(Received June 17, 2004)

Transcription

1 TRANSPORTATION THE MALAYSIAN GOVERNMENT S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 200 LAW, T.H. RADIN UMAR, R.S. WONG, S.V. Road Safey Research Cener Professor, Road Safey Research Cener Mechanical and Manufacuring Deparmen Universii Pura Malaysia Universii Pura Malaysia Universii Pura Malaysia Serdang, Malaysia Serdang, Malaysia Serdang, Malaysia (Received June 7, 2004) Objecive: This paper makes a projecion of he vehicle ownership rae o he year 200 and o use his projecion o predic road acciden deahs in year 200. The projecion served as an indicaor for he Malaysian governmen o achieve a 4 road acciden deahs per 0,000 vehicles safey arge in year 200. Mehod: The sudy included he predicion of vehicle ownership and he analysis of pas rends in he road acciden deah rae. Gomperz growh model was used o projec vehicle ownership and he predicion of road acciden deah rae was done using Auoregressive Inegraed Moving Average (ARIMA) model wih ransfer noise funcion. Resuls and Conclusions: The Gomperz model prediced ha vehicle ownership would be equal o by he year 200. The road acciden deah rae is projeced o decrease o 4.22 in year 200, a an average decline rae of 2.4% per annum. This resul suggess ha a minimum 2.8% reducion per annum is required o achieve he naional arge in year 200. Key Words: Road safey arge, Auoregressive Inegraed Moving Average (ARIMA), Gomperz growh model, Vehicle ownership rae, Transfer noise funcion. INTRODUCTION In he year 996, he Malaysian governmen esablished a 5-year naional road safey arge o reduce road acciden deahs by 30% by he year During he 5- year period, several road safey iniiaives from naional o communiy levels were iniiaed. A series of inervenion programs on sraegic issues, such as lack of conspicuiy and proecion, speeding, bad driving behavior and unsafe road condiions, were proposed. An inegraed safey program was inroduced o boh preven and reduce fuure raffic accidens, as well as o reduce injuries during and afer accidens. Sraegies were caegorized ino: (a) acciden prevenion and reducion, (b) injury conrol and (c) pos injury reducion. Targeed elevised moorcycle safey campaigns, more sringen raffic legislaion, naional acciden blackspo programs, road safey audiing, consrucion of new moorcycle lanes and beer proecion for moorcycliss were among he inegral componens of his comprehensive approach. By 200, he concered effors resuled an %, 0.7% and 29% decrease in he number of deahs, serious and sligh injuries, respecively, in spie of a dramaic increase in vehicle ownership in he same period 2. The road acciden deah rae dropped from 6.2 deahs per 0,000 vehicles in year 999 o 5.6 deahs per 0,000 vehicles in year 200. However he naion s safey performance is sill far behind world-class sandard, which is below 3 deahs per 0,000 vehicles. Hence, in year 200, he Malaysian governmen adoped a new naional road safey arge of 4 road acciden deahs per 0,000 vehicles by year 200. This paper makes a projecion of he vehicle ownership rae o he year 200 and o use his projecion o predic he road acciden deah in 200. This was underaken using an Auoregressive Inegraed Moving Average (ARIMA) model wih ransfer noise funcion, developed o projec road acciden deahs in year 200. The projecion akes ino accoun changes in populaion and he vehicle ownership rae. The relaionship beween deah rae and populaion, vehicle ownership rae, are described uilizing ransfer noise funcion in ARIMA analysis. Prior o road acciden deah rae projecion, he predicion of vehicle ownership rae using he Gomperz growh model was done separaely. The projecion may be served as an indicaor for he Malaysian Governmen o achieve he 4 road acciden deahs per 0,000 vehicles safey arge in year IATSS RESEARCH Vol.29 No., 2005

