Analysis of Journey to Work Travel Behavior by Car and Bus in the Sydney Metropolitan Region

Car dependence is a fundamental problem in the sustainability of cities with lowdensity suburban sprawl. Increasing the use of public transport is one of the policy objectives commonly adopted to overcome this problem. It is essential to study journey to work travel behavior by car and bus. This paper applied preference function to analyze travel behavior and Moran’s I spatial statistic to evaluate the spatial association. The results indicated that the commuting preferences of residents have moved towards distance maximization. In general, bus was preferred for shorter distance trips whilst car was preferred for longer distance trips. Unlike car, by increasing distances from the Central Business District, residents tended to use bus for shorter distance trip. A significant positive spatial association was identified for both the slope preferences by car and bus where zones with a preference towards longer or shorter trips tended to travel to zones with similar preferences.


Introduction
The internal structures of metropolitan regions have changed.Decentralization of employment towards the outer areas and suburbanization of residential areas with lower population densities has arguably increased car dependence.This condition has negative effects, among others; lost time and productivity, vehicular accidents, greenhouse gas emissions, deteriorating air quality and associated risks on respiratory and cardiovascular health [1].Evidence in Australia, and other countries, suggests that urban form is a significant factor in car dependence [2].
The reduction in Vehicle Kilometer of Travel (VKT) is one of the policy objectives adopted by many cities in order to achieve environmentally sustainable transportation.Intuitively, a more convenient location of employment relative to housing is expected to reduce the length of trips.Several studies argued that distance from the Central Business District (CBD) influences travel behavior.Empirical study conducted by Yang [3] indicated that decentralization was followed by different transportation outcomes.The academic literature on the impact of urban form on travel behavior has increasingly recognized that residential location choice and travel choices may be interconnected [4].
Improving the quality of urban public transport is one of many strategies proposed to improve mobility options and to address car dependence [5].However, Holmgren et al [6] identified that local public transport development in many European countries, has for a long time been on the decline.In developing country, Joewono and Kubota [7] stated that paratransit has an important role in providing feeder service to public transport user that has to be considered.According to Mulley and Nelson [8], public transport should be demand responsive.Therefore, it is important to understand factors influencing commuting preferences by public transport.
The journey to work is one of the most commonly experienced forms of every-day travel, encompassing almost all transport modes, and making a substantial contribution to urban traffic congestion [9].Montis et al [10] found that similar commuting networks emerge in similar geographical settings.Pattueli et al [11] applied spatial interaction models, which are modifications of gravity models, to study commuting networks by a comparative static approach using journey to work data in Germany.The weakness in most of the journey-to-work trip studies was the use of a static approach (i.e. the analysis was done at one point in time).It is essential to understand how commuting behavior contributes to either longer or shorter journeys.One way of doing this is to examine the commuting preferences of residents, and to establish how they have changed over time since the redistribution of employment and residential workers.Preference functions can be used to evaluate the behavioral response change of the residents following the change in urban form over time at the zonal level [12].However, it is quite difficult to find historical data where significant change in urban form followed by significant change in travel behavior.During 1981 to 1996 period there had been significant change in urban form and travel behavior in Sydney, Australia which was caused by massive decentralization.Using journey-to-work (JTW) census data over a 15-year period (1981 to 1996) in Sydney, this paper applies preference functions to study the journey-to-work commuting preferences by car and bus.The objectives of this study are: to analyze the stability of commuting distance preferences by car and bus of the Sydney's residents and to analyze spatial association of the slope preference functions among zones.

