MODELING INTER-URBAN ROAD PASSENGER
TRAFFIC IN NIGER STATE
By
WOLE MORENIKEJI
ABSTRACT
The study examined the factors that explained the volume of road passenger traffic from Minna to 24 other destinations within and outside Niger State. The regression analysis reverted that only three of the hypothesized eight variables were significant accounting for appreciable 72% of the variations in the traffic data. These are trip frequency, rail connectivity and bus trips. The findings suggest that social and economic factors are much more important than the traditional population and distance factors associated with gravity models.
Introduction
The gravity model calibrated using the ordinary least square (OLS) method has been found to be capable of production spurious results, due mis-specification, for instance, estimating nonlinear relationship using a linear relationship. The greatest source of worry is the influence of distance. Curry (1972) found out the even if there is no frictional effect of distance, the gravity model will still give distance considerable importance. He attributed this to the influence of map pattern.
Various authors have also found that distance parameter actually vary from town to town. O’Sullivan’s (1970) study of 78 zones is Britain resulted in p values ranging from 61.3 to 14.8 for freight flows. Alberet, al (1977) reported a.p value of 1.88 for commodity shipment between California and 47 other states. Abumere’s(1982) study of bus passenger’s traffic in 34 Nigerian town resulted in p values ranging from -1.55 to – 3.71. There were attempts to account for traffic variations by including other variables. E.g. accessibility (Forheingham 1983) vehicle ownership, road kilometerage, vehicle ownership, bus roate kilometer, annual income e.t.c. (Fouraacer and Sayer 1977). Other studies broken away from the gravity model and multiple regression method completely such studies include that of Filani (1973) (input-out). Nihan and Holmesland (1980). Box and Jerkins Time series Technique and Okuani (1984)-Kalman Filtering Theory. The Present study will explore the utility of the regression model and consider other relevant variables in the traffic data in the study area.
The Aim the Research
The aim of this study is develop a model that will explain the volume of inter-urban passenger traffic in Niger state. The study will focus on how trips generated in Minna. Are distributed to other selected urban centers in Nigeria.
The Objectives of Study
The objectives of this study are to:
1.Identify the variables accounting for the volume of traffic attracted by the various destinations.
2.Build a quantitative model to explain the volume of traffic attracted from Minna by these urban centers.
3.Discuss the planning Implications of the findings.
Scope and Limitation of Study
The study is limited to road transport and its focus is on commercial passenger vehicles. Private road transport is excluded because of the problems of getting relevant data. Even if it were possible to carry out a 100% origin and destination survey, it would not have been possible to get similar data for the previous years for a time-series analysis unless the study is conducted few years into the future date: Moreover, this study is geared forwards generation a forecasting model for mass transit planning and not for individual transport.
Survey in all the urban centers within the study area which usually entails great costs terns if money, men and materials. Such a study can only be financed by the public authorities or research agencies which only few countries can afford.
This accounts for the scarcity of data on inter-urban flows. Since the 1974 inter State flows survey in Nigeria, on other one has been carried out. A similar study carried out in Malawi in 1974 by the Transport and Road Research Laboratory focused on three towns. In similar vien, the scope of this present study will extend only Minna as the trip generating center. The concern is on how all the trips generated in Minna are distributed on the urban centers.
Passenger traffic data used for this analysis has its inherent problems and should be interpreted with caution. The register from which the data was extracted recorded not the numbers of passengers carried but the number of vehicles that carried passengers to different locations outside Minna.
Through, in all cases, the record clearly distinguished between modes such as bus and car, however, it failed to distinguish between type based on capacity. That is, the record did not tell whether the car was salon or station wagon or whether the bus was small, medium or big size.
This problem was circumvented by observing the present proportion of vehicles type operating along each route and assumed that proportion is constant of the pass years. The average capacity value of this mixture of vehicles type was used to multiply the total number of vehicles that operated each day for each route. For instance, if a route is characterized by a mixture of saloon (1 passenger) and station wagon (8) an average value of 6 passengers was used as a constant to multiply the number of vehicles operating along the rote per day. This appears not to pose any serious problem since the aim of the study is not estimate passenger traffic but to account for the variations in the observed traffic. Bus capacities were estimated through the same method
Methodology
Predicting inter-urban road passenger traffic in Niger State requires the collection of data on daily movement of passengers from the designated motor parks in Minna and on various independent variables that might affect the volume of flow. These data were obtained from the primary sources during the author’s held work in 1995-1996. Collection of data on daily passenger flow from Minna to other urban centers was made possible by the availability of daily vehicle movement register in all the motor parks. The collection of the data was further entranced by the issuance of a letter of authority to the researcher to do so by the state secretary of the National Union of Road Transport Workers, Niger state chapter upon request.
