The National Capital Territory (NCT) of Delhi is the largest city in India with a population of about 17 million at present [1] and is expected to be 24 million by 2021. The primary reason for this enormous growth is that Delhi is the National Capital and provides for attractive commercial avenues as well as better health and education facilities [2, 3]. With increase in population, the number of private motor vehicles (PMVs) plying on Delhi roads have also increased from 5.36 lakh in 1981 to 88.27 lakhs in 2014 [4]. All this growth and expansion comes with big issues around mobility. On an average 48,621 cars and 99,340 two-wheelers (2Ws) were added annually to the Delhi roads from 1991-2000, and the respective numbers have increased to 114,386 and 187,065 in the last decade (2001-2010). According to the latest available data, the number of additional cars and 2Ws per year are 153,916 and 310,617 respectively [4]. Further, the number of cars have been growing at higher rates than of 2Ws [5, 6]. A recent WHO report revealed that the pollution level in Delhi is three times higher than the level prescribed by WHO and is continuously increasing [7]. Thus, there is a strong need to shift people from PMVs to public transport. This is only possible by making public transport as attractive as PMVs.

Therefore, there has been a growing interest among policymakers about the relevance of rail-based systems in India to address the mobility needs of the ever expanding population in the cities. While evaluating different mass transit options for Indian cities, metro systems are often given priority due to the belief that road-based bus systems cannot cater to capacity requirements as much as metro systems [8]. Sreedharan [9] also predicted that by the end of 2007, the metro will be able to take the load of 40,000 PMVs. Also, the Delhi metro is in line with rapid transport systems globally, and as a result, is a welcome step in the popular perception.

However, there is a need to determine whether the shift to metro happened from PMVs or existing public transport such as buses. Various passenger mode choice models have been developed [10-12] in the literature, but no work, to the best of our knowledge has attempted to study this cannibalization effect in Delhi, i.e. the shift of commuters from one mode of public transport (buses) to the other (metro). Thus, an objective of the research is to develop a mode choice model to estimate the mode used by the metro commuters before the commencement of metro services. We also analyse the factors that encourage commuters to opt for the metro as their preferred mode of commute. The paper also develops a binary logistic model to predict the probability of non-metro commuters of a given profile shifting to the metro.

Pavlyuk and Gromule [13] perform an econometric analysis of the behaviour of bus and train passengers and their choices between different transportation modes using the Nested discrete choice model. To model the mode behaviour of car and bus use, a study [14] is conducted in Tripoli, Libya (which has high car ownership) using a binary logistic model. The results show that some measures have to be taken to encourage car users to use other forms of public transport. Transit Oriented Developments (TODs) are often designed to promote the use of sustainable modes of transport and reduce car usage. The effects of personal and transit characteristics on travel choices of TOD users can be investigated using binary logistic regression models. One such model is developed to determine the probability of choosing sustainable modes of transport including walking, cycling and public transport at Brisbane, Australia [15].

The Binary Logistic models reveal that personal and transit characteristics have an impact on the decision of mode selection [16, 17]. One of the most critical issues in travel behavioural modelling is to select the most appropriate mode of daily commute [17]. The quantification of this interaction in terms of mathematical relationships is known as modal split and the travel demand models are referred to as modal split or mode choice models. Stated preference survey is conducted to forecast travel behaviour in a hypothetical travel environment whereas the revealed preference survey is used to study the current travel behaviour [16]. To reflect the travel characteristics of the targeted population, precise data is collected from this survey and used as an input to the logistic regression model developed to predict mode shifts.

In this paper, a binomial logistic regression model is formulated to predict whether existing metro users have shifted from buses or are new additions to the public transport system, having shifted from PMVs. The mode shifted from is used as the categorical dependent variable and is correlated with categorical and continuous independent variables responsible for the shift. More details of the model are presented in section 3.1.

3.1. Logistic Regression Model

In this section, a binary logistic regression analysis is applied to predict the, mode a given metro commuter has shifted from. The predicted values are PMVs (0) and buses (1). A total of five explanatory variables are considered out of which two are categorical and three are quantitative in nature. The details of the explanatory variables are as follows:

Categorical Variables

Gender (Male/Female)                                 X₁

(Coded as 1 for Female and 0 for Male)

PMV Owned (Yes/No)                              X₂

(Coded as 1 for Yes and 0 for No)

Quantitative Variables

Ingress distance to the Metro (Km)           X₃

Age (Years)                                               X₄

Income (in thousands per month)               X₅

Let p is the probability that the mode used prior to metro was a bus and B_i (i=0, 1, 2, 3, 4, 5) are coefficients of the Binary Logistic Regression model to be estimated from the data. Then according to standard theory of logistic regression [18], the value of Logit is given by:

(1)

(2)

The model analysis is done using SPSS software and the output is given in Table 4.

