From the step-wise discriminant analysis, it was found that all factors were important in discriminating the three development groups. Table 2 shows the constant and coefficients of the unstandardised discriminant functions of the original model. These constant and coefficients can be substituted into equation (2) and use to calculate the discriminant score for each function. The equations can be stated as follows:
Function 1 = -.72608 + .00029X1
Function 2 =
-2.05831 + .00011X1
+ - .00010X3
Group means derived from the discriminant analysis
Discriminant score derived from the two functions can be used to predict/determine the grouping of the unclassified cases. There are several ways to determine the grouping. One way is to compare the discriminant score with the group means. Table 3 shows the group means for the original model. From the table, it can be seen that Function 1 is useful for discriminating group 1 from groups 2 and 3. This is because the mean for groups 1 is positive while the means for group 2 and 3 are negative. On other hand, Function 2 is useful for discriminating group 2 from group 1 and 3. This is because the mean for groups 1 and 3 is positive while the means for group 2 are negative. The fact that cases with positive discriminant score in Function 1(X<0.0) will be classified to belong to group 1. By leaving out cases in group 1, the cases with negative discriminant score will be classified to belong to group 2 and group 3.
Classification accuracy of the original model
Percentage of group correctly classified: 74.9 %.
||No. of cases
||2856 (87.5 %)
||186 (6.3 %)
||201 (6.8 %)
||146 (18.4 %)
||467 (58.9 %)
||180 (22.7 %)
||431 (21.0 %)
||315 (15.3 %)
||1311 (63.7 %)
Table 4 shows the accuracy of the original model. From that table, the accuracy for group 1 is highly (87.9%) compare with group 3 (63.7%) and group 2 (58.9%) as well. From group 2 the error or confusion matrix is 22.7%. This is because the factors have been identified confused to differentiate between commercial land use development and other development. However the accuracy for group 3 are not very differ with group 2 namely 63.7% was correctly classified and 15.3% has been classified belong to group 2. The overall of the original model derived from discriminant function analysis is relatively highly i.e 74.9%. It is means that, the overall of factors has been identified earn to discriminate all groups.
Evaluation of Commercial Land Use Model
The original commercial land use development model was developed based on the land use changes between year 1992-1994 as input. To evaluate the effectiveness of the original model, it was used to predict commercial development (as well as the other two groups) that has occurred between year 1995-1998 based on the factors available in year 1994. A total of 5636 samples of undeveloped lots was used in the evaluation. It was known that in year 1998, 450 lots (7.9%) were developed for commercial (Group 2), 2753 lots (48.8%) for other urban development (Group 3) and the rest were still undeveloped. To predict the type of development for an unknown land parcel using the original DFA model, the year 1992 data value for each independent variables were used to calculate the discriminant score for each function using the two functions (Eq. 4.1 and 4.2) calibrated earlier. As mentioned earlier, function 1 is useful for discriminating non-developed areas (Group 1) with urban development (Groups 2 and 3). While function 2 is useful in discriminating Group 2 from Group 1 and Group 3. Using the discriminant scores of the two functions, land parcels with negative score in Function 1 were assigned to Group 1 - non-developed areas, and then Function 2 was used to discriminate the remaining unclassified samples either to Group 1 or 3. Land parcels with positive score on Function 2 will be assigned to Group 2 - commercial development and the rest to group 3.
Classification accuracy of the model evaluation
Percentage of group correctly classified: 98.6 %.
||No. of cases
Table 5 shows the result of the evaluation. The model accurately predicted about 98.6% of the development in the sample area between year 1995 and year 1998, slightly better than could be achieved by chance (50%). Further examination of the classification results reveals that the accuracy of the group classification was not in-line with the original model. In the evaluation model the accuracies for Group 1, 2 and 3 were quite high namely 98.8%, 99.1% and 98.3 % respectively.
Discussion and conclusions
This paper has described an initial attempt to provide a framework for the development and evaluation of commercial land use development model especially in the context of developing countries. Models have been used in land use planning since the early 1960s. However an using and development process become more viable in recent years due to the rapid advances in the information technology such as geographic information system (GIS), which provide additional capabilities for spatial data handling. In this study, a spatial commercial land use development model was developed using discriminant function analysis. The model was developed based on the year 1992 to 1994 land use changes and factors existed in year 1992. The overall accuracy of the original model is quite good i.e about 74.9% for commercial development. The same model accurately predicted 98.6% of the year 1995 to 1998 overall development. For commercial development the accuracy was only 57%, with high confusion with other types of urban development. The relatively low accuracy may be due to factors that were not included in the model such as land ownership and land value, which is an important to determining the availability of land for development. Therefore, it is suggested that future attempts should include other relevant variables in the model. Other possible reason may be related to changes in government policy in 1980s that might have affected the land development structure of the study area that was not accounted in the original model such as the construction of a major highway passing nearby the study area. Such changes were not captured in the model because of data availability problems. It is hoped that such developments would further encourage urban planners to use and further develop more urban models in the future.
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