An analysis of travel time elements and the interconnectivity ratio 1
6.8 Regression models
e regression models attempts to explain the infl uences of various explanatory factors on the separate travel time elements (access, egress and line-haul times) and the resultant interconnectivity ratio. Less emphasis is placed on the predictability of travel time (and the ratio) and, as such, fi ndings of non-signifi cance are as important as fi ndings of signifi cance. e time elements were transformed (log for access, egress and line-haul time and square root for the interconnectivity ratio) to obtain more normal distributions. As such, interpretation of the coeffi cients should be treated with the necessary caution.
In addition to the variables discussed, extensive sets of variables were tested for their infl uence on the diff erent time elements. ese variables include socio-demographic characteristics, land-use and urban form attributes, trip and transport characteristics, and individual activity programme variables. Only variables that showed some discernible diff erences or were considered to be of particular relevance (based on past approaches and policy infl uence) were included in the models.
e process of estimating the regression models consisted of two phases. In the fi rst phase, a base model, which only included the socio-economic and transportation variables – the control variables – were estimated. Land use models were subsequently estimated by adding the land- use (density and speciality indices) and urban form (trip orientation) variables. For the land- use models, hierarchical regression was used. e order of entering of the variable blocks was determined by their additive power to the R²
determined by their additive power to the R²
determined by their additive power to the R , determined in extensive pre-analysis. Only the results for the fi nal land-use models are presented. Access and egress results are presented in Table - while Table - shows the results for the line-haul time and interconnectivity ratio.
Only the main fi ndings are reviewed.
.. Access and egress
Generally, the explained variances for the access and egress models are rather low, i.e. and
(Table -). Previous research also suggested that it is notoriously diffi cult to estimate these stages of public transport trips, and travel time in general (Bovy and Jansen, ; Levinson and Kumar, ; Ortúzar and Willumsen, ).
Few of the socio-demographic variables were signifi cant and their infl uence was rather limited (i.e. less than of the total explained variance is contributed by the socio-demographic variables for the access and egress time models). Males have a shorter egress time while travellers from households with children (< ) have a shorter access time. Individuals with young children will arguably choose closer transfer locations to counter the added burden of accompanying young children.
More signifi cant fi ndings were obtained with the transport variables. Transfers lead to shorter access times, which might point to the inverse relationship between access time and transfers.
By assuming longer access time, people may be in a position to get to a more direct connection requiring fewer transfers. e non-signifi cant relationship for egress and transfer might imply that people are less well informed about transfer locations at their destination, as they are generally less well informed about the destination.
e use of the bicycle leads to respectively shorter and longer access and egress times; however, as also supported by Figure -, the coeffi cient is much stronger for egress than access. Access as well as egress time is positively associated with line-haul time and again the coeffi cient is much larger for egress than access. is relationships holds even after controlling for trip orientation, i.e. intra- vs inter-urban and other trip orientations.
e urban form and land-use variables showed diff ering infl uences on access and egress, but also non-linear properties. e diff erent coeffi cient signs for access and egress might indicate that access and egress respond diff erently to density and, importantly, factors associated with density. For example, access travel time might increase as a result of pedestrian congestion associated with higher densities as travellers converge on a single station. On the other hand, egress travel time might refl ect the shorter distances between station and the fi nal destination associated with higher densities and less congestion as travellers diverge from the station.
Although not all the density variables are signifi cant, the coeffi cient signs for the access and egress time models are the same for both sides of the reference category (i.e. positive for the access time and negative for the egress time). is might imply a non-linear relationship between density and access/egress travel behaviour. Frank and Pivo (), in studying the impacts of land-use on travel behaviour, also found a non-linear relationship with an infl ection point for density around persons per acre. is translates into roughly persons per hectare, which is very similar to the intermediate density category (± persons/ha) used in this research as reference category (Frank and Pivo, )⁶.
.. Line-haul and interconnectivity ratio
For the line-haul model, the explained variance is well above that obtained for access and egress, i.e. . e two socio-economic variables signifi cant on the .-level are intuitively appealing. Males (compared to females) travel longer while persons younger than years old travel shorter. It is generally supported in the literature that those younger than work closer to home than the older age categories while men tend to have a longer commute. Transfers, as expected, lead to signifi cantly longer line-haul times while the use of ‘other’ egress modes (car driver, passenger or taxi) is associated with signifi cantly longer line-haul times. Longer access time is associated with longer line-haul time (as also shown by the access model) but the fi nding for egress time is not signifi cant (possibly as the result of diff erent variables in the line- haul model). As Table - shows, all the other trip motives are associated with shorter line-haul times compared to the reference category.
As discussed, the interconnectivity ratio is a composite function of all the other travel time elements. eoretically, all the variables that infl uence the other elements will infl uence the interconnectivity ratio and are, therefore, candidates for entry into the regression models. In
Table -: Regression models: access and egress time
Access Time Egress Time
B t B t
(Constant) 1.763*** 4.762 2.262*** 5.238
Socio-Demographic
Female vs Male -0.006 -0.115 -0.150** -1.955
Car vs No Car Car vs No Car
Car -0.045 -0.691 0.099 1.107
Age: 30-40: < 25 0.387** 2.122 0.030 0.121
25-30 0.010 0.104 0.166 1.274
40-50 -0.034 -0.458 0.036 0.377
50-65 0.058 0.679 0.133 1.255
Household with no child: 0 -17
HH with Child < 6 -0.135** -1.789 -0.046 -0.462
HH wit Child 6-17 -0.026 -0.356 -0.052 -0.557
Dual Income vs Non-dual Income 0.100* 1.599 -0.001 -0.009
Transport
Off-Peak (Peak) -0.052 -0.644 0.257** 2.298
Transfers # -0.134*** -2.851 -0.065 -1.031
Walking vs.