Table 4. Variables in the logit equation.

	B	S.E.	Wald	Df	Sig.	Exp(B)
Vehicle (0)	1.405	.273	26.566	1	.000	4.075
Access	.008	.035	.058	1	.810	1.008
Age	-.008	.010	.640	1	.424	.992
Income	-.023	.007	9.671	1	.002	.977
Gender (1)	.617	.320	3.721	1	.054	1.854
Constant	1.150	.397	8.378	1	.004	3.159

The equation of the logistic regression line is given by:

(3)

The two variables having the highest effect on the logit (log of odds of using a bus prior to the metro) are vehicle owned and gender. From Table 4, two observations stand out: Commuters not owning a vehicle are almost 4 times more likely to shift to the metro from buses compared to people owing a vehicle (Exp(B) for vehicle (0) = 4). Similarly, females are almost twice more likely to have shifted from buses to metro than the male counterparts (Exp(B) for gender (1) = 1.8).

3.2. Logistic Regression Model for Different Stations

The binary logistic regression analysis discussed in section 3.1 is then is carried out for all the five stations separately. The resultant equations are given as (4), (5), (6), (7) and (8) respectively for KG, CC, ND, RC and CS respectively. The significant coefficients corresponding to each station are highlighted in bold in the following equations:

(4)

(5)

(6)

(7)

(8)

The main findings of this analysis are; i) Females are generally more likely to have shifted from buses to metro than the male counterparts. The same is strongly evident from the analysis of CC, ND, RC and CS data (Exp(B) for female varies from 1.54 for CS to 20 for ND). ii) Commuters not owning a PMV are much more likely to shift into metro from buses than commuters owning a PMV (Exp(B) varies from 1.822 for CS to almost 7 for RC metro station data).

In this section, the results of the logistic regression model are validated using three methods to conclusively demonstrate a good fit and validity of the model. Further, a vehicle ownership split model is developed to get better insights on how the PMV type influencing mode shift to the metro.

4.1. Model Validation

The model is validated using three methods, namely; classification table, receiver operating characteristic (ROC), and cross-validation and their details are presented in section 4.1.1-4.1.3.

4.1.1. Classification Table

Table 5 shows that this model allows to correctly classify 96 / 183 = 52.5% of the commuters earlier using PMVs. We also see that the model correctly classifies 269 / 317 = 84.9% of the commuters earlier using buses. Overall 365 predictions are correct out of 500 times, for an overall success rate of 73% which is well within the acceptable range [19].

Table 5. Classification table.

Observed		Predicted
		Mode		Percentage Correct
		0	1
Mode	0	96	87	52.5
	1	48	269	84.9
Overall %				73

4.1.2. ROC Curve

A measure of goodness-of-fit often used to evaluate the fit of a logistic regression model is based on the simultaneous measure of the sensitivity (True positive) and specificity (True negative) for all possible cut-off points. First, we calculate sensitivity and specificity pairs for each possible cut-off point and plot sensitivity on the y axis Vs (1-specificity) on the x axis. This curve is called the receiver operating characteristic (ROC) curve. The area under the ROC curve ranges from 0.5 and 1.0 with larger values indicative of better fit. The area under the curve for the model developed in this paper is .723 (Fig. 3) indicating a very good fit of model [19]. Further, areas under ROC curves for CC, ND, RC, CS, and KG are 0.813, 0.825, 0.785, 0.719, and 0.72 respectively.

4.1.3. Cross Validation of the Logit Model

Cross-validation is the process of assessing how the results of a statistical analysis will generalize to an independent data set. Two fold cross-validation method is used in this research: it assigns data points to two sets d₀ and d₁ so that both sets are of equal size (this is usually implemented by shuffling the data array and then splitting it in two). The method then involves training (compute coefficients) on d₀ and testing (the ability of the resulting model to predict) on d₁, followed by training on d₁ and testing on d₀. In this study training and test sets are both large, and each data point is used for both training and validation.

(a) Cross Validation for Total Data (500 entries)

Both d₀ and d₁ have 250 data entries each. These are obtained by randomly picking these data entries. Firstly, d₀ is considered as given dataset of known data on which training is run (training dataset). The model is developed on data set d₀ and tested against the testing data set. The logit equation is given by equation (9) and the results of model validation using classification table are presented in Table 6.

Fig. (3). Receiver operating characteristic (ROC) curve.

Table 6. Validation of d₀ data entries using the logit model.

