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Given the presence of spatial dependence in the residuals, it then made sense to fit a GLSM, maintaining four explanatory variables and assuming an exponential model for the process S(x).
A study of the spatial dependence of the GLSM residuals indicated that the spatial component had been correctly modelled on this occasion.
The ROC curve and AUC were calculated for the GLSM. The AUC of the binary spatial model was 0.99, which indicates a substantial improvement in the precision of the GLSM.
Randomly selected for the first scenario was 95% of the 313 initial observations, composing the training set that was used to fit the GLM and GLSM. The fitted models were then validated with the remaining 5% of the observations.
In all the cases, it can be observed that the GLSM provided a better explanation not only of the effect of the variables determining slate quality, but also of the spatial behaviour of exploitable slate, thereby producing lower prediction error rates.
A general interpretation of the GLSM used in our analysis is that the spatial term S represents the accumulative effect of possible explanatory variables with an undetermined spatial structure, which have, therefore, not been observed.
Based on the comparison of the semivariograms of the GLM and GLSM residuals, we would like to draw attention to the presence of spatial dependence in the GLM residuals, in contrast to what occurs when a GLSM is implemented.
The simulation study demonstrates that, for varying levels of prediction difficulty, the GLSM had lower error rates than the GLM.
Although the parameters of the GLSM must be interpreted conditionally rather than marginally to S, the results of the statistical analysis denote the broader potential of the GLSM compared to the classic GLM in analysing spatial data.
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