Significance Test of Model and Predictors

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4.3.2. Significance Test of Model and Predictors

And if an acceptable model is found, the statistical significance of each of the coefficient is evaluated . Table 4.3 . Variables in the Equation of null model β S.E. Wald df Sig. ExpB Step 0 Constant -.272 .019 200.330 1 .000 .762 The initial test for the null model which the coefficients for all independent variables are 0. The finding of significance in Table 4.3 indicates this null model should be rejected, because of Sig. = 0 or 0.05 and β ≠ 0. Table 4.4. Omnibus Tests of Model Coefficients Chi-square df Sig. Step 94.011 1 .000 Block 94.011 1 .000 Step 1 Model 94.011 1 .000 Step 57.422 1 .000 Block 151.433 2 .000 Step 2 Model 151.433 2 .000 Step 52.756 1 .000 Block 204.189 3 .000 Step 3 Model 204.189 3 .000 Step 18.473 1 .000 Block 222.662 4 .000 Step 4 Model 222.662 4 .000 Step 5.379 1 .020 Block 228.041 5 .000 Step 5 Model 228.041 5 .000 Step 3.967 1 .046 Block 232.009 6 .000 Step 6 Model 232.009 6 .000 55 Table 4.5. Hosmer and Lemeshow Test Step Chi-square df Sig. 1 .000 . 2 .000 . 3 28.804 2 .000 4 26.016 3 .000 5 24.907 4 .000 6 44.944 6 .000 Table 4.6. Contingency Table for Hosmer and Lemeshow Test LU_90_97 = 0 LU_90_97 = 1 Observed Expected Observed Expected Total Step 1 1 6252 6252.000 4762 4762.000 11014 1 2596 2570.541 1549 1574.459 4145 Step 2 2 3656 3681.459 3213 3187.541 6869 1 2091 2014.536 1063 1139.464 3154 2 2655 2731.464 2149 2072.536 4804 3 505 556.129 486 434.871 991 Step 3 4 1001 949.871 1064 1115.129 2065 1 2091 2016.910 1063 1137.090 3154 2 2354 2401.158 1787 1739.842 4141 3 505 549.390 486 441.610 991 4 301 327.932 362 335.068 663 Step 4 5 1001 956.610 1064 1108.390 2065 1 1828 1779.887 941 989.113 2769 2 263 236.411 122 148.589 385 3 1991 2064.714 1542 1468.286 3533 4 789 775.948 601 614.052 1390 5 779 751.959 712 739.041 1491 Step 5 6 602 643.082 844 802.918 1446 1 1240 1166.615 554 627.385 1794 2 588 615.602 387 359.398 975 3 1093 1048.434 656 700.566 1749 4 1161 1249.071 1008 919.929 2169 5 608 594.415 447 460.585 1055 6 642 668.763 639 612.237 1281 7 607 574.291 558 590.709 1165 Step 6 8 313 334.809 513 491.191 826 56 The chi-square goodness-of-fit test tests the null hypothesis that the step is justified. Here the step is from the constant only model null model to the all-independents model. When as here the step was to add a variable, the inclusion is justified if the significance of the step is less than 0.05. Table 4.4 Step 6, is showing value of Sig. is 0 or less than 0.05 so means that the model is fit to predict deforestation The Hosmer and Lemeshow Goodness-of-fit Test computes a chi-square from observed and expected frequencies. The p-value Sig. = 0, here is computed from the chi-square distribution with 6 degree of freedom df and indicates that the logistic model is a good fit. That is, if the Hosmer and Lemeshow Goodness-of-Fit test statistic is 0.05 or less, it reject the null hypothesis that there is no difference between the observe and predicted value of deforestation dependent variable. Table 4.7. Classification Table Observed Predicted LU_90_97 1 Percentage Correct LU_90_97 6165 87 98.6 1 4552 210 4.4 Step 1 Overall Percentage 57.9 6165 87 98.6 LU_90_97 1 4552 210 4.4 Step 2 Overall Percentage 57.9 5251 1001 84.0 LU_90_97 1 3698 1064 22.3 Step 3 Overall Percentage 57.3 4950 1302 79.2 LU_90_97 1 3336 1426 29.9 Step 4 Overall Percentage 57.9 5650 602 90.4 LU_90_97 1 3918 844 17.7 Step 5 Overall Percentage 59.0 5381 871 86.1 LU_90_97 1 3884 878 18.4 Step 6 Overall Percentage 56.8 a The cut value is .500 57 The classification table above Table 4.7 is a 2x2 table which tells correct and incorrect estimates for the full model with