Estimation of Model 1 with OLS and GWR

This section starts with OLS regression in Model 1 defining poverty as a dependent variable, and investment and deforestation as explanatory variables. The OLS tool in the ArcToolbox, was run: the key OLS results are illustrated in Table 6.2 while its full results are displayed in Figure 6.11 at the end of this chapter. In this Table, the coefficient of investment b1 was

negative and statistically significant at 5%, while that of deforestation b2 was positive and

significant at 1%. These two coefficients were likely suggested that for each additional district investment, the predicted rate of poverty would reduce by 0.32% on average, ceteris paribus. Likewise, each increasing percentage of deforestation predicted an increase in the poverty rate by approximately 2%, ceteris paribus. In addition, the small value of the variance inflation factor (VIF), which was less than 7.5, indicated that the explanatory variables were not redundant in the model.

In the OLS statistical diagnostics, the adjusted R2 was relatively low at 0.16, signifying that it accounted for approximately 16% of variation in the dependent variable. This low

performance may suggest that some variables were missing from the model. The significance of the F–Statistic and Wald Statistic indicated a robust overall model. Moreover, the

insignificances of the Koenker (BP) Statistic and Jarque-Bera Statistic suggested that the OLS standard errors were unbiased and that its residuals did not deviate from a normal distribution.

Table 6. 2: Estimated results from OLS tool on Model 1

Variables Coefficient t_Statistic Prob

Intercept 0.4413 25.8112 0.0000 Investment -0.0032 -2.1791 0.0310 Deforestation 1.9631 4.6465 0.0000 AICc -160.6960 Wald-Prob 0.0000 R2 0.1727 K(BP) 0.5022 Adjusted R2 0.1606 K(BP)-Prob 0.7780 F-Stat 14.3019 JB 2.1288 F-Prob 0.0000 JB-Prob 0.3450 Wald 39.5685 Sigma2 0.0182

Source: Output from ArcMap, computed by Author.

However, the OLS full results in Figure 6.11 showed a warning sign; that is, autocorrelation as the residuals could be spatially autocorrelated as a result of spatial dependence. Thus, it was deemed important to test whether spatial autocorrelation was present in the residuals. If present, then the results of the OLS technique should be considered unreliable. To construct this test, the use of Moran’s Index as a measure of the level of spatial autocorrelation in the residual was advised (see Charlton & Fotheringham, 2009a). Its tools are available in Spatial Statistics Tool located in the ArcToolbox. As noted in Chapter 4, the null hypothesis of this test stated that the observed pattern was randomly distributed.

Moran's I Summary Moran's Index: 0.722078 Expected Index: -0.007194 Variance: 0.002775 z-score: 13.844228 p-value: 0.000000

Figure 6. 1: Spatial autocorrelation report on OLS residuals in Model 1 Source: Output from ArcMap, computed by Author.

Following this advice, the testing report for the OLS spatial autocorrelation was obtained from the ArcMap as shown in Figure 6.1, where it was also found that the value of Moran’ Index was 0.72 with a Z score of 13.84, and that the p-value for the hypothesis was

significantly different from zero. The Bell – shape in Figure 6.1 indicates that there was less than 1% likelihood that this clustered pattern was the result of random chance. In other words, this report confirmed that spatial autocorrelation was present in the residuals; thus, the OLS results detailed above could not be trusted.

Therefore, it was necessary to further investigate the spatial relationships in Model 1 by employing GWR techniques. After running the GWR tool for modelling spatial relations in ArcToolbox with the options mentioned above, the statistical results were reported in Table 6.3. Before identifying the spatial relationships in this model, the statistical diagnostics of the GWR results needed to be investigated in four stages. First, it seemed useful to start with comparisons, that is, to compare the GWR results with those of the OLS techniques in terms of the model fitness of their adjusted R2 and AICc. The adjusted R2 was increased from 0.16 in the OLS to 0.67 in the GWR results, which suggests that the performance of the GWR was better than that of the OLS. In addition, the decrease in AICc from –161 in the OLS to – 239.72 in the GWR was strong evidence of improvement in the fit of the model to the data in the GWR (the smaller AICc being the better of the two).

Table 6. 3: Statistical results from GWR tool on model 1

Variable Name Variable

Results from OLS Neighbours 21.0000 Residual Squares 0.6168 Effective Number 52.5613 Sigma 0.0840 AICc -239.7220 -161 R2 0.7952 0.17 Adjusted R2 0.6745 0.16

The GWR tool generated the values of its standardised residual (StdResid): these values were mapped to distinguish the districts in which the Model was under –or over –predicted. The GWR standardised residuals were mapped and appear in Figure 6.2. This map suggests that overall the GWR model was well predicted. However, the map shows only one under predicted district, Xaiphouthong in Savannakhet province with a StdResid less than –2.5, where low poverty with low investment and deforestation was observed. In addition, Karum and Dakchung districts in Sekong province were over-predicted by the Model: their StdResid

were greater than 2.5 where the poverty rate was high but where investment and degradation were relatively low.

