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Procedía - Social and Behavioral Sciences 54 (2012) 483 - 492

EWGT 2012

15th meeting of the EURO Working Group on Transportation

Application of Mixture-Amount Choice Experiment for Accumulated Transport Charges

Elaheh Khademi* , Harry Timmermans

Urban Planning Group, Eindhoven University of Technology, P.O.Box 513, 5600 MB Eindhoven, The Netherlands

Abstract

Despite the vast literature on transport charges, several aspects of this issue still have not been studied in much detail. For example, traveller adaptive behaviour to accumulated transport charges has not yet been subject of a considerable amount of empirical work. To address this issue, this paper describes an experimental approach to analyze how travellers respond to mixtures of transport charges, which vary in terms of their potential travel time gains, subject to budget constraints. Accordingly, we construct a mixture-amount experiment with three attributes: toll road; congestion pricing; and parking price and three different budget levels per day. In addition, each attribute has three different levels of saving travel time. Seven mixtures of the simplex lattice design were used for the allocation process and a second-degree polynomial model is estimated with 6 parameters using a BIB design. Also, we measure the effects of attribute levels using linear regression. An internet-based stated experiment was conducted in The Netherlands to collect data for estimating the model. 304 respondents participated in this survey and a mixed logit model was used to estimate the model of behavioural response. The results indicate the negative attitude of the Dutch population regarding their willingness to pay for pricing policies. Moreover, they showed more sensitivity to congestion pricing compared to the two other policies.

© 2012 PublishedbyElsevier Ltd.Selection and/or peer-reviewunderresponsibilityofthe ProgramCommittee

Keywords: Pricing policy; mixture-amount experiment; BIB design; mixed logit model

1. Introduction

Transport charges or road pricing as a Transportation Demand Management (TDM) instrument have received much attention in recent years. Many academics and transportation planners seem convinced that these policies may be one of the most effective policy instruments to change travellers' behaviour to minimize congestion,

* Corresponding author. Tel.: +31-40-247-2934; fax: +31-40-243-8488. E-mail address: E.khademi@bwk.tue.nl.

1877-0428 © 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Program Committee doi: 10.1016/j.sbspro.2012.09.766

emissions or to optimize system use otherwise. Road pricing may affect many dimensions of travel behaviour, specifically departure time choice, route choice and transport mode choice. Not surprisingly, therefore, different kinds of pricing strategies have been studied and implemented in practice in various cities and countries. Since decades, tolls have been charged on certain roads, not only to stimulate particular behaviour but also to recuperate building and maintenance costs. In addition, various congestion pricing or value pricing strategies have been discussed at length in countries such as the Netherlands, and such schemes have been implemented in some cities elsewhere in the world. Finally and more recently, parking charges have become popular across the world, not only in commercially managed parking garages and related to public inner-city parking spaces, but also in and around shopping centers in neighbourhoods and at peripheral locations.

The impact of these pricing policies has been studied at length, especially in the context of congesting pricing. For example, Arentze et al. (2004) found that for the work activity, route change is the most important adaptation of people under congestion pricing, followed by departure time adjustment. In the case of non-work trips, the willingness to adapt is smaller, and changing route and switching to bike are the dominant responses. Similarly, Keuleers et al. (2005) investigated the effect of a hypothetical road-user charging scheme on travel behaviour, activity participation and rescheduling patterns in the city of Newcastle upon Tyne, UK. Results implied that the scheme was effective in reducing car use during peak times in the city but that overall activity participation remained largely unchanged. Yan et al. (2002) studied the effect of value pricing, where the traveller is offered a choice of price and service quality in Orange County (California). Results confirmed the reported ability of the operators of both value pricing experiments in California to fine tune toll in order to keep the toll lanes busy while maintaining congestion-free conditions. Others, also, found that shifts to different vehicle occupancies or times of day in response to toll changes are very small because of the existence of the option to change route [4, 5, 6].