2 THE MALAYSIAN GOVERNMENT S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 200 LAW, T.H., RADIN UMAR, R.S., WONG, S.V. 2. QUANTIFIED ROAD SAFETY TARGETS: OTHER COUNTRIES' EXPERIENCE Of all modes of ranspor, ranspor by road is he mos dangerous and mos cosly in erms of human lives. Alhough exensive effors has been made in many counries in reducing boh risk and he absolue number of accidens, he presen number of accidens is sill far oo high in mos counries. Improved road safey is achievable if suiable safey arges in respec o ime frame, as well as ambiiousness are adoped 3. This is suppored by Elvik 4, who poined ha he bes performance in road safey was achieved by counries wih highly ambiious quanified arges. The European Union counries wih he bes road safey records, such as Sweden, he Unied Kingdom and he Neherlands, were he firs o se quanified arges o reduce he number of vicims o derive maximum benefi from poenial improvemens in road safey from increased knowledge, accumulaed experience and echnical progress. I is broadly acceped ha argeed road safey programs are more beneficial in erms of effeciveness of acion, he raional use of public resources and reducions in he number of people killed and injured han non-argeed programs. In 997, Sweden adoped an ambiious road safey program o aim o achieve zero deahs and serious injuries on he road for he counry as a whole. The program addresses all areas in which local auhoriies and companies have a leading role o play. Sysemaic improvemens o he road nework have been underaken o reduce he severiy of accidens, and incenives have been provided in conjuncion wih he privae secor, o reduce he demand for road ranspor and hus he exposure of road users o risk. Ausralia has adoped a naional arge o achieve a 40% reducion in he number of faaliies per 00,000 populaion, from 9.3 in 999 o no more han 5.6 in 200. A series of wo-year Acion Plans was developed o monior he road safey program and a review wih recommendaions for a new Acion Plan is required. This arge provides a framework for coordinaing he road safey iniiaives of he federal, sae, erriory and local governmens and of ohers capable of influencing road safey oucomes. 3. THE VEHICLE OWNERSHIP MODEL Growh in vehicle ownership is ofen seen as an ineviable oucome of increasing per-capia Gross Domesic Produc (GDP) 5. In his sudy he Gomperz growh model, proposed by Dargay and Gaely 6 is used o describe he growh of vehicle ownership as a funcion of per-capia GDP. The main advanage of his equaion is ha is asymmeric sigmoidal naure can fi a vehicle growh curve well. I was proven o be highly effecive in generaing he growh curve and for relaing he impac of variables on differen vehicle ownership growh phases. Of paricular significance is ha he Gomperz growh funcion allows a slow vehicle ownership growh in he lowes per-capia GDP level, followed by an increasing rae of growh as per-capia GDP rises, and finally reaches a sauraing level. The vehicle ownership model is expressed by: V = ( γ exp( α exp( βgdp))) + ( θ ) V θ () where V is he rae of vehicle ownership a ime, θ is he adjusmen of vehicle ownership and per-capia GDP growh (0<θ<), and γ is he asympoic vehicle ownership as increases indefiniely. Parameers α and β are curvaure parameers. Analogously, he parameer α deermines he value of Gomperz growh funcion a percapia GDP is equal o zero and he parameer β plays a role in deermining he per-capia GDP value a vehicle ownership sauraion level. The smaller he value of β, he greaer he per-capia GDP a sauraion level. Long-run elasiciy of he vehicle per populaion raio wih respec o per-capia GDP varies wih economic performance. Long-run per-capia GDP elasiciy is presened as,. GDP. e. LR β GDP τ = αβ (2) Fiing of daa for he Gomperz growh model was performed by he Marquard-Lebenberg algorihm 7. The algorihm calculaes he regression coefficien α, β, γ and θ. The goodness of fi was checked by he esimaion of he regression coefficien, coefficien of deerminan (R- Square) and he associaed p-values for he model parameers. IATSS RESEARCH Vol.29 No.,

