Model Validation 2 MLR Model using Observed Variables 2

88 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 probability value range from 0 to 1. 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 Figure 36. Conditional Probability Maps of Land Use Transitions 2 nd Scenario 89 Probability Map for GF PY11 Probability Map for GC PY12 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 Figure 36. Conditional Probability Maps of Land Use Transitions 2 nd Scenario Continue 90 Probability Map for OC PY23 Probability Map for OG PY24 Probability Map for OS PY25 Probability Map for OO PY26 Figure 36. Conditional Probability Maps of Land Use Transitions 2 nd Scenario Continue The conditional probability maps of land use transitions 2005 – 2008 using observed variables have been produced are shown in Figure 36 above. Compare to the result of MLR model simulation using all significant variables as the parameters which only 63.45 of the total area of Siak District could be simulated, the conditional probability maps of land use transitions using observed variables show that the result of this MLR model simulation could cover the whole area of Siak District. This condition could be happen because of this model simulation involved only 5 variables into the model which means its MLR model only forces fewer variables easily rather than the MLR model developed in the 1 st scenario of MLR model analysis. This result strengthens the research findings on land use change modeling using MLR model which the MLR model is a generalized logistic regression model which conditioned all response categories having the same parameters, and forces every land use transitions to be driven by the significant parameters which have been determined. The next procedure of model validation which is the same with the 1 st scenario is comparing the conditional probability maps of land use transitions 2005 – 2008 and 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 in order to examine the statistical properties 91 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 research found that the statistical properties of MLR conditional probability values for each land use transition in actual condition 2005 - 2008 are various. However, the model validation done using MLR Model which developed from observed variables show that only 3 land use transitions CC, GG, and WW which have Max value higher than 0.5, and the rest 23 land use transitions have Max value less than 0.5. Furthermore, the land use transition CC cropland in stable condition has a good distribution of probability values which range from 0.42 to 0.72, while other land use transitions that have large range of values and they are distributed under the threshold of 0.5. Similar with the 1 st scenario, these statistical properties show that the final model could not fit the actual spatial data layers into the actual condition of land use change 2005 – 2008. 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 ilit y Min Max Mean Std Dev Figure 37. The Statistical Properties of MLR Conditional Probability Values in Actual Land Use Change 2005 – 2008 2 nd Scenario 92 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 38. The Distribution of MLR Conditional Probability Values in Actual Land Use Change 2005 – 2008 2 nd Scenario The model validations have been conducted in two scenarios regarding to the two models developed using all significant variables 24 variables and observed variables. These two scenarios of land use change modeling using MLR model could give better understandings on advantages and disadvantages of MLR model for modeling land use change. These research findings on land use change modeling using MLR model would be concluded in the next chapter.

4.5 Research Findings on Land Use Change Modeling using MLR Model

Based on the result of model validation that has been discussed, there are some research findings and recommendations, which can be concluded, which may improve the land use change modeling by using logistic regression model in the future research. The significant test for the final models from two scenarios done in statistical MLR model analysis indicate the land use change models which have been developed are adequate models which can explain many variability of the land use transitions, however, the model validations which have been conducted spatially indicate the final model could not fit the actual spatial data layers into the actual condition of land use change 2005 – 2008. The land use change model that has been developed by using MLR model is a generalized model of logistic regression, which forces every land use 93 transitions to be driven by all significant parameters, while in the real condition each land use transition probably has unique combination of parameters which drive its land use transition. Probably, it will be better to use the binary logistic regression in order to find the best fit model for each land use transition individually by considering unique combination of parameters of each land use transition which may involve into its model. Hopefully, by doing this method it will produce the conditional probability maps of land use transitions which can cover the whole area or most of the research area, increase the probability values for each projected land use transition, and also narrow the range and data distribution of the probability values of each projected land use transition when it is compared to the actual land use change, in order to develop the adequate land use change model which is good statistically and spatially. However, the binary logistic regression model analysis which should be done in order to find the significant variables and the best fit model for each land use transition will be time consuming since the model analysis should be done individually regarding to the land use transitions that happen in the research area. The other issue which is considered in this research is about the effects of the predictor variablesparameters on the dependent variable. The individual coefficients of the parameters of the multiple regression can only be interpreted for direct effects on the dependent variable when the other predictor variables are held constantly James and McCulloch 1990 in Millington et al. 2007, and this issue also happen in multinomial logistic regression. Millington et al. 2007 proposed Hierarchical Partitioning HP method might be chosen to address that issue. HP estimates the contribution of each predictor variable to the total variance explained by a model, both independently and in conjunction with all other variables by separating all possible candidate models that is, combination of predictor variables into a set of hierarchies and comparing them Millington et al. 2007. Hopefully, by doing the HP method the effects of the predictor variablesparameters to land use change can be observed, both independently and in conjunction with all other variables.