As for toll roads, Dissanayake, and Kouli (2007) investigated driver response to a proposed toll motorway project connecting the cities of Corinth and Patras in Greece. The overall objective of this research project was to develop discrete choice models to investigate driver behavior on inter-city route choices and to explore driver attitudes to road pricing. Results showed that drivers prefer the new toll motorway over the existing alternative routes. In the model, both the travel time and travel cost coefficients were negative and highly significant, indicating that travel utility decreases with increasing travel time and cost. The study reported by Danwen et al. (2010) is an example of studies which focus on effects of parking charges on travel behaviour. Using elasticity analysis, the paper concluded that residents' travel modes change with increasing parking rates. It also revealed the proportion variation between car and bus transit for different parking rates, and analyzed the elasticity of parking rates and bus fares. Guan et al. (2005) also assessed the effects of parking policies in the form of meters; discounted transit passes; and other transportation demand management (TDM) strategies on travel and parking behavior, with an emphasis on the relationship between parking pricing and mode choice. Results showed that the installation of the meters and the discounted transit pass program had a significant effect on decreasing the drive-alone mode.

Thus, this brief review suggests that traveller adaptive behaviour to various transport charges has been subject of a considerable amount of empirical work. As a result, our understanding of the impact of transport charges has increased substantially over the years. Nevertheless, several aspects of transport charges have still not been studied in much detail. A key question concerns the accumulation of possible charges. Most studies have typically addressed only a single charge. However, consumer response to for example parking policy may depend on other charges. Moreover, travellers will face the problem on how to allocate their available budget to alternative transport charges or other expenditures.

To address this question, this paper describes an experimental approach to better understand how travellers respond to such accumulated pricing schemes, subject to budget constraints. More specifically, it allows conclusions concerning questions such as (i) how do travellers allocate part of their travel budget to different types of pricing policies; (ii) to what extent does this allocation depend on the total available budget; and (iii) how do they trade-off the budget allocation and the gain experienced by choosing the priced choice alternatives.

The paper is organized as follows. First, we will discuss the basic principles of mixture and mixture amount experiments and how they can be applied to the research issue at hand. As part of this section, we will also explain the elaboration to the case which includes the trade-off between budget allocation and varying gains. Next, we will discuss operational decisions in the design of the experiment, and the sample. The paper will be completed with results and conclusions finally.

2. Mixture and Mixture-Amount Experiments

"An experiment in which the factors are the ingredients or constituents of a mixture is called a mixture experiment." [10]. In this experiment, response is a function of the proportions of the ingredients present in the mixture which usually measure by weight, volume, or the like. These proportions must be non-negative and if expressed as fractions of the mixture, they must sum to unity. The general purpose of mixture experimentation is to make possible estimates, through a response surface exploration, of the properties of an entire multi-component system from only a limited number of observations. These observations are taken at preselected combinations of the components (resulting in mixtures) in an attempt to determine which of the combinations in some sense maximize the response [11].

A mixture consists of q linearly independent variables that are constrained to a (q-J)-dimensional dependent space. The levels of the q variables sum to a constant, which equals the total amount. Figure 1 gives an illustration, showing three linearly independent variables; xj, x2, and x3, with standardized ranges from 0 to +1.

Fig. 1. Mixture space for three variables

Within the standardized independent space, the (q-1)-dimensional constrained space is represented by the triangle within the cube. This space is called a simplex space. The mixture constraint is presented in equation

form below.

X x = 1 (1)

Because of this constraint, the level of the variables in a mixture experiment cannot be chosen independently. Figure 2 shows the (q-1)-dimensional simplex space for three experimental variables. All points on the surface or in the interior of the simplex sum to one. It shows the typical simplex coordinates of the three vertices; (1, 0, 0), (0, 1, 0), and (0, 0, 1), and the center point; with coordinates (1/3, 1/3, 1/3). In addition, it shows the three edge midpoints; with coordinates (1/2, 1/2, 0), (1/2, 0, 1/2), and (0, 1/2, 1/2), and three interior points; with coordinates (2/3, 1/6, 1/6), (1/6, 2/3, 1/6), and (1/6, 1/6, 2/3).

