10 3. How to build a model for clustered nested data with multinomial ordinal
response, and how to estimate the model parameters. 4. How is the influence of working correlation matrix structure on the
estimation of model parameters for nested correlated data? 5. How are the differences of the model parameters estimate between Nested
GLM and Nested GLMM?
1.2 The Purpose of Research
Based on several initiatives and issues described in section 1.1, the purpose of this dissertation is
1. To determine sub districts level of severity poverty in Java. 2. To obtain the best hotspot detection method between the two methods that
will be studied and to apply this best method on a factor for modeling. 3. To build a model for nested data with multinomial ordinal response, and to
estimate the model parameters. Furthermore, to know parameter estimate of explanatory variables in every province used in modeling.
4. To study the influence of the working correlation matrix structure on the estimation of model parameters for data with clustered nested condition.
5. To study the differences of the model parameter estimation between Nested GLM and Nested GLMM.
The purpose of this study have been achieved and described in chapters 2, 3, and 4. The first purpose is achieved in chapter 2, as the study of ORDIT ranking
method and its implementation on the poverty data. The second purpose is achieved in Chapter 3 as the study and comparison of two hotspot detection
methods. The best method has been used to detect bad nutrition hotspot area. Finally, the third, fourth and fifth purposes are achieved in Chapter 4, modeling
and its implementation on poverty data using the result of Chapter 2 as the dependent variable, while the result of chapter 3 is used as an independent variable
in the modeling.
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1.3 The Research Framework
The systematic of the research is described in Figure 4. The left side of diagram in Figure 4 is ORDIT ranking method, which is studied and implemented
on poverty data in Java. This method is built to carry on ranking of individuals based on several indicators, but due to the limitation of data, this study uses only 2
indicators of poverty, i.e. health insurance for the poor hip or askeskin and statement of inability to pay or poverty letter pl or surkin. The result of ranking
is grouped into three levels and used as ordinal response in the modeling. The right side of the diagram is a study and comparison between two hotspot
methods, i.e. Circle based Scan Statistics SS hotspot detection and Upper Level Set Scan Statistics ULS hotspot detection. As a result, the best method is ULS,
which is used to detect hotspots of bad nutrition in some districts. The result of this detection is used as an explanatory variable in the modeling.
In the middle of diagram is the development of GLM and GLMM modeling. The spatial GLMM of Zhang and Lin 2008, spatial correlated in modeling from
Cressie 1993, and the problem related to global variance variance among subjects and local variances variance among sub subjects in the spatial data
Goldstein 1995, and Managing Clustered Data Using Hierarchical Linear Modeling Warne et.al. 2012 are the support theory of working correlation
matrices WCM determination for nested GLM and nested GLMM. The work on modeling is as follows. The determination of a working
correlation matrix is the beginning step to estimate the model parameters. In this study, two types of working correlation matrices are discussed and the most
appropriate type for the data in this research is determined. The model parameters of GLM are estimated by the GEE method Hardin and Hilbe 2003, while the
model parameters of GLMM by Pseudo likelihood approach Wolfinger and O’Connell 1993. Furthermore, multinomial ordinal response variables gives
complexity to the model building and parameters estimation. Applications presented in this dissertation are analysis of poverty data. The source of the data is
the Statistic Bureau BPS and Ministry of Health DepKes RI.
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F igure
4 T he
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1.4 The Outline of Dissertation
