"Scientists usually need to understand the extent of the association of two attributes, and the data are typically presented in two-way categorical tables. In science, the chi-squared test is routinely used to analyze data from such tables. However, in many applications the chi-squared test can be defective. For example, when the sample size is small, the chi-squared test may not be applicable. The terms small area" and local area" are commonly used to denote a small geographical area, such as a county. If a survey has been carried out, the sample size within any particular small area may be too small to generate accurate estimates from the data, and a chi-squared test may be invalid (i.e., expected frequencies in some cells of the table are less than ?ve). To deal with this problem we use Bayesian small area estimation. Because it is used toorrow strength" from related or similar areas. It enhances the information of each area with common exchangeable information. We use a Bayesian model to estimate a Bayes factor to test the independence of the two variables. We apply the model to test for the independence between bone mineral density (BMD) and body mass index (BMI) from 31 counties and we compare the results with a direct Bayes factor test. We have also obtained numerical and sampling errors; both the numerical and sampling errors of our Bayes factor are small. Our model is shown to be much less sensitive to the speci?cation of the prior distribution than the direct Bayes factor test which is based on each area only."

Enrollment projections are used by school administrators to predict the number of students expected to attend a school district within a defined period of time. This dissertation examines methods used for making enrollment projections and seeks to improve these methods through the application of geographic principles. The presented thesis challenges the existing aspatial framework used to calculate grade progression rates, arguing that a spatial framework improves projection accuracy. Grade progression rates are the critical element in enrollment projections and this dissertation's major contribution is the analysis of four different grade progression rate calculations at the school district level. This dissertation also argues that grade progression rates represent spatial relationships of migration that exist between adjacent school districts and uses these spatial relationships to create a new spatial Bayesian approach. This dissertation demonstrates that geographic methods can be successfully integrated to improve enrollment project accuracy through the reduction of the small number problem. In addition, this research identifies the importance of smoothing effects of the modified cohort progression method when compared to Bayesian approaches.

No description available.

This paper demonstrates the utility of small area estimation (SAE) of poverty methods for researchers that wish to conduct a detailed welfare analysis as part of a larger survey of a small geographic area of interest. Researchers studying context-specific technologies or interventions can incorporate the survey-based SAE of poverty approach to conduct detailed poverty analyzes of their specific area of interest without the expense of collecting household consumption data. This study applies SAE methods as part of an impact assessment of a locally adapted conservation agriculture production system in Uganda's Tororo District. Using SAE, I assess the Tororo District's Foster-Greer-Thorbecke (FGT) rural poverty indices, estimate the effects of per acre farm profit increases to poor households on the district's rural poverty indices, and compare the findings to current estimates of the net returns from conservation agriculture in the Tororo District. The SAE results suggest that increasing the farm profits of the bottom 30% of households by two U.S. dollars per acre per season could reduce the district's rural poverty incidence by one percentage point. The available data on the net returns to conservation agriculture in the Tororo District, however, indicate that these modest increases may only be achievable for adopting households that face high land preparation costs. / Master of Science

Direct survey estimates for small areas are likely to yield unacceptably large standard errors due to the small sample sizes in the areas. This makes it necessary to use models to“borrow strength" from related areas to find more reliable estimate for a given area or, simultaneously, for several areas. For instance, in many applications, data on related multiple characteristics and auxiliary variables are available. Thus, multivariate modeling of related characteristics with multiple regression can be implemented. However, while model-based small area estimates are very useful, one potential difficulty with such estimates when models are used is that the combined estimate from all small areas does not usually match the value of the single estimate on the large area. Benchmarking is done by applying a constraint to ensure that the“total" of the small areas matches the“grand total". Benchmarking can help to prevent model failure, an important issue in small area estimation. It can also lead to improved prediction for most areas because of the information incorporated in the sample space due to the additional constraint. We describe both the univariate and multivariate Bayesian nested error regression models and develop a Bayesian predictive inference with a benchmarking constraint to estimate the finite population means of small areas. Our models are unique in the sense that our benchmarking constraint involves unit-level sampling weights and the prior distribution for the covariance of the area effects follows a specific structure. We use Markov chain Monte Carlo procedures to fit our models. Specifically, we use Gibbs sampling to fit the multivariate model; our univariate benchmarking only needs random samples. We use two datasets, namely the crop data (corn and soybeans) from the LANDSAT and Enumerative survey and the NHANES III data (body mass index and bone mineral density), to illustrate our results. We also conduct a simulation study to assess frequentist properties of our models.

Bayesian hierarchical models are effective tools for small area estimation by pooling small datasets together. The pooling procedures allow individual areas to “borrow strength” from each other to desirably improve the estimation. This work is an extension of Nandram and Choi (2002), NC, to perform inference on finite population proportions when there exists non-identifiability of the missing pattern for nonresponse in binary survey data. We review the small-area selection model (SSM) in NC which is able to incorporate the non-identifiability. Moreover, the proposed SSM, together with the individual-area selection model (ISM), and the small-area pattern-mixture model (SPM) are evaluated by real crime data in Stasny (1991). Furthermore, the methodology is compared to ISM and SPM using simulated small area datasets. Computational issues related to the MCMC are also discussed.