the independents as well as the constant. The effectiveness of the model is prediction of the phenomenon can be summarized in a simple data Table 4.7 from the total 11,014 sample pixels, 4762 were changed deforested and 6252 pixels were unchanged forest and non forest stable. In every step of the regression, all pixels are evaluated by the model and a value is predicted for each pixel. The value of both correctly and wrongly predicted pixels for each step is shown in Table 4.7. In other words, in this table, the group of changed forest and unchanged area pixels are compared with what is predicted for them by the model. From the sixth step last step in Table 4.7 is clear that 18.4 of deforested pixels correctly classified by the model, and 86.1 of stable pixels are classified correctly. In this step also is showed overall percentage correct 56.8, means a total prediction accuracy is 56.8. The accuracy of prediction is 56.8 is actually too small for being used the model for predicting deforestation rate at the same location and different time 1997 – 2001 according to available data. This less overall accuracy was caused by there are many independent variables contributed deforestation driving force that being assumed are able to increase deforestation occurrence. For instants, center of population LogR_CP contributed only 7.4 of value 1 deforestation, shore line LogR_SL less than 1 km is only 25, distance from river less than 1.000 meters contributed just 38.9 percents from total area, and distance from existing road less than 1 km contributed the worst value only 2.7. At least, all independent variables except altitude can be used to predict deforestation, and good-fit for the model of logistic regression and its equation. This reason is based on the statistical significance testing. The Wald test is a way of testing the significance of particular explanatory variables in a statistical model. In logistic regression we have a binary outcome variable and one or more explanatory variables. For each explanatory variable in the model there will be an associated parameter. Table 4.8. Variables in the Equation and Wald test 95.0 C.I.for EXPB β S.E. Wald df Sig. ExpB Lower Upper Step 6f LOGR_RIV -.232 .042 30.593 1 .000 .793 .730 .861 LOGR_ROAD 1.130 .135 70.293 1 .000 3.097 2.378 4.033 LOGR_SL .348 .046 57.956 1 .000 1.416 1.294 1.548 LOGR_CP .354 .080 19.584 1 .000 1.425 1.218 1.667 LOGR_COM .082 .041 3.968 1 .046 1.086 1.001 1.177 LOGR_SLP -.150 .055 7.506 1 .006 .861 .773 .958 Constant -.238 .055 18.903 1 .000 .788 The Wald test, described by Polit 1996 and Agresti 1990 in Blackwell 2006, is one of a number of ways of testing whether the parameters associated with a group of explanatory variables are zero. If for a particular explanatory variable, or group of explanatory variables, the Wald test is significant, then we would conclude that the parameters associated with these variables are not zero, so that the variables should be included in the model. If the Wald test is not significant then these explanatory variables can be omitted from the model. In Table 4.8 it can be seen that none of the explanatory variable or predictor is zero, it means that Wald test is failed to reject null hypothesis and It means that all variables of road, river, distance from population center, distance form coast line, slope, and aspect can be used to predict deforestation. LogR_COM or independent variables of aspect and LogR_Slp Slope have higher Sig. value. In Appendix IV, it can be seen that, 58 59 aspect and slope have contributed more cells that being assumed for deforestation occurrence. Slope has contributed 83.8 of value 1 as indicated tends to be deforested, and aspect contributed 43.4.

4.3.3. Logistic coefficients and correlation