Theory of Preference Functions
Preference function is an aggregate of individual travel behavioral responses by a zonal grouping given a particular opportunity surface distribution of activities surrounding those travelers.Operationally, a journey-to-work preference function is the relationship between the proportions of travelers from a designated origin zone who reach their workplace destination zones, given that they have passed a certain proportion of the total metropolitan jobs.Conceptually, the raw preference function is simply the inverse of Stouffer's intervening opportunity theory [13].The intervening opportunity theory relates the proportion of migrants (travellers) continuing given reaching various proportion of the opportunities reached [13].Stouffer's hypothesis formed the basis of operational models of trip distribution in some early land-use and transporttation studies in the United States of America (for example, the Chicago Area Transportation Study during the late 1950s) [14], and is expressed as: Where: P(dv) : probability of locating within the dv opportunities (dv is the differential of v), P(dv) = dP; P(v) : probability of having found a location within the v opportunities; 1-P(v) : probability of not having found a location within the v opportunities; and f(v).dv: probability of finding a suitable location within the dv opportunities given that a suitable location has not already been found.
The term f(v) is often called the l parameter, or calibration parameter.It is the ordinate of a probability density function for finding a suitable location given that a location has not already been found.So, Equation 1 may be rewritten as: If l is a constant and the initial conditions are P=0 when v=0 then: Hence, Whereas Equation 4is used to derive trip distribution models, Equation 3 is the mathematical expression for the preference function.The relationship between the cumulative total number of opportunities passed, v, and the natural logarithm of the cumulative total number of opportunities taken, Ln (1-P), is assumed to be linear.One of the issues was calibrating the l-factor parameter [14], and whether there was a break of slope to justify different parameters for "short" and "long" trips.The logarithmic curve of the preference function might be linearized using natural logarithmic transformation.The shifting trend of the preference function can then be evaluated by analyzing the change in the slope of preference instead of using visual inspection on the superimposed curves.The shape of the observed preference functions is transformed as follow using regression analysis: where: Y = cumulative proportion of zonal metropolitan jobs taken from each origin zone; X = cumulative proportion of zonal jobs reached from each origin zone; a = regression coefficient; b = regression constant.
Unlike the raw preference functions these are the transformed preference functions with negative gradients.In the above formula, small (absolute) values of parameter a are associated with a preference for shorter trips whilst large (absolute) values are associated with a preference for longer trips, everything else being equal.The slope of these empirically determined preference functions tells us much about travel behavior as a pure response to opportunities, and not to transport impedance (distance, time or cost) as in the gravity model of trip distribution.

Spatial Statistics
To test the hypothesis of spatial stability, which implies that the preference function is similar across all geographical units, Moran's I statistic of spatial association [15,16] is used.There are qualitative differences among zones in terms of the preference function gradient, but a more rigorous test is required to discard the possibility that variation is random.A statistic of spatial autocorrelation, such as Moran's I [15,16], provides the tool to test this hypothesis.Spatial association is a measure of a variable's correlation in reference to its spatial location.In the case of Moran's I, the measure is that of covariance between variable values at locations sharing some sort of common boundary or connection.In general, when values are interrelated in meaningful spatial patterns it is said that there is spatial association.The statistic then measures the strength of the relationship, and its general quality.When similar values (in deviations from the mean) are found at neighboring locations, positive spatial autocorrelation results.When dissimilar values are found at neighboring locations, negative spatial association is said to ensue.Zero association is obtained when there are no significant similarities, or dissimilarities, amongst values, as would be the case for instance of a very homogeneous set of observations.Spatial association is computed by: (1) assigning weights to the cases, based on number of trips in a (square) Origin-Destination (O-D) matrix and the transpose Destination-Origin (D-O) matrix; (2) row-standardizing the matrix to obtain zonal trip proportions (so that the sum of proportions equals one in each row), to facilitate the comparison across zones to allow for spatial stability test.
The result is a connectivity matrix W that defines the 'neighborhood' (the zones with which there is interaction) for each zone.When using rowstandardized connectivity matrices, computation of Moran's I is achieved by division of the spatial covariation by the total variation: x ˆ= the weighted value of the observations wij = the proportion of trips between i and j , with respect to the total from i. A I is interpreted as the slope of a line passing through the origin.This decomposition into two variables, with one spatially lagged, can be illustrated as a scatter-plot to obtain a Moran's Scatter-plot [17].

Methodology
Sydney Metropolitan Region is selected as a case study area.The configuration of the 44 Local Government Areas (LGAs) is shown in Figure 1.Inter-zonal (LGA) distances over the road network were provided by the New South Wales State Transport Study Group, now the Transport Data Centre.Preference function is applied to study the journey-to-work commuting preferences by car and bus.Descriptive statistics and analysis of variance are applied to evaluate the trends in the slope preferences over time.Moran's I statistic of spatial association is used to study the spatial distribution of preference functions, and the pattern of interactions between zones, to assess the level of interaction and to test their statistical significance.The findings indicate that decentralization of employment towards the outer areas increased the behavioral preferences by car of residents in these outer areas towards longer trips, or a maximizing behavioral response.Therefore, future distribution of employment needs to be carefully located, because decentralization of employment is not associated with minimizing distance behavior for travel to work by car for outer ring residents.