The register are being kept for accounting purposes since the union collects tax on each vehicle loading in each motor park. The 1996 register for vehicles were obtained from the secretaries in charge of each route at the motor parks, that is: Kontogora route comprising Kontogora, Zungeru, Lafia, Kafin-Koro; Suleja made up of Suleja and Abuja, Kaduna, and Lagos route comprising of Bida, Ilorin and Lagos. To arrive at the total number of passengers travelling out to each urban centre from Minna, the numbers of vehicles were multiplied by the maximum passenger capacity of the vehicle type. The maximum capacity was used because, on vehicle leaves a motor park until it is fully loaded. If few cases where there are on enough passengers fill a vehicle, it was assumed, (and this is often the case) that the driver will pick passengers along the trip. In extranet cases where the number of passenger in the vehicle are not sufficient to make up the trip economically viable for the driver (being and economic man), the trip is usually cancelled and the passengers, advised to seek alternative means of making the trip.
Supplementary data were collected to enhance accurate understanding of the commuters’ behavior and to estimate some of the independent variables. Two sets of questionnaires were designed to elicit information from the union officials (National Union of Road Transport workers Union) and from the road passengers.
Information requested from the union officials included operating hours, vehicle types and capacity, official maximum carrying capacity, e.tc. The passengers on the other hand, were asked such question as to their place of usual residence, origin and destination of tirp, frequency of trip of current destination within the last one year, reason for choice for mode, purpose of trip at destination and other soci-economic questions that my influence propensity to travel.
A two stage sampling procedure was followed in carrying out the socio-economic characteristics survey of the passengers. To take care of any variations in the journey characteristic of the passengers that may be due to time of the day and day of the week, the survey was conducted two times a day for five days in the week that is weekdays (Monday, Tuesday and Wednesday) and weekends (Saturday and Sunday) for the two months of March and October, 1995. The two months are assumed to be free from the unusual traffic, that is, the end-of the-year rush. The number of vehicles that move within a particular time period depends on the availability of passengers, therefore it was decided that 150 samples be taken. That is, for every route, a systematic sampling of 10 passengers was done in each of morning (6.00am to 7.00am) and 5 in the afternoon 11.00 am to 1.00pm). Most passengers travel early in morning.
The average number of passengers interviewed per route per day was thus 15 making a total of 75 samples for five days in a month and 150 in the two months. A total sample of 1500 passengers were thus sampled in Minna.
Data Analysis
It has been observed (Kosing 1980 p. 165) that many current models of traffic generation are based solely upon socio-economic characteristics of the different zones (population, employment income, car ownership). However it is obvious that the number of trips made by people will also depend on the quality of transport and on the availability of attractive destinations and the inclusion of the trip rate into the traffic generation models could be expected to the value of these models and bring them closer to equilibrium models.
In view of the observations made above, it can be hypothesized that the degree of spatial interaction between Minna and other towns as measured by the volume of road passenger traffic is a function of:
- Age of the travelers.
- Mean annual trip frequency.
- Population
- Distance in kms.
- Cost of transport.
- Influence of competing modes of transport (bus trips, bus frequency and rail connectively).
The danger of incorporating so many variables in one equation is that there is the likelihood of pair-wise correlation among the Independent variables which may lead to multicollinearity problems.
A vicariate correlation analysis of the variables were performed shows that it is only in one case population versus distance (0.8362) is the bench mark value of 0.80 (Hauser 1974) was exceeded. This appears not to be a big problem.
The regression analysis was thus perfumed with all the eight variables In explaining the variations in the passenger traffic, all the eight variables were forced to enter the equation using the step-wise option of the SPSS. The following are the steps at with each variable enters the equation in order of importance.