Figure 6. 2: Map of GWR standardised residuals in model 1 Source: Output from ArcMap, computed by Author.

Moran's I Summary Moran's Index: 0.040481 Expected Index: -0.007194 Variance: 0.002756 z-score: 0.908126 p-value: 0.363812 Figure 6. 3: Spatial autocorrelation report on GWR residuals in model 1

Source: Output from ArcMap computed by Author.

Following the same process as the above OLS, the residuals in the GWR results also needed to be tested in order to detect whether spatial autocorrelation was present in its residuals, and its null hypothesis was stated the same as above. If so, this suggested that the GWR results were not reliable. After running its Moran’s Index tool, the spatial autocorrelation of the

GWR results were reported in Figure 6.3, which shows that Moran’s Index of the residual was 0.04 with a p-value of 0.36 and the z-score of 0.91. Thus, the pattern did not appear to be significantly different from random. In other words, this result suggested that spatial autocorrelation was not present in the GWR residuals; thus, the GWR results were reliable Finally, after all of the statistical diagnostics confirmed the reliability of the GWR results, the next interesting part of the GWR technique was to interpret the values of the coefficients in order to understand their estimated spatial relationships among variables in the PIPEN model. Unlike the OLS, the GWR techniques in this model had created two sets of coefficients. This means that each district had two coefficients, representing the predicted association of

additional investment and deforestation with the poverty rate. These two coefficient sets are displayed in two maps in Figure 6.4. Each map in this Figure displays 140 coefficients classified into seven ranks marked by three different colours from the darker green indicating high prediction of decrease in the poverty rate to the darker red indicating high prediction of increase in the poverty rate. The white colour signals insignificant prediction of change in poverty.

Panel A: Investment coefficient, b1 Panel B: Deforestation coefficient, b2

Figure 6. 4: GWR coefficient maps in Model 1 Source: Output from ArcMap computed by Author.

Panel A in Figure 6.4 shows the map of 140 investment coefficients b1, varying from –1.4%

to 0.74%, and representing estimated values of the poverty rates in each district for each percentage increase in number of district investments. Panel A shows most of the districts

from North to South in green, meaning that the poverty rate is predicted to decline when these districts receive additional investment. Their prediction degree may be different according to their values and colours. For example, the colour dark green signifying many districts in Luang Prabang, Xieng Khuang, Huaphanh, Sekong and Attapeu provinces, is used to indicate that the poverty rate in these districts predicts to decline when they receive additional

investment. The red and white colours that appear in Panel A, showing districts including Vientiane Capital, Vientiane, Xayabury and Savannakhet province, suggest that any

additional investment is estimated to have less impact on–even might raise–poverty rates in these districts. Note that the red colour in all of the districts in Vientiane Capital is attributable to the fact that Vientiane Capital, as the capital city of Laos, has no private investment in the resources sector in those districts.

Panel B in Figure 6.4 shows 140 coefficients b2 of deforestation on the poverty rate: these

coefficients varied from –3.63% to 5.07%. Similar to the above, the darker red indicates the higher prediction of increase in the poverty rate due to additional deforestation rate: the darker green signifies high estimation of reduction of poverty rate; and, the white suggests

insignificant impact of deforestation on the poverty rate. In this map, the red colour is highly evident in most of the districts in the central provinces including Vientiane, Xieng Khuang, Borikhamxay, Khammuane, some districts in the Southern provinces of Savannakhet and Saravane, as well as some northern districts in Xayabury and Phongsaly provinces. The poverty rate in these red districts is predicted to increase in tandem with the additional deforestation rate. In addition, all of the districts in the far southern provinces, including Champasack, Sekong and Attapeu and some dispersed districts in the northern province of Huaphanh, are depicted in white to imply insignificant predictions vis–a–vis deforestation and the poverty rate. Several districts in the Northern provinces appear in a mix of light and dark green. These contrasting colours suggest that in some districts in Luang Prabang, Bokeo, Luang Namtha, and Oudomxay, and in some districts in Xayabury and Vientiane province, the poverty rate is estimated to decrease in line with the additional deforestation rate.

Drawing upon the two maps of GWR coefficients based on Model 1 that appear in Figure 6.4, the different values of the coefficients imply that the poverty rate in each district will be determined by the different degrees of investment and deforestation across the country. Note that unlike other maps of data set, the two maps intend to indicate regional patterns of coefficients in Laos as outcomes from mathematical modelling (see the three main elements of spatial analysis above). Thus, it is useful to view the colours and values assigned to the

seven ranks in each district to ascertain whether their patterns are dispersed, clustered or randomly scattered.