Fig. 2. 2-Dimensional simplex space for three experimental variables

Simplex-Lattice and Simplex-Centroid are two designs used to provide design points in mixture experiment. In 1958, Scheffe introduced simplex-lattice designs for mixture experiments and developed polynomial models which have exactly the same number of terms as there are points in the associated designs. The designs, consisting of a symmetrical arrangement of points, are referred to as {q, m}-lattices. The models, expressed in canonical form by Scheffe, are characterized by their relatively simple form and thus possess the property that they are easy to use for predicting the response over the simplex factor space. Corresponding to the points in a {q, m}-lattice, the proportions used for each of the q components have the m + 1 equally spaced values from 0 to 1, that is, x¡ = 0, 1/m, 2/m, ... , 1, and all possible mixtures with these proportions for each component are used. The number of points in a {q, m}-lattice is (m+q-f| and the lattice designs are characterized by their simplicity of construction [12]. I m I

With a simplex-Centroid design, the design points correspond to q permutations of (1, 0, 0, ..., 0), | q| permutations of (.5, .5, 0, ..., 0), I q| permutations of (1/3, 1/3, 1/3, 0, ..., 0), ..., and finally the single (1/q, 1/q, ..., v2J 1/q) mixture. The number of distinct points is 2q - 1 [10].

In mixture experiments, the measured response is assumed to depend only on the relative proportions of the components in the mixture and not on the amount of the mixture. However, the amount of the mixture (i.e. the total available budget) can also be varied as an additional factor in the experiment. These are so-called mixture-amount experiments. In fact, a mixture-amount experiment describes the relationship between the values of one or more response variable and allocation of available budgets or resources to a group of attributes. Accordingly, in a cost-based mixture approach, alternatives consist of profiles in which the costs of attributes satisfy the inequalities and the combined cost of the attributes is the same for all profiles. That is,

Yet / U = 1,

where ci is the cost of attribute i, U is the total amount to be spent across all attributes, and ci /U = xi. According to the simplex-lattice design, the canonical form of the first-order mixture model is defined:

E (y) = X PiXt i = 1

Equation 3, also, shows the second-degree model:

E (y) = ¿ Px + ¿ pijxixj,

i , j =1 i < j

where E(y) is the response of a mixture (xi, x2. . . xq ). It may be noted that not all simplex mixtures of {q, m} are needed to estimate the parameters of a second-degree canonical model. As total amounts and their allocation can affect the response, different levels of total amount can be considered in a mixture-amount experiment. It means for the total amount, U, that r different levels indicated by u1, u2, ..., ur (r>2) may be considered [13].

In addition to different amounts, attributes may also have different gain levels and this point has to the best of our knowledge not received attention in mixture-amount experiments yet. As an illustration, in selecting between

transportation modes for a trip to work, consider three different kinds of trains as our attributes. Each of these attributes is different in terms of safety, comfort, and travel time and so on. Moreover, mentioned benefits may also have different levels. For example, travel time can have three different levels of t1, t2, and t3 minutes per day and low, medium and high can be defined as three levels of safety and comfort's benefits. So, when people want to trade-off across attributes they may think about the amount they spend and the benefit (safety, comfort or travel time) they gain by choosing each attribute. Accordingly, the allocation for any amount may be influenced by varying attributes levels. We address this issue by attaching the levels to the attributes and as a result, we go beyond a classical mixture-amount design.

3. Experimental Design

According to the existing literature, the design of a mixture experiment typically involves the following steps [14]:

3.1. Define the objectives of the experiment:

Formally, the choice problem addressed in the previous section is a combination of (i) a budget allocation task, repeated for (ii) multiple amounts in which (iii) the allocations for any amount may be influenced by varying attributes levels.

3.2. Select the mixture components and any other factors to be studied:

In the present study, we assume a mixture-amount experiment with three attributes as pricing options which are toll road, congestion pricing and parking price and three different budgets, u1, u2, and u3, to be allocated. The mixture of the attributes is denoted by x1(toll road), x2(congestion pricing), and x3 (parking price), (0< x1, x2, x3 <1 and x1+x2+x3=1). Moreover, each attribute has a combined level as time benefits owing to the pricing strategies.