3 TRANSPORTATION 4. ROAD ACCIDENT DEATH RATE PROJECTION MODEL Many saisical mehods are available o explain acciden-relaed variables, such as log-linear model, generalized linear model and muliple-linear model. Daa observed over ime usually have srong correlaions among neighboring observaions. Therefore he ordinary mehods are no appropriae for his analysis because hese mehods assume ha he observaions over ime are independen 8. In ligh of he problem associaed wih ordinary mehods, several researchers have urned o he ARIMA model as a means o beer predic acciden variables. The ARIMA model is a useful saisical mehod for analyzing longiudinal daa wih a correlaion among neighboring observaions. This mehod has proven o be very useful in he analysis of mulivariae ime series 9-. In ARIMA analysis, here are wo simple componens for represening he behavior of observed ime series processes, namely he auoregressive (AR) and moving average (MA) models. The AR model is used o describe a ime series in which he curren observaion depends on is preceding values, whereas he moving average (MA) model is used o describe a ime series process as a linear funcion of curren and previous random errors. I is possible ha a ime series model will consis of a mixure of AR and MA componens. In his case he series are said o be compued by an auoregressive moving average process of order (p,q), where p and q are he orders of he AR and MA componens, respecively. The selecion sraegy for such models was developed and seleced by he Box and Jenkins mehod 2. A general ARIMA model can be wrien as: d θ ( B) a B N = (3) φ ( B) where a is assumed o have whie noise, B is he backshif operaor, N represens sochasic par, d is he order of regular differencing needed o achieve ime series saionariy, and oher parameers in he model are defined as follows: θ ( B) = θ... q P 2 q θ 2B θ q B (4) φ ( B) = φ... 2 P φ2b φp B (5) where φ φ p are auoregressive (AR) parameers, θ θ q are moving average (MA) parameers. ARIMA model developmen consiss of a hreesage ieraive process, which consiss of idenificaion, model parameers esimaion, and diagnosic checking of he residuals of he fied model 3. In he process of idenificaion, he firs sep is o deermine wheher he ime series is saionary or no saionary. If he series indicaes nonsaionariy, he ime series is firs convered o a saionary series by appropriae ransformaive and differencing operaions. TheDickey and Fuller es 4 was used o examine he ime series daa saionariy. The Augmened Dickey-Fuller regression is given as follows: y k + β + φi y i + ε i= = α + ρy (6) where is a ime rend, y represens he road acciden deah rae, y -i is he lagged change in road acciden deah rae, and ε is a whie noise error erm. Null hypohesis ρ=0 versus alernaive hypohesis ρ<0 was esed. Failure o rejec he null hypohesis is evidence ha he series y is non-saionary. A he idenificaion sage, he appropriae AR and MA parameers are found by examining auocorrelaion funcion (ACF) and parial auocorrelaion funcion (PACF) of he ime series. Auocorrelaion and parial auocorrelaion analyses were conduced on he saionary ime series. Auocorrelaion measures he uncondiional relaionship of values beween ime lags, while parial auocorrelaion measures he condiional relaionship beween series observaions. Based on he characerisics of ACF and PACF, a variey of possible ARIMA models was esablished for he road acciden deah rae in he firs sage, and hen esimaed in he second sage. In conras o he ARIMA model, which describe he behavior of single ime series, ARIMA model wih ransfer noise funcion model can represen more complex sysems which are able o connec one series no only wih is own pas values, bu also wih pas and presen values of oher, relaed ime series. In his sudy, ARIMA wih ransfer noise funcion was used o assess he effec of vehicle ownership and populaion on alering he rend of he road acciden deah rae (per 0,000 vehicles). The general form of he ransfer funcion ARIMA model comprises a par relaing o he ransfer funcion and a par relaing o he error erms, is defined as: Y ( + N (7) = v B) x + v2 ( B) x2 where Y is he road acciden deah rae, x i is he explanaory variable (x represens populaion number; x 2 represens vehicle ownership) and N is he sochasic 44 IATSS RESEARCH Vol.29 No., 2005

4 THE MALAYSIAN GOVERNMENT S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 200 LAW, T.H., RADIN UMAR, R.S., WONG, S.V. componen assumed o follow a general ARIMA srucure. In equaion (7), v i (B) is he ransfer noise funcion deermining he naure of he influence of he backward shif operaor. Specifically v i (B) can be expressed as: i [ ω( B) / ( B ] B b v ( B) = δ ) (8) where he numeraor can be expanded o ω(b) = (ω 0 ω B ω s B s ), he denominaor can be expanded o δ(b) = ( δ B δ r B r ), s, r and b represen he orders of he polynomials and he degree of seasonaliy, respecively. Combining equaion (3) and (7) yields: Y ω ( B) B ω ( B) B θ ( B) b b 2 = x + x2 + a (9) δ( B) δ 2 ( B) φ( B) The idenificaion of a ransfer funcion ARIMA model was accomplished by calculaing he sample cross correlaion funcion (r xy (k)) a various lags, k, and hen comparing i o heoreical impulse response funcions of differen orders in order o obain some idea of he delay parameer b and he orders r and s of he operaors in he ransfer noise funcion beween an oupu and an inpu series. In he modeling effor presened in his paper, he model error erm was esimaed using he leas square esimaion mehod 5, in which he leas square funcion is calculaed via non-linear leas-squares ieraions. Diagnosic check is needed o deermine he bes model among he enaive adequae models. A number of crieria for model comparisons have been proposed. The diagnosic ools used include he saisical significance of he parameers, he Box-Ljung (Q) saisic and he Akaike informaion crierion (AIC). The bes model should have he lowes AIC value, a saisically insignifican Q saisic a a lag of abou one-quarer of he sample size. Afer carrying ou he complee idenificaion, esimaion and diagnosic ieraive scheme of Box- Jenkins, he final ARIMA model can be used for predicions of he fuure road acciden deah rae (per 0,000 vehicles). 5. DATA Regisered vehicle number daa from 976 o 200 were aken from he Malaysia Traffic Police annual saisics 2 while he per-capia Gross Domesic Produc (GDP) and populaion daa were obained from he Cenral Bank of Malaysia. Per-capia GDP and populaion projecion figures were obained from Malaysia Third Ouline Perspecive Plan Per-capial GDP and populaion were expeced o grow a 2.3% and 7.5% per annum beween , respecively. 6. RESULTS AND DISCUSSIONS 6. Projecions of vehicle ownership Projecion of vehicle ownership rae was made on he basis of he Gomperz growh model of vehicle ownership described above and assumpions concerning populaion and per-capia GDP growh. Fied parameers for all he growh models are shown in Table. Table Esimaed parameers of vehicle ownership model Parameer Parameer Definiion Coefficien θ Speed of adjusmen γ Sauraion level β Shape or curvaure of he funcion α Shape or curvaure of he funcion R-square (Significan level, p<0.05) The esimaed Gomperz growh model for vehicle ownership was significan a a significance level of The Gomperz growh model yielded he bes fi o daa, as shown by he high R 2 value (0.962). Based on he Gomperz growh equaion, he adjusmen parameer, θ, is esimaed o be 0.267, indicaing ha 26.7% of he oal response could be aribued o per-capia GDP changes in ha paricular year. The esimaed sauraion level is 0.96 vehicles per populaion and vehicle ownership sauraion occurs when per-capia GDP reaches million annually (Figure ). Value β deermines he maximum per-capia GDP elasiciy level. The smaller he β, he greaer he percapia GDP required o reach sauraion level. In his analysis β is equal o and maximum per-capia GDP elasiciy is esimaed o occur when per-capia GDP is 0.04 million (Figure 2). The GDP is assumed o increase by 2.2% per year for he enire forecas period 6. The resuling projecions yield an esimae of vehicles per capial in year 200 (Table 2). The esimaed relaionship beween vehicle ownership and per-capia GDP is illusraed in Figure 3. IATSS RESEARCH Vol.29 No.,