		TRAINING SET(250)			TESTING SET(250)
Observed		Predicted(Based on d0)			Predicted(Based on d1)
		Mode		%	Mode		%
		0	1	Correct	0	1	Correct
Mode	0	34	56	37.8	46	44	51.1	specificity
	1	20	140	87.5	33	127	79.4	sensitivity
Overall %				69.6			69.2

(9)

As shown in Table 6 the testing results have an accuracy of 69.2% in data set d₁ which is fairly acceptable. Next, both the data sets are interchanged. Based on the variables, the logit Equation (10) is derived. The model is validated using a similar classification table. The accuracy of prediction is found to be 68.9% and 68.4% for the training and testing data set respectively, again well within the acceptable region [19].

(10)

(b) Cross Validation for individual stations (100 entries each)

Cross validation of the model using the entire data set provided convincing evidence of the validity of the model. However to still probe further and strengthen the evidence of the predicting ability of logistic regression, cross-validation for data from each station has also been performed. Two data sets of 50 data entries each from every station are used. Then cross validation is performed as detailed earlier. The results again demonstrate the validity of the model even for individual stations and are presented in Table 7.

Table 7. Cross validation output for all five data sets.

DATA SET	Observed		TRAINING SET (50)			TESTING SET (50)
			Predicted
			Mode		% correct	Mode		% Correct
			0	1		0	1
KG	Mode	0	16	9	64.0	10	6	62.5
		1	13	12	48.0	14	20	58.8
	Overall percentage				56.0			60
CC	Mode	0	4	8	33.3	13	5	72.2
		1	1	37	97.4	6	26	81.3
	Overall percentage				82.0			78
ND	Mode	0	16	3	84.2	35	4	89.4
		1	11	20	64.5	4	7	63.7
	Overall percentage				72.0			84
RC	Mode	0	12	7	63.2	29	8	78.4
		1	8	23	74.2	5	8	61.5
	Overall percentage				70.0			74
CS	Mode	0	4	16	20.0	14	7	66.7
		1	8	22	73.3	8	21	72.4
	Overall percentage				52.0			70

4.2. Vehicle Ownership Split Model

To gain further insights into the mode shift, the effect of 2Ws and cars individually on the shift to metro is also studied. For this study, two additional categorical explanatory variables are defined to explain vehicle ownership (i.e., car and 2-Ws). The details of explanatory variables now are as follows:

Quantitative Variables

Ingress distance to Metro (Km)                     X₁

Age (Years)                                                   X₂

Income (in thousands per month)                  X₃

Categorical Variables

Gender (Male/Female)                                  X₄

(Coded as 1 for Female and 0 for Male)

Car Ownership (Yes/No)                               X₅

(Coded as 1 for Yes and 0 for No)

Two-Wheeler (2W) Ownership (Yes/No)      X₆

(Coded as 1 for Yes and 0 for No)

Standard Logistic Regression is performed using SPSS and the results are summarized in Table 8.

Table 8. Results (with mode split).

	B	S.E.	Wald	Df	Sig.	Exp(B)
Access	0.024	0.038	0.386	1	0.534	1.024
Age	-0.011	0.011	0.976	1	0.323	0.989
Income	-0.006	0.008	0.58	1	0.446	0.994
gender(1)	0.635	0.334	3.621	1	0.057	1.888
car(1)	-2.012	0.291	47.644	1	0	0.134
2Ws(1)	-0.561	0.279	4.049	1	0.044	0.571
Constant	1.903	0.414	21.116	1	0	6.707

(11)

As shown in Table 8, three variables viz., gender, car ownership and 2W ownership are significant. The females are almost twice (1.888) more likely to have shifted from buses to metro than the male counterparts (Exp(B) for gender (1) = 1.888). Commuters not owning a car are 7.4 times (1/.134) more likely to shift to the metro from buses than commuters owning a car (Exp(B) for car (1) = 0.134). Similarly, commuters not owning a motorcycle are 1.75 times more likely to shift to the metro than commuters owning a motorcycle (Exp(B) for 2Ws (1) = .571).

Further, the analysis is also carried out for each station separately and the findings of the model above are reinforced. The detailed results are presented in Table 9 and the highlights are as follows:

Table 9. Variables in the equations station wise (split).

