Local Analysis and Rail Demand Modelling

It seems obvious that some form of local analysis should be incorporated in rail demand models, and Table 3.1 outlines the key strengths and weaknesses of the various techniques when applied to modelling rail demand. This comparison indicates that the two methods with most potential for enhancing rail demand modelling are geographically weighted regression and the spatial expansion method. GWR is undoubtedly a more powerful method, because it can account for much more complex spatial variation than the

expansion method, and if it can be implemented successfully should give a more reliable indication of the local impact of different factors on rail demand. It is though significantly more complicated than the simple form of the expansion method as outlined in equations 3.7-3.10, and as it requires much more processing the use of both methods will be

investigated to establish whether the results from GWR are sufficiently superior to justify the extra time required.

Table 3.1: Strengths and weaknesses of local analysis techniques

Technique Strengths Weaknesses

Geographically

weighted regression Results not affected by zoning system or edge effects Local parameter estimates can be mapped

Software inexpensive and easy to use Regression points need not coincide with data points – important for modelling new stations

Outliers harder to detect than in global regression models

Moving window regression

Local parameter estimates can be mapped

Relatively simple to use

Results dependent on zoning system Edge effects likely to occur

Spatial expansion

method Similar principles to some existing rail demand models Recognises explicitly that parameters in regression models can be function of context

Can be calibrated using SPSS

Form of expansion equations must be determined in advance

Complexity of trends identified depends on complexity of expansion equations, so local variation may be obscured

Spatially adaptive

filtering Local parameter estimates can be mapped Results highly dependent on specification of zoning system Zones have multiple neighbours and thus processing times may be lengthy

Model iterations may not always converge

Spatial smoothing of parameter estimates unrealistic in some cases

Multilevel modelling Explicitly distinguishes between

personal and place characteristics Highly complex modelling frameworkUnrealistic reliance on precisely defined set of spatial units

Difficult to obtain suitable data for rail demand modelling at individual level Random coefficient

models

Allow high levels of variation Local parameter estimates can be mapped

Not intrinsically spatial

Random coefficients pay no attention to parameter location

Spatial regression

models Local relationships incorporated into modelling framework Limited diagnostic potential – difficult to identify factors causing variation Does not produce local parameter estimates

No universally accepted method for estimating weights

Calibration far from straightforward Local spatial

interaction models

Yield more information than global spatial interaction models

Disaggregation for discrete points rather than continuous space

Not appropriate for trip end models

GWR has been applied extensively to explore a range of spatial phenomena, but while its use has been investigated for some transport-related applications (Du & Mulley (2006), Clark (2007)), as far as the author is aware it has not previously been applied to rail demand modelling. There are some specific problems involved in using GWR to forecast local rail demand. Data on the independent variables for such modelling (the factors determining demand) is not usually collected at the same points as the dependent variable (the number of trips from a particular station). If detailed information has been collected on the actual start and end points of trips then population units such as census output areas can be used as the data points for GWR, but such data is far from universally available.

Otherwise it will be necessary to aggregate data on independent variables for entire station catchments and use the stations themselves as the data points for regression. If this method is used it is desirable to use a large dataset so that patterns in variation between stations in different areas can be adequately illustrated, as otherwise there will be insufficient data points to give reliable results. This is not an ideal solution as it requires that some prior assumptions about the nature of station catchment areas must be made, and these

assumptions will affect the parameter estimates. An alternative way around this problem would be to concentrate on investigating variations in rail trips to work, as country-wide data is available on the number of rail trips to work from individual census output areas, which are the smallest spatial units at which data on variables such as population is available, although in practice there are problems with this dataset (see Section 3.6.2.4).

Whichever solution is ultimately adopted, both the spatial expansion method and GWR should provide additional information to that provided by simply mapping the residuals from a global regression model as they make it possible to establish which parameters are responsible for variation in the size of the overall residuals. Local analysis can be seen as a model-building procedure (Fotheringham et al., 2002) in which the ultimate goal is to produce a global model of rail demand that exhibits no significant non-stationarity. By identifying variations in parameters it should be possible to hypothesise on the causes of these variations, and thus develop extra parameters to improve the fit of global demand models.