5 TRANSPORTATION Vehicle per populaion Per-capia Gross Domesic Produc (million) Esimaed Saurae Level Fig. Esimaed vehicle ownership funcion 0.9 Income elasiciy of vehicle per populaion Per-capial Gross Domesic Produc (million) Fig. 2 Esimaed per-capia Gross Domesic Produc elasiciy for vehicle ownership Table 2 Projecion of vehicle ownership, Projecion Year Per-capia GDP Vehicle per populaion Projecion of road acciden deah per 0,000 vehicles The resuls of he Augmened Dickey Fuller (ADF) saionariy es are summarized in Table 3. The ADF es saisic is compared wih he criical values from he Dickey-Fuller disribuion wih a rend a he 5% significance level. Since he absolue value of ADF saisics for road acciden deahs series are more han he criical value of Thus, he null hypohesis of he ADF es is rejeced. This resul reveals ha he road acciden deah series is saionary. 46 IATSS RESEARCH Vol.29 No., 2005

6 THE MALAYSIAN GOVERNMENT S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 200 LAW, T.H., RADIN UMAR, R.S., WONG, S.V. Vehicle ownership per populaion Acual Prediced Year Fig. 3 Vehicle ownership esimaion and projecion, Table 3 Resul of Augmened Dickey Fuller (ADF) es for road acciden deah rae Variable ADF saisic 5% Criical value Road acciden deah From he plos in Figure 4, he auocorrelaion funcion appears o be dying down exponenially, while he parial auocorrelaion funcion cus off o zero afer lag, hus suggesing a Moving Average MA() model. The cross-correlaion plo beween inpu and oupu series shows a posiive correlaion a lag 0 (Figures 5 and 6). This resul implies ha he road acciden deah rae increases wih he growh in populaion and vehicle ownership. Based on he above auocorrelaion and parial auocorrelaion funcions observaion, he ARIMA model wih ransfer noise funcion is esablished as follows:.0 8 N Y = X X 2 + (0) ( B) A diagnosic check was performed using Q-saisic, which ess for he non-randomness of he residual auocorrelaions. The model had insignifican Q-saisics a he 0% level, implying ha he residual auocorrelaions are independen. Hence, i may be inferred ha he residual auocorrelaions are no significanly differen from zero. The Box-Ljung analysis implies ha he model is adequae. This is furher enhanced by he lowes AIC value and he model parameers are significan a 0% significan level (Table 4). The road acciden deah rae is projeced o decrease o 4.22 in 200, a an average decline rae of 2.4% per annum (Figure 7). This resul suggess ha o achieve a new naional arge of 4 deahs per 0,000 vehicles, he decline rae has o be 2.8% per annum Fig. 4 Parial auocorrelaion (lef) and auocorrelaion (righ) funcions of road acciden deah rae IATSS RESEARCH Vol.29 No.,