The simplex lattice design {3, 3} creates 10 mixtures and the second-degree canonical model has 6 parameters. We consider three amounts of budgets to be allocated to attributes and combine the mixtures with amounts to form the choice sets of size 3, using Balanced Incomplete Block (BIB) design with seven symbols. Table 1 shows seven mixtures of three attribute mixture design.

Considering three amounts, a mixture design of 7 is used three times of each allocation which creates 21 profiles. With v = 7 = b, r = k = 3, X = 1, 21 profiles are organized into 7 choice sets of 3 profiles each (plus a no-choice option in each set). The 7 choice sets with these 21 profiles are given in Table 2.

3.3. Identify any constraints on the mixture components or other factors in order to specify the experimental region and the response variable(s) to be measured:

As can be seen in Table 2, the mixtures show the proportions of the budget allocation to the attributes. In each mixture, the sum of attributes should be equal to the budget constraint. Furthermore, amounts to be allocated should be restricted not to dominate the other choice alternatives. Therefore, we apply xmax*umax < umin where umax=max (ui) and umin=min (ui). This restriction depends on the mixture level used in the experiment as xmax is the maximum mixture level and xmax<1[13]. As we consider three-attribute mixtures, our restriction will be 2/3 *

umax — umin.

Stated preference (SP) models, commonly used in transportation research, systematically vary the levels of a set of attributes, according to an orthogonal fractional factorial design and ask respondents to rate the resulting attribute profiles on some preference scale. When the purpose of the study is to estimate a choice model, these attribute profiles are placed into choice sets and respondents are asked to choose the choice alternative they like best. In this experiment, respondents were asked to make explicit choices.

Table 1. Three attribute mixture design

Mixture Attribute 1 Attribute 2 Attribute 3

1 1 0 0

2 0 1 0

3 0 0 1

4 2/3 1/3 0

5 0 2/3 1/3

6 1/3 0 2/3

7 1/3 1/3 1/3

Table 2. Choice sets for three-attribute mixture design with three amounts (ui(t) denoted the t-th mixture with amount ui,t=1,2,..7; i=1, 2, 3)

Choice Set Profile a Profile a Profile a Base Alternative

1 u1(1) u2(2) u3(4) No Choice

2 u1(2) u2(3) u3(5) No Choice

3 u1(3) u2(4) u3(6) No Choice

4 u1(4) u2(5) u3(7) No Choice

5 u1(5) u2(6) u3(1) No Choice

6 u1(6) u2(7) u3(2) No Choice

7 u1(7) u2(1) u3(3) No Choice

3.4. Propose an appropriate model for modeling the response data as functions of the mixture components and other factors selected for the experiment:

We use a second degree mixture model for a given amount which allows interaction between amounts and mixture proportions. Also, it should be noted that this model allows us to determine the optimum amount in the range of experimentation. Equation 4 shows the second degree mixture-amount model.

q-1 q q

E(y) = au + pu2 + Y, Yiuxi + Z Sixi + Z Sijxixj (4)

i=1 i=1 i, j= 1 i < j

where E(y) is the choice response of a mixture (x1, x2. . . xq ) with given amount of u. In addition to this, each attribute has its own attached levels which bring additional utility. Linear regression was used to estimate the effect of those attached levels. Equation 5 shows the utility function regarding attributes' level.

E (t) = Xytt + X2tc + Xtp (5)

where tt shows the effect of the saving time levels for toll road, tc is related to congestion pricing, and tp has the same definition for parking. Accordingly, our utility function is equal to:

U T = E ( y) + E ( t )

3.5. Select an experimental design that is sufficient not only to fit the proposed model, but which allows a test of model adequacy as well:

To examine how these allocations may be influenced by corresponding benefits, captured in terms of attributes, the three attribute levels for each of the three pricing options should also be varied. Commonly in stated preference experiments, orthogonal fractional factorial designs are constructed. The issue of orthogonality however is problematic in the current situation. Since the mixture amount needs to meet the budget constraints, in general these are non-orthogonal. Likewise, due to the number of choice sets, it is impossible to create an experimental design for the attribute levels which is orthogonal in it and in relation to the mixture amount design. In the present study, it was therefore decided to create an orthogonal Latin Square design for 3-level factors.