Analysis of Commuting Preferences by Bus
Table 2 summaries descriptive statistics of the slope preferences by bus in Sydney over a 15-year period from 1981 to 1996.The descriptive statistics reveal that the absolute value of the slope preferences by bus has increased from 0.150 in 1981 to 0.169 in 1996.This indicates that the behavioral preference of residents for commuting by bus has moved toward longer trips or distance maximizing trends.
By increasing LGA distances from the CBD, Figure 4 shows that the absolute value of the slope preferences by bus tend to decrease.This indicates that LGAs located further away from the CBD have preferences towards shorter trips to work by bus.
Residents in the outer ring tend to use bus for local or short distance commuting trips only.

Spatial Analysis of the Commuting Preferences by Car
Figure 6 shows the Moran's scatter-plot for the slope preferences by car in Sydney in 1996.To facilitate interpretation, the variables have been normalized with respect to the mean (PF) and standard deviation (s).The PF is used as a spatial variable and analyzed using Moran's I.The result indicates a positive spatial autocorrelation where similar values are found at neighboring locations with I = 0.562.The Z-statistic, Z(I) = 11.729(α = 0.05) shows that the pattern deviates significantly from a random pattern where the zones interact with others with similar preference.Figure 6 shows that the zonal slope preferences by car in Sydney in 1996 are predominantly within one standard deviations of the mean.However, Parramatta (Zone 30) is found to have a value of the slope preference by car that is more than two standard deviations higher than the mean (on horizontal axis of Figure 6) despite the fact that it has a relatively high concentration of employment and is regarded as the second CBD in Sydney.On the other hand, Wyong (Zone 44) and Gosford (Zone 15) have values that are more than two standard deviations lower than the mean (negative side of the horizontal axis).The relative isolation of Wyong and Gosford from the other LGAs has shaped residents preference for shorter travel and many find their jobs locally.
At the bottom part of Figure 6, a scatter-plot of the average change in the slope preference by car per five years is presented.It is shown that the LGAs in Sydney mainly experienced changes in the slope preferences by car with values within one standard deviation of the mean.However two extreme cases were identified.Although having a low slope preference by car (absolute), Gosford (Zone 15) and Camden (Zone 9) experienced an increase in the absolute value of the slope preference by car per five years and was over two standard deviations higher than the mean.Increasing numbers of job opportunities available in this LGA and surrounding LGAs over time as a result of decentralization, have changed the behavioral response of residents towards distance maximization, where an increasing number of people are employed in the other surrounding LGAs.By considering the destination-origin (D-O) matrix, a positive spatial association is also experienced as shown in Moran's scatter-plot (Figure 10).Zones with preference towards distance maximization tend to attract trips from zones which also show maximization preferences.On the other hand, zones with preference towards distance minimization tend to attract trips from zones with similar preferences.This positive spatial association is confirmed further from Moran's I statistic with I = 0.589 and Z(I) = 4.90 (α = 0.05).

