Geoscience Reference
In-Depth Information
As with the retail example, the SRMSE is used as the calibration statistic, and the absolute
entropy difference (AED) and R 2 are utilised as additional goodness of fit measures; see Knudsen
and Fotheringham (1986) for a further discussion of these measures.
7.8.5 r eSultS
The results presented here focus on the equation generation and calibration process to identify
appropriate SI model equations to represent the different categories of pupils based on the NCCOA
for the city of Leeds in the United Kingdom (see Table 7.5). Ultimately, each of the categories will
form a layer within the final model. One of the interesting findings from the GA was the breed-
ing of an alternative distance deterrence function to the standard negative exponential: a modified
gamma Tanner's function. As Openshaw (1998) notes, Tanner's distance deterrence function is
capable of representing more complex distance deterrence profiles than the smooth decreasing pro-
file produced by a negative exponential or power function. Both the standard negative exponential
and Tanner distance deterrence functions have been applied to Euclidean and network distances to
see which produces the optimal solution for this research problem. The final model configuration
and calibrations for the seven model equations bred by the GA for representing the pupils in each
NCCOA group are shown in Table 7.8.
An obvious point of note is that the SRMSE values for each of the SI model layers are greater
than one. This is due to (1) the size of the underlying origin-destination matrix and (2) the high
number of zero values within it. For example, in the 2004/2005 data, there were 2504 possible ori-
gin output areas (OAs) and 41 possible destination schools; this gives a matrix size of 102,664 cells
with 8,953 pupils. In 2005/2006, there were 2,411 possible origin OAs and 40 possible destination
schools resulting in a matrix size of 96,440 cells with 8,094 pupils. This led to the resulting interac-
tion matrices being sparse and produced high values of SRMSE.
7.8.6 i MPact of ga c aliBration on the SeM
The layers calibrated by the GA were input into the SEM; layer order was determined by the pro-
portion of pupils from each NCCOA group allocated to attend the school they expressed as their
TABLE 7.8
Summary of the Final Model Layer Configuration and Calibration
Calibration Parameters
Goodness of Fit Statistics
NCCOA
Group
Equation
d ij
par 1
par 2
par 3
SRMSE
R 2
AED
1
Euc
1.01
-1.40
3.07
0.69
0.03
exp(
D par
)exp(
d par
)
j
1
ij
2
2
Euc
0.45
-0.67
5.22
0.28
0.22
D par
exp(
d par
)
j
1
ij
2
3
Euc
1.59
-0.60
-2.15
2.92
0.81
0.03
exp(
D par
)exp(
d par d
)
par
3
j
1
ij
2
ij
4
Euc
0.84
-1.13
3.36
0.69
0.07
exp(
D par
)exp(
d par
)
j
1
ij
2
5
Net
0.96
-1.10
0.43
3.52
0.58
0.08
exp(
D par
)exp(
d par d
)
par
3
j
1
ij
2
ij
6
Euc
0.99
-1.28
3.71
0.63
0.06
exp(
D par
)exp(
d par
)
j
1
ij
2
7
Euc
0.70
-1.91
-1.33
3.58
0.50
0.25
exp(
D par
)exp(
d par d
)
par
3
j
1
ij
2
ij
Source: Harland, K. and Stillwell, J., Commuting to school: A new spatial interaction modelling framework, in
Technologies for Migration and Population Analysis: Spatial Interaction Data Applications , eds.
Stillwell, J.C.H., Duke-Williams, O., and Dennett, A., IGI Global Snippet, 2010.
 
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