4. SAMPLE

An internet-based questionnaire was conducted in February 2012 to collect the data and estimate the model. The questionnaire was generated using Pauline, a platform for the generation of Web-based questionnaire, created by and for our research group. This platform consists of various simple and some more advanced template for creating questions. One such template is for creating choice experiments. The system also has multiple features to manage the implementation of choice experiments (blocking, randomization of attributes, attribute levels and choice sets, etc.).

The questionnaire consisted of two main parts. The first part concerns a set of questions related to personal and household characteristics. The second part concerned the choice experiment. As we were interested in how sensitive travelers are to price level, and whether the same preferred mixture of allocations applies at different expenditure levels, we consider three levels of the amount in a day (u1, u2, and u3) that they can spend on those policies in their daily travel: 6 €, 7.50 €, and 9 € per day. We also considered three time levels (5, 10 and 15 minutes), which they can save each day in their trip from home/work to their destination, according to their willingness to pay for a particular pricing policies. As mentioned before, we attached these levels to the attributes using an orthogonal Latin square design. According to Table 2, we have 7 choice sets from which respondents were asked to choose their best option. Table 3 shows an example of the choice sets in this experiment. In fact, it shows the fourth row in the Table 2.

According to the forth row in table 2 and the proportions in the table 1, in case of allocation 1, travelers spend

4 € (6*2/3) on toll roads which saves them 15 minutes of time, 2 € (6*1/3) on congestion pricing which again saves them 15 minutes, and they do not pay for parking. In case of allocation 2, there is no allocation on toll road,

5 € (7.50*2/3) spent to congestion pricing which saves them 5 minutes and 2.50 € (7.50*1/3) to parking which saves 15 minutes. Alternatively, in allocation 3, 9 € is equally allocated to toll road, congestion pricing and parking, saving 10, 5, and 15 minutes respectively.

In total, 304 respondents participated in this survey. Table 4 presents an overview of sample characteristics. Also, 63% of respondents mentioned that the main reason of their trip during the morning peak hours is going to work and 43% travel back from work and 24% attend to leisure and social activities in the evening peak hours. As work is a mandatory activity, it means there is more willingness to adapt for that compared to other activities. Thus, the sample is relevant for analyzing the effects of pricing policies as in the most countries mandatory activities, especially work activity are the target groups for policy makers.

5. Model Estimation

In this section, we will describe the results of a mixed logit model that was used to capture the relationship between the observed choice probabilities and the factors varied in the experiment. The parameters of the utility function, defined by Eq. 6, were estimated using Nlogit 4.0 [15] in a stepwise manner. We tried to keep the standard canonical form of the second degree model at a significance level of 10%. But after the first run, some

parameters were removed from the estimation, as they were highly insignificant. Interaction terms x2x3 (congestion pricing and parking price), x1x3 (toll road and parking price) and also interactions between amounts and toll road and congestion pricing, ux1 and ux2, were highly insignificant and therefore removed from the base part of the model. There are many distributions that can be used for the random parameters in the mixed logit model, the normal distribution being the most commonly used form. Nevertheless, if a researcher wishes to restrict a particular coefficient in the model to be positive or to restrict the range of variation of a parameter, then other distributions like the lognormal and triangular distribution can be used. In the current study, the triangular distribution was used for the random parameters in the utility function. The estimated parameters are presented in table 5.

