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This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their

This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their

This thesis develops and evaluates Small Area Estimation (SAE) methods to provide estimates of prevalence rates of health risk factors for Local Government Areas (LGAs) in NSW using data from the NSW Population Health Survey. All outcome variables considered are dichotomous. The aim is to produce estimates that are an improvement over direct survey estimates based on a single year of data as well as over direct estimates based on data aggregated over seven years. Modified direct estimators, conventional synthetic and composite estimators, Empirical Best Linear Unbiased Predictors (EBLUP), complex synthetic estimators using a linear model, Empirical Best Predictors (EBP) and associated synthetic estimators based on the logistic model are assessed initially for the outcome variable ‘Current Smoking’ using 2006 survey data. All estimates are produced using SAS Version 9.2. Model-based SAE methods using regression models and area level random effects are found to be the most effective approach to create unbiased LGA-level estimates for ‘Current Smoking’, and are successful in creating estimates with face-validity when based on a single year of data. Of the other methods assessed neither LGA-based weighting nor generalised regression (GREG) estimates are shown to improve the direct LGA-level estimates sufficiently for them to be more useful than the current direct estimates. Conventional synthetic and composite estimators produce over-smoothed LGA-level estimates. In addition the n¨aive estimates of the mean square error (MSE) of these estimators underestimate the bias, and estimation of the root mean square error (RMSE) is difficult. The EBLUP and EBP estimates and their associated synthetic counterparts are created and evaluated for four key outcome variables (‘Current Smoking’, ‘Risk Alcohol Consumption’, ‘Overweight or obese’ and ‘Have difficulties getting health care when needed’), by sex, for survey years 2006, 2007 and 2008. These outcome variables differ in their

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations. This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations. This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.

Many different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable estimates for small domains. Often, the required data for various research purposes are available at different levels of aggregation. Based on the available data, individual-level or aggregated-level models are used in SAE. If unit-level data are available, SAE is usually based on models formulated at the unit level but they are ultimately used to produce estimates at the area level. However, parameter estimates obtained from individual and aggregated level analysis may be different in practice. Individual-level analysis usually results in small area estimates with smaller variances. However, if the unit-level working model is misspecified by exclusion of important auxiliary variables, parameter estimates obtained from the individual and aggregated level analysis will have different expectations. This thesis investigates the circumstances when using an area-level model may be more effective. This may happen due to some substantial contextual or area-level effects in the covariates which may be misspecified in an individual-level model. Ignoring these contextual effects leads to biased estimates. In particular, if an existing contextual variable is ignored, the parameter estimates calculated from an individual-level analysis will be biased, whereas an aggregated-level analysis can lead to small area estimates with less bias. Even if contextual variables are included in unit-level modeling, there may be an increase in the variance of parameter estimates due to increased number of variables in the working model. In this thesis, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are evaluated in SAE based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual effects is examined for models used in SAE.