7 TRANSPORTATION Fig. 5 Cross-correlaion funcions of he pre-whiening ime series beween road acciden deah rae and populaion series Fig. 6 Cross-correlaion funcions of he pre-whiening ime series beween road acciden deah rae and vehicle ownership series Table 4 Esimaion for he model of annual road acciden deah rae Condiional Leas Squares Esimaion Parameer Esimae Sd Error T-value Lag Consan Moving Average () Populaion Vehicle Ownership Q-Saisic Prob Q(6)=0.869 Prob Q(2)=0.897 Prob Q(8)=0.435 (Significan level, p<0.0) Acual Predicion Acciden Deah Rae (per 0,000 vehicles) Year Fig. 7 Road acciden deah per 0,000 vehicles esimaion and projecion, IATSS RESEARCH Vol.29 No., 2005

8 THE MALAYSIAN GOVERNMENT S ROAD ACCIDENT DEATH REDUCTION TARGET FOR YEAR 200 LAW, T.H., RADIN UMAR, R.S., WONG, S.V. 7. CONCLUSION Planning Uni, Malaysia. (200). This paper provides he numerical conex for recommendaions for he reducion arge of he road acciden deah rae for he year 200 ha was announced in he Malaysian Road Safey Council annual meeing in The research included he predicion of vehicle ownership and he analysis of pas rends in he road acciden deah rae. Projecions of he road acciden deah rae were underaken for 200 aking ino accoun he assumpion of per-capia GDP, vehicle ownership and populaion growh. The Gomperz model prediced ha he vehicle ownership per populaion would be equal o by he year 200 while he ARIMA model wih ransfer noise funcion reveals ha a minimum 2.8% reducion per annum is required o achieve he naional arge in year 200. ACKNOWLEDGEMENTS The auhors would like o express heir graiude o he Minisry of Transpor of Malaysia for providing he financial suppor for his projec. They also wish o acknowledge he cenral bank of Malaysia and Police headquarer s conribuion o his research by providing he daa. REFERENCES. Radin Umar R.S. Faaliy Models for Malaysia: Towards Year Peranika Journal Science and Technology 6: pp.-3. (998). (in Malay). 2. Royal Malaysia Police (PDRM). Saisical Repor Road Accidens Malaysia 200. Traffic Branch, Buki Aman, Kuala Lumpur. (2002). 3. Haldorsen, I. Mål for rafikksikkerhesarbeide i ulike land. Noa av Oslo: Vegdirekorae. Trafikksikkerheskonore. (990). 4. Elvik, R. Quanified Road Safey Targes: A Useful Tool for Policy Making? Acciden Analysis and Prevenion 25(5): pp (993). 5. Waler, H. and Micheael, R. Moorizaion and non-moorized ranspor in Asia: Transpor sysem evoluion in China, Japan and Indonesia. Land Use Policy 3(): pp (995). 6. Dargay, J. and Gaely, D. Vehicle Ownership o 205: implicaions for energy use and emission. Energy Policy 25: pp (997). 7. Marquard D. W. An algorihm for leas squares esimaion of nonlinear parameers. Journal of he sociey of Indusrial and Applied Mahemaics : pp (963). 8. Wagenaar, A. C. Effecs of macroeconomic condiions on he incidence of moor vehicle accidens. Acciden Analysis and Prevenion 6: pp (984). 9. Sales, J.D., Delleur, J.W., Yevjevich, V. and Lane, W.L. Applied Modeling of Hydrologic Time Series. Waer Resources Publicaion, Lileon, CO. (980). 0. Pankraz, A. Forecasing wih Univariae Box-Jenkins Models: Conceps and Cases. Wiley, New York. (988).. Shumway, R.H. Applied Saisical Time Series Analysis. Prenice- Hall, Englewood Cliffs, NJ. (988). 2. Box, G.E.P. and Jenkins, G.M. Time Series Analysis: Forecasing and Conrol. Holden-Day, San Francisco, C.A. (976). 3. Brockwell P.J. and Davis R.A. (2 nd Eds.) Time series: Theory and mehods. Springer-Verlag, New York. (99). 4. Dickey, D.A. and Fuller, W.A. Disribuion of he Esimaor for Auoregressive Time Series wih a Uni Roo. Journal of he American Saical Associaion 74: pp (979). 5. Marquard, D.W. An algorihm for leas square esimaion of nonlinear parameers. Journal of he sociey of indusrial and applied mahemaics 2: pp (963). 6. The Third Ouline Perspecive Plan Malaysia Economy IATSS RESEARCH Vol.29 No.,