Step 1
Logy=3.41 + 0.058x1
t=17.05 2.674
p 0.0000 0.0130
R = 0.47 R2 = 22% R2 (adj)=19% S=0.645 F=7.15 p=0.0130
Step 2
logy = 2.987+ 0.78x1 + 0.917x2
t16.14 4.469 4.169
P 0.0000 -0.0002 00003
R=0.74 R2 =55% R2(adj). 51% S=0.501 F =14.608 p= 0.0001
Step 3
2.864 + 0.065x, + 0.990x2+ 0.1317x3
t18. 849 4.459 5.577 3.782
P 0.0000 0.0002 0.0000 0.0010
R=0.849 R2=72% R2(adj) =69% S=0.402 F=19.91 P=0.0000
Step 4
Logy=3.37+0.56x1 + 1.05x2 + 0.127x3 – 0.32logx4
t 5.793.5635.8103.683-1.308
p 0.0000.00170.00000.00130.2045
R=0.86 R2=74% R2(adj)=70S=0.396 F=15.8 p=0.000
Step 5
Logy =4.078+0.047x1+1.0111x2+0.11930.517logx4+0.055logx5
t6.482 2.992 5.916 3.625 -2.038 -1.925
p0.000 0.0069 0.0000 0.0016 0.0544 0.0679
R= 0.88 R2=78% R2(adj)=73% S=0.374 F=14.995 p=0.0000
Step 6
Logy =4.73+0.49x1 +0.119x3.0519 logx4+0.666logx5-0.199logx6
t 5.641 3.14 5.627 3.658 -2.062 2.215 -1.175
p 0.0000 0.0049 0.0000 0.0016 0.0524 0.386 0.2540
R=0.89 R2=79% R2(adj)=73% S=0.37 F=12.91 p=0.0000
Step 7
Logy =4.975+0.042x1+0.864x2+0.864x3-0.991logx4+0.063logx5
t 5.796 2.524 4.432 3.001 -2.067 2.140
p 0.000 0.0207 0.0003 0.0073 0.0526 0.0455
-0.227logx6+0.214logx7
t -2.0671.154
p 0.0526 0.2530
R=0.90 R2=81% R2(adj)=74%S=0.36 F=11.44 P=0.0000
Step 8
Logy =6.383+0.049x1+0.110x3-0.890logx4+0.072logx5
t 3.203 2.582 4.426 3.067 -1.776 2.259
p 0.0049 0.0188 0.0003 0.0066 0.0926 0.0365
-0.238logx6+0.185logx7-1.077logx8
-1.3400.970-0.785
0.1970 0.34470.4429
R=0.90 R2=81% R2(adj)=73% S=0.37 F=9.88 P=0.0000
The full equation and the contribution of each variable to the explanatory power of the model is thus set out.
Logy =6.383+0.049x1+0.911x2+0.110x3-0.890logx4+0.076logx5
R222.254.972.274.278.1
Contribution 22.232.717.32.03.9
-0.230logx6 + 0.185logx7 – 1.077logx8
R279.580.881
Contribution1.41.30.2
Where
X1=Trip frequency
X2=Rail connectivity
X3=Bus Irip/day
X4=distance (dm)
X5=Income
X6=Bus trip frequency
X7=Population
X8=Age
A closer observation of the model suggests a good predictive model that accounts for about 81% of the variations in city-pair passenger traffic but containing some insignificant variables.
It can be observed that after step 3. All other variables become in elegant as their t-values were insignificant at the probability value of 0.5(that is their p-values exceeded 0.05) and their contribution to the models is less than 10%. The analysis thus suggests that three variables – Trip frequency, Rail connectivity and number of bus trips are the only good predictor variables.
The predictive model therefore takes the form
Log Y = 2.864 + 0.0645 Trpfrq + 0.9899 Railocon + 0.1317 bustrp
R2=72% F=19.91 S=0.402
Fitting the model
The model was fitted to the 1996 data. The predicated, residuals and the standardized predicated and residuals were obtained. These values are presented in table 1. The line graph of the predicated and the actual values were then plotted. This is shown figure 1.
Table 1: Predicted and Residual Values based on the model
S/N / Town / Actual / Predicted / Residual / Sid Prd / Std Res1. / Kotogora / 4.34 / 3.85027 / 0.485950. / 04064 / 1.20877
2. / Rijau / 3.11 / 3.67317 / -0.55989 / -025003 / -1.39270
3. / Sokoto / 2.64 / 3.06038 / -0.42389 / -1.25576 / -1.05441
4. / Gawu / 2.85 / 3.12218 / -0.26909 / -1.15432 / -0.66936
5. / Gwagwalada / 2.99 / 3.35891 / -0.36636 / -076580 / -0.91130
6. / Jos / 3.17 / 3.33968 / -0.17118 / -1.05673 / -0.42181
7. / Makurdi / 3.41 / 3.18165 / 0.22845 / 2.00077 / 0….56827
8. / Suleja / 4.55 / 5.4456 / -0.49006 / -0.09103 / -1.21899
9. / Abuja / 4.20 / 3.77004 / 0.43470 / -1.40099 / 1.08130
10. / Enugu / 2.73 / 2.97189 / -0.23950 / -1.25576 / -0.59574
11. / Lemu / 3.54 / 3.06038 / 0.47907 / 0.09973 / 1.19166
12. / Wushishi / 4.46 / 3.88627 / 0.57493 / 1.01713 / 1.43010
13. / Zungeru / 4.76 / 4.44523 / 0.31629 / -1.41866 / 0.78675
14. / Adunu / 2.95 / 2.96092 / -0.01056 / 0.01040 / 0.78675
15. / Kafinkoro / 4.33 / 3.42342 / 0.49979 / -0.65993 / -0.02627
16. / Kwadudi / 3.43 / 4.83113 / 0.00407 / 1.65047 / 1.24319
17. / Lapai / 4.29 / 4.42641 / -0.54069 / 0.98623 / 0.01013
18. / Kaduna / 4.60 / 4.27611 / 0.17268 / 0.73956 / -034494
19. / Kano / 4.01 / 3.98315 / -0.26999 / 0.25873 / 0.42953
20. / Zaria / 3.62 / 4.54110 / -0.35979 / 1.17447 / -0.67159
21. / Bida / 5.12 / 4.07115 / 0.57769 / 0.40317 / -0.89497
22. / Kutigi / 3.83 / 4.28996 / -0.23743 / 0.76179 / 1.43697
23. / Mokwa / 4.13 / 3.08993 / -0.15494 / -1.20726 / -0.59060
24. / Adure / 3.11 / 4.17936 / 0.02401 / 0.58076 / -0.38541
25. / Ibadan / 3.81 / 4.44523 / -0.37122 / 0.58079 / 0.05973
26. / Ilorin / 4.52 / 4.14247 / 0.37767 / 0.52022 / -0.92338
27 / Lagos / 4.77 / 4.47736 / 0.28930 / 1.06986 / 0.93944
Source: 0.71962
The plot shows that the model produced a fairly good fit as the residuals are generally very smal. If the predicted values are accepted as the theoretical values, they can be used to measure whether each town is receiving ther expected traffic from Minna.
