Generalized linear mixed models of ordinal poverty response in nested area

Abstract

The Linear Mixed Models in this study is a development of Spatial Generalized Linear Mixed Model proposed by Zhang and Lin (2008). As in Zhang’s and Lin’s model, spatial (regional) data in this study is concerned on the hotspot detection. Hotspot detection method used by Zhang and Lin was Circle Based Scan Statistic (SS) method of Kulldorf (1997), while research in this dissertation using Upper Level Set Scan Statistic (ULS) hotspot detection method of Patil and Taillie (2004). Application of this hotspot detection method begins by comparing the two methods through simulation to obtain 14 performance criteria, resulting that the ULS hotspot detection method is better than the other one. Furthermore, the ULS method is performed to detect hotspot of bad nutrition in some districts, the results are used as a covariate in the modeling. This study focuses on the development of models for regional data viewed from the proximity of nested observations. According to Cressie (1993) there is a tendency for adjacent observations have a stronger correlation than distant observations. In statistics, also could be said there are differences in the variation of individuals within a group with individuals between groups. This condition must be considered in the modeling. Generalized estimating equation (GEE) is a parameter estimation method accounts for the correlation between observations. Working correlation matrices (WCM) is an important part in the parameters estimation process. Three structures of correlation matrices are studied and implemented to know which structure is the most appropriate to the data. The results of parameters estimation of Nested GLM and Nested GLMM based on combinations of some WCMs and parameter estimation techniques were compared. Response variable used in the model is in ordinal scale having complexity in the modeling, which also a focus of this research, while response variable used in Zhang’s and Lin’s model is a count variable with Poisson distribution. This ordinal response is obtained by grouping the ranking result by ORDIT (Ordering Dually in Triangles) ranking method from Myer and Patil (2010). Through the development of the model in this study involving nested spatial data, better results is provided especially when using diagonal working correlation matrix.