105 seem the data is appropriate to the unstructured correlation structure, but this value
shows that the best model of Nested GLMs is the model with independent structure.
Furthermore, random clustering effects include in modeling to control the correlation arise from recording multiple locations. The result is shown at Nested
GLMM column, where ratios of exchangeable and unstructured are slightly smaller than independent. Exchangeable and unstructured WCM is not
vehemently
2
rejected, because the ratios are smaller than independent and the difference is not significant.
Table 19 Averages of SE
R
SE
M
Nested GLM Nested GLMM
Exchange -able
Unstruc -tured
Indepen- dent
Exchange -able
Unstruc -tured
Indepen- dent
Average 0.63
1.5 0.56
0.57 0.57
0.59
Through this study, it is believed that the poverty data tends to have independent correlation structure. It can be seen through the value of SE
R
SE
M
in Nested GLM modeling, independent WCM has the smallest SE
R
SE
M
. After the random effect is included to the model Nested GLMM is used for modeling,
where the correlation structure is controlled, Nested GLMM provides better fit to the data than Nested GLM with exchangeable and unstructured WCM, showed by
the values of SE
R
SE
M
= 0,57 in GLMM, which is smaller than 0.63 and 1.5 in GLM.
4.4.2 Significance p-values
Appendix 23 and Appendix 26 show the p-values for Nested GLM and Nested GLMM, respectively.
Nested Generalized Linear Model Explanation for p-values is divided into three parts, as follows
1. robust and model-based parameter estimates with exchangeable WCM comparison
2
strong
106 As the model has 3 levels of ordinal responses, there are two thresholds. Both
thresholds are statistically significant p-values = 0.049 and 0.00005 for and
, respectively for robust parameter estimate, while only is
statistically significant in model-based. Parameters prov2, farm12, school11, and ULS2 are statistically
significant for both methods p-values 0.048. The rest of parameters are not statistically significant, except school21,
school22, ULS1 of the robust parameters estimation p-values 0.022. 2. robust and model based parameters estimate with unstructured WCM
comparison Parameters prov2, farm12, school11 are statistically significant for both
methods p-values 0.008, while p-value = 0.041 and ULS3 p-value =
0.018 are statistically significant for model based method and ULS1 p- value = 0.003 and ULS2 p-value = 0.080 are statistically significant for
robust method. 3. Exchangeable and unstructured comparison
The result of model based estimator with exchangeable and unstructured WCM are almost the same: prov2, farm12, and school11 are statistically
significant for both working correlation matrix p-values 0.04. For exchangeable and unstructured robust method, ULS parameters are
statistically significant even though with different p-values. According to this result, province 2 is different from province 3 for all models p-
values 0.000. Number of farm worker families is significant as a contribution to
determine the poverty level in Central Java. Furthermore, it is believed, number of school is also significant as a contribution to determine the poverty level in West
Java. Exchangeable working correlation matrix has low values, i.e.
, , and
, while correlations in unstructured working correlation matrix are vary. Some
correlations are 1 in some locations not in the main diagonal Appendix 28.
107 Interpretation of a parameter:
School1 in prov1 with model based and exchangeable WCM p-value = 0.047
In West Java, probability a sub district with category of school1 be the more severe is exp1.86 = 6.42 times of sub district with category of school3, with
other values of variables are fixed. ULS
in prov2 with model based and exchangeable WCM p-value = 0.031: Probability of sub district with category hotspot to be the more severe is exp2.94
= 18.91 times of sub district with category not hotspot, with values of other variables are fixed.
Nested Generalized Linear Mixed Model Explanation in this part is divided into three parts, as follows
1. robust and model-based parameters estimate with exchangeable WCM comparison.
In Nested GLMM with robust method, many more parameters are statistically significant, i.e.
, prov2, farm21, far12, farm22, farm23, school21, school12, school22, medis12, medis22, ULS1, and ULS2, while
from model based method only school11 and ULS2. 2. robust and model-based parameters estimate with unstructured WCM
comparison. This part gives the same result with exchangeable type.
3. robust and model-based parameters estimate with independent WCM comparison.
This part gives the same result with exchangeable type, except for thresholds and provs parameters. The values of threshold 1 and 2, and prov 1 and 2
parameters estimate of independent are different from those of exchangeable and unstructured, but the same in significance. Threshold 2 and prov 2 are
statistically significant, while threshold 1 and prov 1 are not statistically significant.
Interpretation of parameters: School1
in prov1 with model based and exchangeable WCM p-value = 0.030:
108 In West Java, probability a sub district with category of school1 to be the more
severe is exp3.06 = 21.3 times of sub district with category of school3, with values of other variables are fixed.
ULS in prov2 with model based and exchangeable WCM p-value = 0.024:
Probability of sub district with category not hotspot to be the more severe is exp- 4.08 = 0.017 times of subdistrict with category hotspot or
probability of sub district with category hotspot to be the more severe is exp4.08 = 59.15 times of sub district with category not hotspot, with values of other
variables are fixed.
Classification Tables Appendix 24 shows classifications result of observed and predicted of
Nested GLM, which classification for level 2 are rare. The highest classification for this level is in independent crosstabs with count 4 and percentage 10.8 for
model-based and robust estimation, whereas it is empty for unstructured robust
crosstab. Table 20 shows percentages of true classification result of Nested GLM, where the best estimation is from independent WCM, 60.94 true classification.
Table 20 Percentages of true classification result of Nested GLM
exchangeable unstructured
independent model based
robust model based
robust model based
robust 49.22
49.22 49.22
48.44 60.94
60.94
Classification results of Nested GLMM are showed by Table 21. The result is far better than those of Nested GLM, where percentages in the main diagonal
are the highest, that is 84, 54.1, and 85.4, for all models. The true classification result of Nested GLMM is 75.78, where it is the same for all types
of covariance structures.
109 Table 21 Classification result of Nested GLMM for all WCMs
group of ranking prediction Crosstabulation prediction
Total 1
2 3
The result of
groups of ranking
1 Count
42
8 50
within response
84.0
16.0 0.0
100.0 2