Table 3. An example of a choice set

Choice Set 4 Toll Road Congestion Pricing Parking Price Choice

Expenditure (€/day) Saving Time(Min) Expenditure (€/day) Saving Time(Min) Expenditure (€/day) Saving Time(Min)

Allocation 1 4,00 15 2,00 15 0,00 0

Allocation 2 0,00 0 5,00 5 2,50 15

Allocation 3 3,00 10 3,00 5 3,00 15

Allocation 4

I don't want to choose any of those

Table 4. Composition of the sample

Sample Percentage

Gender

Female 146 0.48

Male 158 0.52

Younger than 25 37 0.12

25-40 88 0.29

40-60 124 0.41

Older than 60 55 0.18 Education

University Education 25 0.08

Higher professional education 78 0.26

Secondary vocational education 78 0.29

General and higher education 44 0.14

General secondary education 41 0.13

Other 38 0.13 Income

No more than € 650 20 0.07

€625-1250 61 0.20

€1251-1875 88 0.29

€1876-2500 90 0.30

More than € 2500 45 0.15

Table 5. Estimated parameters

Description P P{IZI>z} St. dev. P{IZI>z}

u Travel expenditure 1.122 0.0801 1.9590 .0000

u2 Second-degree travel expenditure -0.155 0.0005 0.1704 .0000

tt Travel time savings related to toll road 0.054 0.0004 0.2728 .0000

tc Travel time savings related to congestion pricing 0.132 0.0000 0.1591 .0000

x1 Toll road -3.839 0.0937

x2 Congestion pricing -4.842 0.0422

x3 Parking price -3.485 0.1394

x1x2 Interaction between toll road and congestion pricing -5.253 0.0007

tp Travel time savings related to parking 0.021 0.0848

Log-likelihood=-1489.147; Rho2 =0.495

As table 5 shows the estimated model has a pseudo-R2of 0.495. The p-value for all random parameters is less than alpha equal to 0.10 (i.e. 90 percent confidence interval). Thus, the mean of each random parameter is statically different from zero. Significant parameter estimates for derived standard deviations for the random parameters shows the existence of significant heterogeneity in these parameters estimate across the sample around the mean parameter estimate. The linear term of the travel budget has a positive sign and the quadratic term has a negative sign which is the expected form for the second-degree canonical model. It suggests decreasing utility with increasing amount. The single effects for toll road, congestion pricing and parking price are negative which shows that utility decreases if the share in the mixture for each of these policies increases and this reduction is higher for congestion pricing compared to other policies. However, the parameter related to parking is not significant at the predetermined significance level. The negative sign of the interaction term between toll road and congestion shows respondents' tendency to attach less utility to the combination of these policies. This finding strongly suggests that the Dutch population is not willing to pay for pricing policies which is in line with commonly held opinions that led to the current policy in the Netherlands.

Regarding time gained by choosing the priced choice alternatives, respondents showed similar patterns for all policies. The positive slopes for the travel time savings attributes indicate that respondents' utility increases for increasing savings in travel time associated with the various pricing policies. The relative size of estimates coefficients suggests that they are more sensitive to the benefits of travel time savings related to congestion pricing compared to toll roads and parking. More sensitivity of Dutch population to congestion pricing in both, share in the mixture and time benefits is expected. It may be because they are more familiar with the two others policies which have been implemented in practice in the Netherlands for some time while they know less about congestion pricing and its effects.

6. CONCLUSION

Pricing policies as examples of Transport Demand Management (TDM) have received increasing attention during the last decade and have been implemented around the world for different reasons. Accordingly, adaptive behaviour to different pricing strategies has been the focus of many studies lately. However, various aspects of this issue have not been studied yet. To address how travelers respond to accumulated pricing schemes, subject to budget constraints, we applied a mixture-amount design to study the effect of changing both the amount and the mixture of attributes. To the best of our knowledge, this is one of the first applications of mixture-amount choice experiments in transportation research. Moreover, by considering the effect of varying attributes levels, we

extend the classical mixture-amount design. The mixed logit model was used to estimate the parameters of the utility function. Results support the potential of the proposed approach. The study also showed that respondents are not overly willing to pay for pricing policies, although the effect of travel time saving is positive. Unobserved heterogeneity is however substantial. In future analysis, it may be relevant to consider the effect of socioeconomic variables that we left out from this analysis and categorize the sample according to travel time and further estimate the model on that segmentation.

Acknowledgement

The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 230517 (U4IA project). The views and opinions expressed in this publication represent those of the authors only. The ERC and European Community are not liable for any use that may be made of the information in this publication.

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