Conclusions
The results of preference functions analyses indicated that the mean slope preference by car has increased over time showing an increasing preference of residents towards distance maximization for traveling to work by car.The slope preferences by car for the inner and middle ring residents are relatively stable over time whilst the outer ring residents (beyond 20 km from the CBD) experienced a dramatic increase.
Similarly the commuting preference by bus is found to move towards distance maximization over time.By increasing distances from the CBD, the absolute values of slope preferences by bus tend to decrease.This shows that the outer ring residents tend to use bus for shorter distance trips (more than that of the inner and middle ring residents).For the zonal slope preferences by car, a significant positive spatial association was identified for both supply and demand sides.Zones with a preference towards long trips, on average, tend to travel to zones that also prefer longer trips.On the other hand, zones with a preference towards shorter trips, travel to zones that also have preference for shorter trips.
A significant positive spatial association is also identified for the slope preferences by bus for both O-D and D-O matrices.One extreme case is identified where Sydney LGA (Zone 38) has slope preferences beyond four standard deviations on the maximization side.Scatter-plot of the average change in the slope preferences by bus per five years further indicates that the Sydney LGA has an extreme value.The change in the slope preferences by bus in the Sydney LGA is over six standard deviations higher than the mean value.This indicates an increasing preference of residents in the Sydney LGA (CBD) to use bus for traveling to work for longer distances over time.It is clearly shown from these results that when increasing job opportunities are available in the surrounding zones, residents tend to travel longer to reach job opportunities available in the other zones, in particular, in the case of job-skill mismatch.Therefore, it is not surprising that a dramatic increase in preference for longer trips has been experienced by outer ring residents in Sydney where job decentralization continues to occur over time.

Figure 2
Figure2shows the slope preferences by car for 44LGAs in Sydney by increasing LGA distances from the CBD over a 15-year period from 1981 to 1996.The slope preferences by car for the inner and middle ring residents (within 20 km of the CBD) are relatively stable.In contrast, the outer ring residents, beyond 20 km from the CBD mainly experienced a significant increase.SeveralLGAs show drastic changes of the slope preferences as shown in Figure3.South Sydney (Zone 35) experienced the highest increase in the inner ring in absolute terms (about 0.015 per five years).Auburn (Zone 2) had the highest increase in the middle ring.Several extreme cases were found in the outer ring such as in Gosford (Zone 15), Camden (Zone 9), and Wyong (Zone 44).

Figure 3 .
Figure 3. Change of slope preference by car in Sydney per five years by increasing distance from the CBD

Figure 5
Figure5shows the average change of slope preference by bus per five years by increasing distance from the CBD.On average in the outer ring, the slope preference by bus has increased by about 0.091 per five years.On the other hand, residents in the inner ring tend to use bus for traveling to work for longer distance commuter trips.A substantial increase in the absolute value of the slope preferences by bus is experienced in the Sydney (Zone 38) (about 0.145 per five years from 0.240 in 1981 to 0.676 in 1996).

Figure 5 .
Figure 5. Change of slope preference by bus in Sydney per five years by increasing distance from the CBD

Figure 6 .Figure 7
Figure 6.Moran's scatter-plot for slope preferences by car using O-D matrix Figure 7 further shows Moran's scatter-plot for the zonal slope preference by car considering destination-origin (D-O) matrix or demand side.Zones with minimization preferences (low value of slope preference) tend to attract trips from zones with similar preferences whilst zones with maximization preferences (high value of slope preference) tend to attract zones also with maximization preferences.The result of Moran's I (I = 0.710) indicates the existence of positive spatial autocorrelation which is statistically significant (Z(I) = 15.21 for α = 0.05).

Figure 7 .
Figure 7. Moran's scatter-plot for slope preference by car using D-O matrix

Figure 10 .
Figure 10.Moran's scatter-plot for slope preferences by bus using D-O matrix [16]nical details see Cliff and Ord[16]).A useful characteristic of the above statistic, more easily seen if represented in matrix notation, is its formal resemblance to a regression of the spatially lagged variable x Wˆon variable x ˆ: zero value of I represents random variation, and thus no spatial autocorrelation.Values near +1 indicate a strong spatial pattern.Values near -1 indicate strong negative spatial autocorrelation; high values tend to be located near low values.Inference can be carried out by comparing it to its expected value and variance, to obtain a normalized statistic Z(I), since the statistic is asymptotically normally distributed (for

Table 1
is a summary of descriptive statistics of the slope for commuting preferences by car in Sydney over a 15-year period from 1981 to 1996.The absolute value of the mean slope preference by car increased by 0.013 over this period from 0.195 in 1981 to 0.208 in 1996.

Table 1 .
Summary of descriptive statistics of the slope preferences by car in Sydney 35 Figure 2. Slope preference by car in Sydney by increasing distance from the CBD

Table 2 .
Summary of descriptive statistics of the slope preferences by bus in Sydney 38Figure 4. Slope preference by bus in Sydney by increasingLGA distance from the CBD