Walking vs.
Walking Other 0.131 1.159 -0.526** -1.786
Bicycle 0.143** 2.278 0.337*** 3.701
Line-Haul Time 0.090** 1.800 0.134** 1.926
Access/Egress Time 0.055 1.244 0.068 0.869
Trip motive variables
Education 0.017 0.087 0.380* 1.509
Shopping 0.158 0.926 -0.100 -0.522
Leisure 0.015 0.132 0.278* 1.705
Other -0.025 -0.237 0.036 0.251
Urban form variables
Intra-urban vs Inter-urban 0.044 0.531 0.016 0.149
Other (between outlying areas)
0.303** 2.364 -0.084 -0.634
Origin/Destination Location CBD vs Urban, non CBD
0.080 0.085 0.093 1.099
Town Centre -0.080 -0.616 -0.135 -0.726
Other 0.629*** 2.727 0.017 0.137
Land use variables (3) Intermediate density:
(1) Very High 0.255** 2.183 -0.202 -1.140
(2) High 0.128 1.210 -0.371** -1.916
(4) Moderate 0.103 0.727 -0.327* -1.663
Speciality -0.001 -0.166 -0.006* -1.675
(Adjusted) R2 0.13 0.14
Reference category for dummy variables in italic
* P < 0.1; ** P < 0.05; *** P < 0.01
The land-use variables have been operationalised as follows:
• Density (separate for origin and destination) refers to density per neighbourhood and the measure is a refl ection of the density of addresses (Highly urbanised: > = 2500 addresses per km2; Strong urbanised:
1500 – < 2500; Intermediate Urbanised: 1000 – < 1500; Modestly urbanised: 500 – < 1000; Not Urbanised;
< 500 address per km2). Classifi ed as (1) Very high, (2) High, (3) Intermediate and (4) Moderate.
Intermediate used as reference category.
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• Diversity/Speciality index is based on the Hirshman-Herfi ndahl index (Duranton & Puga, 2000) and is given by: Indexi (SI) = MaxMaxMax (land use typeii ij)
Three types of land-uses are considered. Percentage of (1) fi rms in industry and building services, (2) commercial service delivery and, (3) other non-commercial businesses. The higher the value, the more specialised a zone is in a particular land-use. Does not give an indication of the type of specialisation.
Table -: Regression models: line haul time and interconnectivity ratio
Line Haul Time Interconnectivity ratio
B T B T
(Constant) 1.706*** 7.491 0.782*** 22.158
Socio-Demographic
Female vs Male 0.111** 1.855 -0.015 -1.247
Car vs No Car Car vs No Car
Car -0.019 -0.279 0.002 0.140
Age: 30-40: < 25 -0.524*** -2.785 0.034 0.892
25-30 -0.053 -0.509 0.001 0.065
40-50 -0.053 -0.672 -0.013 -0.831
50-65 -0.046 -0.519 -0.005 -0.255
Household with no child:0-17
HH with Child < 6 -0.003 -0.033 -0.020 -1.191
HH wit Child 6-17 -0.109* -1.425 0.011 0.679
Dual Income vs. Non-dual Income 0.039 0.598 0.009 0.705
Transport
Off-Peak (Peak) 0.038 0.441 -0.008 -0.475
Transfers # 0.246*** 5.290 -0.071*** -7.579
Access:Walking vs OtherWalking vs OtherWalking 0.167* 1.355 -0.031 -1.249 Walking vs Bicycle
Walking vs Bicycle
Walking 0.139** 2.123 -0.023* -1.708
Egress:Walking vs OtherWalking vs OtherWalking 0.599*** 3.194 -0.115*** -2.961 Walking vs Bicycle
Walking vs Bicycle
Walking -0.114* -1.504 0.021* 1.406
Access Time 0.165*** 2.610
Egress Time 0.058 1.198
Trip motive variables
Education -0.365** -1.966 0.050 1.342
Shopping -0.523*** -3.295 0.019 0.673
Leisure -0.271** -2.104 0.060** 2.275
Other -0.222** -1.890 -0.018 -0.763
Urban form variables
Intra-urban vs Inter 0.636*** 8.552 -0.053*** -3.623
Other 0.414*** 3.950 -0.039* -1.685
Origin = CBD vs
Urban, Non-CBD 0.026** 1.836
Town Centre 0.028 1.180
Other -0.026* -1.426
Destination = CBD vs
Urban, non CBD 0.017 0.798
Town Centre 0.019 0.783
Other 0.009 0.255
(Adjusted) R2 0.41 0.27
Reference category for dummy variables in italic
* P < 0.1; ** P < 0.05; *** P < 0.01
order to avoid over-fi tting and facilitate the discussion, only the land-use and urban form variables that showed up as signifi cant for the three travel time models are included. e control variables are entered in total.
e adjusted R²
e adjusted R²
e adjusted R () for the interconnectivity ratio is higher than the one for access and egress but lower than the one for the line-haul time model. Generally, the results for the ratio refl ect the results of the separate travel time models and should be interpreted by referring to the separate models. Consider for example, the negative coeffi cient of the transfer variable, which is positive on the line-haul time and negative on the access and egress times, leading to a smaller interconnectivity ratio. e inter-urban and other trip orientations lead to a much smaller ratio as these variables also refl ect longer line-haul times.