Model Validation 1 MLR Model using All Significant Variables 1
75 parameter estimates produced in MLR model analysis and the actual spatial data
layers in 2005 into MLR model equation Equation 1 and 2. The parameter estimates in logistic regression contain the coefficients of the parametersvariables
β included in the final model, and it summarizes the effect of each parameter. The spatial data layers in 2005 see Appendix 4 which would be functioned as
parametersvariables x in the MLR model equation have been prepared by the same procedures when preparing the spatial data layers in 2002 for MLR model
analysis. Table 18. MLR Model Equation: Logit Functions and Conditional Probability
of Each Land Use Transition
Equation 1. Logit Functions Equation 2. Conditional Probability
of Land Use Transition
The coefficient of the parameters β
i
in Parameter Estimates and spatial data layersparameters 2005 x
i
have been simulated on MLR model equation by using raster calculator, so it would produce the conditional probability maps of
land use transitions during 2005 – 2008. Two steps of computations have been done in order to simplify the conditional probability maps simulations that were
Logit Functions Equation 1 and Conditional Probability of Land Use Transition Equation 2.
The computation of coefficient of the parameters β
i
and spatial data layersparameters 2005 x
i
on MLR model equation produced 26 conditional probability maps of outcome categories in accordance with number of land use
transitions in Siak District. These conditional probability maps show the probability of each land use transition may occur in the research area, with
76 probability value range from 0 to 1. The conditional probability maps of land use
transitions 2005 – 2008 which have been produced are shown in Figure 28.
Probability Map for FF PY01 Probability Map for FC PY02
Probability Map for FG PY03 Probability Map for FS PY04
Probability Map for FO PY05 Probability Map for CF PY06
Probability Map for CC PY07 Probability Map for CG PY08
Probability Map for CS PY09 Probability Map for CO PY10
Probability Map for GF PY011 Probability Map for GC PY12
Figure 28. Conditional Probability Maps of Land Use Transitions 1
st
Scenario
77
Probability Map for GG PY13 Probability Map for GS PY14
Probability Map for GO PY15 Probability Map for WW PY16
Probability Map for SF PY17 Probability Map for SC PY18
Probability Map for SG PY19 Probability Map for SS PY20
Probability Map for SO PY21 Probability Map for OF PY22
Probability Map for OC PY23 Probability Map for OG PY24
Figure 28. Conditional Probability Maps of Land Use Transitions 1
st
Scenario Continue
78
Probability Map for OS PY25 Probability Map for OO PY26
Figure 28. Conditional Probability Maps of Land Use Transitions 1
st
Scenario Continue
The conditional probability maps of land use transitions show that the result of the MLR model simulation could not cover the whole area of Siak
District. Only 63.45 of the total area of Siak District could be simulated by the MLR model, and the rest of the area which is 36.55 of Siak District could not be
simulated. This situation revealed after the MLR model computation was conducted in spatial manner. It may be caused by the nature of MLR model which
is a generalized logistic regression model which conditioned all response categories having the same parameters. The MLR model forced every land use
transitions to be driven by all significant parameters which have been determined, while in the real condition each land use transition probably has unique
combination of parameters which drive its land use transition. Eventually, the MLR simulation in this research produced the generalized conditional probability
maps of land use transitions which could not cover the whole area which has been simulated.
Figure 29. The Aggregation of Conditional Probability Maps of Land Use Transitions
79 The conditional probability maps of land use transitions which have been
produced in this research show that the range of probability values for a land use transition varies if it is compared with other land use transitions. In general, the
probability values of all land use transitions range from 0 to 0.999. The ranges of probability values covered only the area which could be simulated by the MLR
model simulation covered 63.45 of the total area of Siak District. In order to examine the performance of final model of land use change in Siak District that
has been developed, this research compares the conditional probability maps of land use transitions 2005 – 2008 with the actual land use transitions 2005 – 2008.
The comparison between the conditional probability maps of land use transitions 2005 – 2008 and the actual land use transitions 2005 – 2008 have been done by
overlaying intersecting the maps individually; the conditional probability map of a land use transition with its actual land use transition map. Then, the basic
statistical properties Min, Max, Mean, and Standard Deviation were derived from the intersected maps in order to examine the statistical properties of the
probability values in actual condition. Furthermore, the distributions of MLR conditional probability values in actual condition were also derived by subtracting
and adding the mean value with standard deviation value which would produce lower bound and upper bound of data distribution respectively. The statistical
properties of MLR conditional probability values in actual condition 2005 – 2008 is shown in the Figure 30, whereas Figure 31 show the distribution of the
most probability values about 68 by assuming its values distributed in normal distribution.
The research found that the statistical properties of MLR conditional probability values for each land use transition in actual condition 2005 - 2008 are
various. The minimum values of every land use transitions are close to 0, but the maximum values vary. There are 14 land use transitions which have Max value
higher than 0.5, and the rest 12 land use transitions have Max value less than 0.5. These conditions have caused the range Min-Max of probability values are also
various for every land use transitions. Furthermore, the distribution Lower-Upper bound of probability values that have been examined show that the data
distributions vary for every land use transitions. There are some land use
80 transitions that have narrow range of data distribution, and some other land use
transitions that have large range of values.
The Statistical Properties of MLR Conditional Probability Values
in Actual Land Use Change 2005 ‐ 2008
0.0 0.1
0.2 0.3
0.4 0.5
0.6 0.7
0.8 0.9
1.0 1.1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Land Use Transition
P ro
b a
b ili
ty
Min Max
Mean Std
Dev
Figure 30. The Statistical Properties of MLR Conditional Probability Values in Actual Land Use Change 2005 – 2008 1
st
Scenario
The Distribution of MLR Conditional Probability Values
in Actual Land Use Change 2005 ‐ 2008
‐0.1 0.0
0.1 0.2
0.3 0.4
0.5 0.6
0.7 0.8
0.9 1.0
1.1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Land Use Transition
P ro
b a
b ilit
y
Mean Lower
Bound Upper
Bound
Figure 31. The Distribution of MLR Conditional Probability Values in Actual Land Use Change 2005 – 2008 1
st
Scenario Actually, the examined Min-Max values and data distribution of
probability values for every land use transitions were expected to have narrow range that is located between 0.5 – 1.0 in order to conclude that the land use
81 change model for Siak District could fit the actual spatial data layers correctly.
However, the result of this model validation can be used as consideration for the future research of land use change modeling using logistic regression model in
order to develop the adequate land use change model which is good in statistical and spatial manners.