Model validation

The observed change trajectories of OL, FL, FC, and VR were overlaid on the four corresponding maps of probability of change produced by logistic regression analysis, respectively, and the percentages of area of observed change trajectories located in the five classes of probability of change were calculated. The results of model validation for four change trajectories were demonstrated below, respectively.

(1) Change trajectories of overall landscape (OL)

The predicted classification accuracy of the testing data set is 81.6% for changed pixels and 64.5% for unchanged pixels. Overall, 72.9% of the pixels are classified correctly (Table 4.25). The AUC value of 0.785, which is considered acceptable discrimination, shows that classification results based on the logistic regression model are satisfactory (Fig. 4.20).

Fig. 4.20 The ROC curve for change trajectories of OL

As for the change trajectories of OL, classes 1 to 5 occupied 32.79%, 17.11%, 18.86%, 25.82%, and 5.43% of the entire study area, respectively (Table 4.36). As shown in Fig. 4.21, the greatest percentage of the entire area of change could be found in class 4. However, as far as the RCI values were concerned, the values were increasing with ascending classes and the greatest value was found in class 5. This result reveals that the observed change trajectories of OL correspond to the zones with higher probabilities of change, which only cover small areas.

Table 4.36 Characteristics of the five classes of probability of change for OL change

Fig. 4.21 Map of RCI and percentage of the entire area of change for OL change trajectories

(2) Change trajectories from forest to landslide (FL)

The overall rate of correct classification of the testing data set is estimated as 71.7%, with 84.0% of the changed group and 59.2% of the unchanged group being correctly classified (Table 4.28). The AUC value of 0.771, which is also considered acceptable discrimination, indicates that the classification results based on logistic regression model are satisfactory (Fig. 4.22).

Fig. 4.22 The ROC curve for change trajectories of FL

In regard to the change trajectories of FL, classes 1 to 5 covered 36.81%, 12.81%, 21.29%, 23.09%, and 6.00% of the entire study area, respectively (Table 4.37). As presented in Fig. 4.23, the greatest percentage of the entire area of change could be found in class 4. However, in terms of RCI values, the values showed an increasing trend with rising classes and the greatest value was also found in class 5. This result demonstrates that the observed change trajectories of FL coincide with the zones that have higher probabilities of change and cover a small area.

Table 4.37 Characteristics of the five classes of probability of change for FL change

Total 100.00 211.53 15.28 7.22 1.00 100.00

Fig. 4.23 Map of RCI and percentage of the entire area of change for FL change trajectories

(3) Change trajectories from forest to channel (FC)

The overall rate of correct classification of testing data set is estimated as 87.3%, with 91.7% of the changed group and 83.0% of the unchanged group being correctly classified (Table 4.31). An AUC value of 0.941, which is considered outstanding discrimination, indicates that the classification results based on the logistic regression model are very satisfactory (Fig. 4.24).

Fig. 4.24 The ROC curve for change trajectories of FC

As for the change trajectories of FC, classes from 1 to 5 comprised 68.63%, 9.86%, 7.46%, 7.73%, and 6.32% of the entire study area, respectively (Table 4.38).

As demonstrated in Fig. 4.25, both the greatest RCI value and percentage of the entire area of change could be found in class 5. The two values were increasing with ascending classes. This result is a little different from the two former cases, although it also indicates that the observed change trajectories of FC correspond with the zones, which have higher probabilities of change and cover a small area. A RCI value up to 10.62 is noteworthy and it reveals that the predicted probabilities of change are very spatially accurate.

Table 4.38 Characteristics of the five classes of probability of change for FC change

Fig. 4.25 Map of RCI and percentage of the entire area of change for FC change trajectories

(4) Change trajectories of vegetation recovery (VR)

Overall, 75.2% of the pixels of testing data set are classified correctly, with 83.5% of the changed group and 67.9% of the unchanged group being correctly classified (Table 4.34). An AUC value of 0.795, which is also considered acceptable discrimination, indicates that the classification results based on the logistic regression model are satisfactory (Fig. 4.26).

Fig. 4.26 The ROC curve for change trajectories of VR

In terms of the change trajectories of VR, classes 1 to 5 contained 40.18%, 15.64%, 17.93%, 21.45%, and 4.80% of the entire study area, respectively (Table 4.39). As were the cases in the change trajectories of OL and FL, the greatest percentage of the entire area of change and RCI value could be also found in class 4 and 5 in the change trajectories of VR, respectively (Fig. 4.27). RCI values showed an increasing trend with ascending classes. This result indicates that the observed change trajectories of VR match the zones with high probabilities of change and a small area.

Table 4.39 Characteristics of the five classes of probability of change for VR change

Fig. 4.27 Map of RCI and percentage of the entire area of change for VR change trajectories

4.4.4 Summary

After the relationships between the changed area and environmental variables are understood, knowledge of further predicting the probabilities that change trajectories will occur for every pixel becomes important. Before logistic regression analysis is applied to produce the change probabilities, multicollinearity between predictor variables has to be diagnosed. When the average rainfall variable was removed, there was no multicollinearity between all predictor variables for four change trajectories, inclusive of OL, FL, FC, and VR. With respect to the classification accuracy assessments for four change trajectories, the results demonstrate that the FC model has a better model fit due to its higher Cox & Snell R² and Nagelkerke R² values and the overall rate of correct classification in the classification table.

By checking the independent variables obtained from the four fittest logistic regression models, five independent variables, including lithology, distance to faults, distance to rivers, elevation, and slope, were all discerned in each logistic regression model. In addition, the aspect variable could be found in OL and FL models, whereas the curvature variable could only be discovered in the former. As regards the signs of regression coefficients for dependent variables, lithology, distance to faults and rivers variables were all negative values in the four models, while elevation and slope variables were all positive values in every model except FL. Concerning the magnitudes of regression coefficients for dependent variables, the coefficient values of the lithology variable were always the largest in the four models and this result revealed that the lithological condition played a crucial role in the four landscape change models. The coefficient values of the aspect variable were the second greatest in the models. When they were absent in the models, the slope variable’s coefficient values became the second biggest. These results indicated that aspect and slope variables played a secondary role in the four landscape change models.

As far as model validation was concerned, the FC model had the highest AUC value of 0.941, representing an excellent ability to classify cases into suitable groups, and the other three models also showed acceptable discrimination. Moreover, the RCI values, assessing the intensity of land cover change in a subregion of the entire watershed, showed an increasing trend with the rising classes of change probabilities in the four models and these results suggested that the prediction of change probabilities could very closely correspond with the actual change trajectories.

Therefore the four logistic regression models are beneficial tools in landscape change prediction.

5. DISCUSSION