From fig. 1 it can then be seen that Rijau (2) and Sokoto (3), are receiving far lass than the expected flow from Minna, that is the model over predicted the passenger traffic for these towns. On the other hand, Konotgora (1), Soleja (8) and Bida (21) are receiving than the expected flow.
6.8Diagnostic checks on the model
The degree of confidence that could be placed on the model was verified by examining the properties of the residuals. As observed by Bright man and Schneider (1922 p), when the four assumptions about the multiple regression model are met, that is normality, linearity, Independence and homoscedasticty, the residuals should oscillate within an equal-width horizontal band centered on zero and should display no systematic pattern of positive or negative residuals.
To check whether the present model display these, the scatter plots of the standardized residual against the actual data and that against the standardized predictive values both show that the scatter of points are random with no systematice pattern. The points are equality distributed (about 13 points each) above and below the zero line and all within an equal width of the zero line (-1,5-1,5) as seen in figures 2 and 3
COMPARISON WITH OTHER RESULTS.
Model Utility
The overall utility of a model can be evaluated by considering the R2 value, the significant of individual variables (t-values) and that of the F-value (Analysis of Variance).
The model in this present study achieved an R2 of 72% with three significant variables. For planning purposed, generally, a model with an R2 of about 70% has been accepted good enough but many models produced in recent years do not meet this criteria and give only the crudest notion of estimated values for the dependent variable.
The Malawian study of Fouracre and Sayer (1977), However arrived R2 values of 93% and 79% ;for Blantyre and Lilongwe respectively. Four variables were forced to enter the regression equation with only 3 and 2 variables found to be significant at a=5% respectively for Blantyre and Llongwe.
The present study revealed that trip frequency, bus trip and rail connectivity are important explanatory factors for inter-urban road passenger variations. This is consistent with the findings of Oum and Gillen (1983 p. 187) who observed the complementary nature of bus and rail modes in the overall inter-city passenger transportation network in Canada through their model suggested a shift in preferences over time towards the mode.
Thus, in the study area, if the level of service of the Nigerian Railway corporation could be improved, the railway has the potential of “snatching” customers away form the high cost of vehicle maintenance, the rail provides a good alternative, especially for long distance journeys. It is suggested that the Minna-Baro extension now in dis-use should be reactivated to improve transport network in the state. This is in additional to the urgent need to build new lines in the country as a whole.
The study also identified the number of bus trips operated daily by the state’s Mass Transit Authority as a very good variable. Given the relatively lower fare charged and accident-free record, the Niger State Transport Authority’s (N.A.T.A.) impact was expected to the greater than was observed. Observation at the N.S.T.A. parks at any time showed the gross inadequacy of buses in coping with the passengers’ demand. It is recommended that luxury buses for long distance trips should be introduced.
REFERENCES
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Abler R.J.S. Adams and Peter Gould (1992): Spatial Organization: The geographers’ view of the World, Prentice Hall Int. Inc. London.
Bright manHarvey and Howard Scneider (1992): Statistics for Business Problem solving. South-west Publishing Co., Cincinati.
Curry L. (1972): A Spatial Analysis of Gravity Flows: Regional studies, Vol. 6 Pp 131147.
Filani M.O (1973): Air Traffic Forecasting: An input Technique Approach’ Regional Studies.Vol. 7.Pp331-338.
Fotheringham A.S. (1983): Some Theoretical Aspects of Destination Choice and their Relevance to Production-Constrained Gravity Models, Environment and Planning. A. 1.5: 1121-32.
Foracre P.R. and I.A. Sayer (1977): Travel Characteristics of Road users in Malawi, Department of Transport, Transport and Road Research Laboratory Supplementary Report 281. Crowthone.