status and ther occupaton as well as the low ownershp of car may explan the concluson that women undertake less trps than men. As expected, hgh ncome, hgh qualfcaton and ownershp of car enhance the demand for travellng. Both covarates are postve and sgnfcant. Ths may have major mplcaton for transport polcy. Due to the recent economc progress n Maurtus, the populaton have a craze for purchasng car and our analyss suggests that the number of trps s lkely to ncrease to Port-Lous and the problem of congeston wll further rse. The covarate wth household sze proxed by the number of chldren s negatve. Ths dffers from our theoretcal expectaton that hgher household sze leads to hgher trps. A possble explanaton s that household wth chldren may choose other destnatons for travellng purposes. V. CONCLUSION The study provdes an analyss of travel behavour usng major determnants at ndvdual level usng a novel regresson technque the Com-Posson model. The analyss consders the number of trps, whch s undertaken towards partcular destnaton, as a count varable. The use of a reference destnaton provdes a close examnaton of the soco-economc determnants for the motve to travel to that partcular destnaton. Such analyss may be use for projectng future moblty n our reference area. The Com- Posson regresson uses the number of trps as account varable and such model may be dstngush between bnary model whch analyses the determnants of the decson whether or not to travel. Plannng polces based on the actvty approach attempt to reduce travel by ncreasng cost or by brngng destnatons closer to orgns. However, our study shows that the frequency of travellng may rse and such concluson should be accounted n transport polces. Usng the number of trps as a count varable and the Com- Posson regresson technque, the analyss may be extended to account for more soco-economc characterstcs such as famly types, purpose of travellng and personal preferences of ndvduals. Compared to bnary models, whch correspond to the decson to partcpate n the actvty, analysng the frequency of trps usng Com-Posson accounts for the skewness of the data. A major lmtaton of the current study s the lmted number of explanatory varables whch are used n the regresson model. Ths provdes opportuntes for further research. REFERENCES [] V. van Acker, F. Wtlox and B. V. Wee The Effects of the Land Use System on Travel Behavour: A Structural Equaton Modellng Approach, Transportaton Plannng and Technology, Vol. 30, No. 4, pp. 33-353, August 2007. [2] P. L. Mokhtaran and I. Salomon, How derved s the demand for travel? Some conceptual and measurment consderatons, Transportaton Research Part A, vol. 35, pp 695-79, 200. [3] A. Anas, A unfed theory of consumpton, travel and trp channg Journal of Urban Economcs, vol. 62, pp.62 86, 2007. [4] A. Schafer, Regulartes n Travel Demand: An Internatonal perspectve, Journal of Transportaton and Statstcs, vol. 3, No. 3. December 2000. [5] G. Jovcc and C. O. Hansen, A passenger travel demand model for Copenhagen,Transportaton Research Part A, vol 37,pp 333-349, 2003. [6] X. Ye, R.M.Pendyala and G. Gottard, An exploraton of the relatonshp between mode choce and complexty of trp channg patterns, Transportaton Research Part B, vol. 4, pp. 96-3, 2007. [7] J.S. Long Parametrc and Sem-Parametrc Modellng of vacaton Expendtures, Journal of Appled Econometrcs, vol.,pp. 59-76. 997. 244
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