Judul: Model campuran linier terampat untuk respon kemiskinan ordinal dalam area tersarang
Abstrak: 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.
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Judul: Pendugaan Area Kecil untuk Data Lognormal dengan Ketergantungan Spasial antar Area Kecil
Abstrak: The need for accurate statistics is currently increasing, not only for the whole population, but also for some parts (subs) of population. Data from a survey can be used as information source for producing the statistics. Unfortunately, most of surveys are usually designed to produce some statistics for a whole population. Consequently, the survey data is often too small (or could be zero) for producing some statistics by direct estimation method in some subpopulations, especially for those are not planned in the survey. Statistics which are produced by direct estimation method will have large standard error if they are based on very small sample size. Moreover, if the sample size is zero then the statistics by direct estimation method cannot be obtained. The subs of population which the selected sample from it is not large enough for producing reliable direct estimates is known by small area. A statistical method that focuses on estimating some parameters in a small area is called by Small Area Estimation (SAE). To increase the effectiveness of small sample size in small areas, it is necessary to consider indirect estimation method which can be implemented by ‘borrowing strength’, utilizing some information from some resources, such as censuses, surveys or administrative records. Furthermore, ‘borrowing strength’ also could be implemented by exploiting data structures, such as considering the possibility of spatial dependence among small areas. SAE is a method for estimating parameter which is model-based. The standard SAE models, which are usually mixed models, are employed for estimating a linear small area parameter. The model assumes that the variable of interest follows normal distribution and there is no correlation among small areas. This dissertation aims to develop the best predictor of linear small area parameter as well as nonlinear small area parameter whenever the variable of interest follows positively skew distribution and among small areas is spatially correlated. A linear small area parameter is a linear function of the population values of a variable of interest in a given small area. On the other hand, a nonlinear small area parameter is a nonlinear function of the population values of a variable of interest. A total or mean population of a variable of interest in a given small area is an example of linear small area parameter whereas a ratio or quantile is a nonlinear parameter. The estimates of linear small area parameter as well as nonlinear small area parameter are derived under our proposed model, namely a unit-level spatial lognormal mixed model. This model assumes that the variable of interest follows log normal distribution and among small areas are spatially correlated by following Simultaneously Autoregressive (SAR) process. To predict the values of variable of interest for non-sampled units, it has been proposed the spatial synthetic estimator (SYNT) and the Spatial Empirical Best Predictor (SEBP). The SYNT predicts the non-sampled values by its unconditional expectation whereas the SEBP predicts them by its conditional expectation. The conditional expectation for obtaining the SEBP of linear small area parameter is calculated analytically. On the other hand, the conditional expectation for obtaining the SEBP of
Keyword: spatial empirical best predictor, spatial synthetic estimator, linear small area parameter, nonlinear small area parameter, unit-level spatial lognormal mixed model

Judul: Definisi Kalsium Dan Fosfor Pada Sapi
Abstrak: Kalsium dan fosfor mempunyai peranan penting dalam beberapa proses faali tubuh. Fungsi utama kalsium adalah mengatur iri tabilitas neuromuskuler, kontraksi otot, pembekuan darah, kofaktor beberapa sistim enzim dan sebagai komponen penting dalam pembentukan tulang (Rechcigl, 1978). Fosfor adalah komponen utama ikatan energi tinggi yaitu ATP (Adenosin Tri Phosphate), merupakan komponen nukleoprotein, mengatur pH isi rumen dan sebagai sumber multiplikasi flora dan fauna rumen (Payne, 1977).
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