Small area estimation is an arena that has seen rapid development in the past 50 years, due to its widespread applicability in government projects, marketing research and many other areas. However, it is often difficult to obtain error-free data for this purpose. In this dissertation, each project describes a model used for small area estimation in which the covariates are measured with error. We applied different methods of bias correction to improve the estimates of the parameter of interest in the small areas. There is a variety of methods available for bias correction of estimates in the presence of measurement error. We applied the simulation extrapolation (SIMEX), ordinary corrected scores and Monte Carlo corrected scores methods of bias correction in the Fay-Herriot model, and investigated the performance of the bias-corrected estimators. The performance of the estimators in the presence of non-normal measurement error and of the SIMEX estimator in the presence of non-additive measurement error was also studied. For each of these situations, we presented simulation studies to observe the performance of the proposed correction procedures. In addition, we applied our proposed methodology to analyze a real life, nontrivial data set and present the results. We showed that the Lohr-Ybarra estimator is slightly inefficient and that applying methods of bias correction like SIMEX, corrected scores or Monte Carlo corrected scores (MCCS) increases the efficiency of the small area estimates. In particular, we showed that the simulation based bias correction methods like SIMEX and MCCS provide a greater gain in efficiency. We also showed that the SIMEX method of bias correction is robust with respect to departures from normality or additivity of measurement error. We showed that the MCCS method is robust with respect to departure from normality of measurement error.

This thesis is an examination of the sex and gender differences in measures of relative deprivation for Winnipeg, Manitoba, and the value of these measures to predict health outcomes. Within theoretical frameworks of relative deprivation and intersectionality, principal component analysis was used to test nineteen different versions of a national area-based deprivation index using Census variables, for the total population and for males and females separately. Only one version of the deprivation index provided consistent factor scores, in keeping with the theoretical constructs, for the total, female-only and male-only populations for Winnipeg. Administrative health data were used to calculate area-level rates of select health outcomes and binomial negative regressions were then used to analyze whether the “best” index was predictive of health outcomes for the three populations. In regression models, only the “material” component of the deprivation index was predictive of the health outcomes, but results varied across the three populations. The application of the “best” deprivation index to health planning may depend on the health issue and the population in question. This thesis confirmed that examining the intersections of sex, gender and deprivation in population health research unmasks important differences that would otherwise be missed and could have implications in health planning.

This thesis is an examination of the sex and gender differences in measures of relative deprivation for Winnipeg, Manitoba, and the value of these measures to predict health outcomes. Within theoretical frameworks of relative deprivation and intersectionality, principal component analysis was used to test nineteen different versions of a national area-based deprivation index using Census variables, for the total population and for males and females separately. Only one version of the deprivation index provided consistent factor scores, in keeping with the theoretical constructs, for the total, female-only and male-only populations for Winnipeg. Administrative health data were used to calculate area-level rates of select health outcomes and binomial negative regressions were then used to analyze whether the “best” index was predictive of health outcomes for the three populations. In regression models, only the “material” component of the deprivation index was predictive of the health outcomes, but results varied across the three populations. The application of the “best” deprivation index to health planning may depend on the health issue and the population in question. This thesis confirmed that examining the intersections of sex, gender and deprivation in population health research unmasks important differences that would otherwise be missed and could have implications in health planning.

Scholars have established that our geographic environments – including infrastructure for walking and food availability - contribute to the current obesity epidemic in the United States. However, the relationship between food, walkability, and obesity has largely only been investigated in large urban areas. Further, many studies have not taken an in-depth look at the spatial fabric of walkability, food, and obesity. The purpose of this study was two-fold: 1) to explore reliable methods, using sociodemographic census data, for estimating obesity at the neighborhood level in one region of the U.S. made up of rural areas and small towns – southern Illinois; and 2) to investigate the ways that the food environment and walkability correlate with obesity across neighborhoods with different geographies, population densities, and socio-demographic characteristics. This study uses spatial analysis techniques and GIS, namely geographically weighted multivariate linear regression and cluster analysis, to estimate obesity at the census block group level. Walkability and the food environment are investigated in depth before the relationship between obesity and the built environment is analyzed using GIS and spatial analysis. The study finds that the influence of various food and walkability measures on obesity is spatially varying and significantly mediated by socio-demographic factors. The study concludes that the relationship between obesity and the built environment can be studied quantitatively in study areas of any size or population density but an open-minded approach toward measures must be taken and geographic variation cannot be ignored. This work is timely and important because of the dearth of small area obesity data, as well an absence of research on obesogenic physical environments outside of large urban areas.