	KG 01-100		CC 101-200		ND 201-300		RC 301-400		CS 401-500
	B	Exp(B)	B	Exp(B)	B	Exp(B)	B	Exp(B)	B	Exp(B)
Access	.179	1.196	.069	1.071	-.961	.383	-.490	.613	.052	1.053
Age	.010	1.010	-.037	.964	-2.667	.069	-2.506	.082	-.008	.992
Income	.020	1.021	-.039	.962	19.098	1.96 x 10^8	1.760	5.813	-.033	.968
Gender	-.160	.852	1.865	6.453	-.005	.995	-.003	.997	.511	1.666
Car	-1.713	.180	-1.724	.178	-.031	.969	.000	1.000	-1.155	.315
2Ws	-.150	.861	-.204	.815	-.036	.964	.053	1.054	-.282	.754
Constant	-.208	.812	3.665	39.066	2.945	19.005	1.829	6.229	2.070	7.929

• The females are generally more likely to have shifted from buses to metro than the male counterparts. The same is strongly evident from the analysis of CC and CS data (value of Exp(B) for gender are 6.45 and 1.67).
• Commuters not owning a car are more likely to shift to the metro from buses than commuters owning a car. Commuters not owning a 2W are more likely to shift to the metro from buses than commuters owning a 2W. Further, motorcycle owners are more likely to shift into metro from buses than the car owners (value of Exp(B) for car and 2Ws).

Several studies [7, 20-24] establish an urgent need to improve the quality of public transport, particularly in terms of comfort, directness, punctuality, travel time, and integration of different modes to reduce the increasing reliance of commuters on PMVs. Studies also reveal that commuters can actually shift to public transport if their concerns are addressed. Tiwari and Jain [25] conclude that commuters can easily travel by bicycles up to a distance of 10 km. Suman et al. [26] reveal that 25% of non-bus users are willing to use bicycles for daily commute if separate lane is reserved for them. Further, 52% bus users can potentially shift to bicycles and consequently free up space inside buses thus increase comfort and enhancing bus attractiveness to non-bus users. Furthermore, Suman et al. [26] also reveal that if a common ticketing system for buses and Delhi metro is available, 36% non-bus users are willing to shift to buses. Additionally, 64% experts believe that implementing common ticketing system is feasible in Delhi. More studies [20, 22, 24] share similar findings and conclude such integrated ticketing systems can improve public transport, a prime need of the current era.

Delhi metro is an attempt to provide quality public transport that is comfortable, quick and safer. Commuters using both PMVs and buses (the existing major mode of public transport) have shifted to the metro for their commuting needs. This paper, as discussed in section 1, analyses the relative mode shifts. The findings suggest that a bulk of the metro users, 57% to be precise, have shifted from buses and only 28.8% from PMVs. Further, commuters not owning car(s) are 7.4 times more likely to shift to the metro than those owning one (or more). Thus, while many bus commuters find the quality of the metro better (hence the shift), commuters using PMVs are less enthusiastic using shifting to metro. This clearly points to two phenomenon and corresponding policy measures:

• The quality of public transport matters. Commuters shift from one mode of public transport to another in search of better quality (bus to metro). A shift from PMVs to a good quality public transport mode (PMV to metro) is also possible. So, all modes of public transport should strive to improve their quality and commuters will respond commensurately. Specifically, busses in Delhi need to improve their service quality attributes significantly to retain their ridership. They are the most cost effective mode of urban transport [27] and are crucial to the success of the public transport strategy of Delhi.
• Improving the quality of public transport alone is not sufficient to affect the desirable mode shift from PMV to public transport (metro in this case). In this study, this is reflected in the low share of PMV to metro and the low likelihoods of commuters owning PMVs shifting to the metro. Therefore, strategies to incentivize the use of public transport, in addition to improved quality of public transport, should include measures to dis-incentivize PMVs. An example of such a measure is congestion charging. Although initially likely to be contested by citizens, these measures can become popular once the benefits are apparent.

Similarly, those who do not own 2W(s) are 1.75 times more likely to shift to metro than those owning one (or more). For example, in 2005, 55% residents of Stockholm were not satisfied with implementation of congestion charging but later accepted it and appreciated the positive effect in reducing travel time and PMVs use [28, 29].

Mode shift from buses to metro occurs because buses take more time, and are more crowded compared to the metro. Further, commuters prefer direct mode of transport that is possible for many of them who shifted to the metro. In addition to this shift, some commuters also shift from PMVs to the metro because it is cheaper and less time consuming as compared to PMVs. The analysis also reveals, as expected, the females perceive the metro to be safer and are more likely to shift as compared to males. The possible drivers for this are CCTV camera availability, security personnel on stations, more space inside as compared to buses even when crowded, and separate coaches for females.

It is important to note, however, that despite, introduction of a good metro system in Delhi, the mode share of public transport is continuously decreasing. Also, majority of the metro commuters have shifted from buses and new addition to the public transport domain is not considerable. Therefore, as presented in the discussion section, improvement in various service attributes is necessary along with dis-incentivising PMVs to enhance the overall mode share of public transport. Possible measures to achieve this include: 1) improved comfort, punctuality, and travel time through addition of more buses, along with optimal route allocation of existing ones and implementation of common ticketing system for buses and the Delhi metro, 2) separate lanes for bicycles, and 3) betterment of dis-incentivization of PMV’s through measures such as congestion charging.