Poverty maps are used to aid important political decisions such as allocation of development funds by governments and international organizations. Those decisions should be based on the most accurate poverty figures. However, often reliable poverty figures are not available at fine geographical levels or for particular risk population subgroups due to the sample size limitation of current national surveys. These surveys cannot cover adequately all the desired areas or population subgroups and, therefore, models relating the different areas are needed to "borrow strength" from area to area. In particular, the Spanish Survey on Income and Living Conditions (SILC) produces national poverty estimates but cannot provide poverty estimates by Spanish provinces due to the poor precision of direct estimates, which use only the province specific data. It also raises the ethical question of whether poverty is more severe for women than for men in a given province. We develop a hierarchical Bayes (HB) approach for poverty mapping in Spanish provinces by gender that overcomes the small province sample size problem of the SILC. The proposed approach has a wide scope of application because it can be used to estimate general nonlinear parameters. We use a Bayesian version of the nested error regression model in which Markov chain Monte Carlo procedures and the convergence monitoring therein are avoided. A simulation study reveals good frequentist properties of the HB approach. The resulting poverty maps indicate that poverty, both in frequency and intensity, is localized mostly in the southern and western provinces and it is more acute for women than for men in most of the provinces.
The simple comparison of two binomial populations is frequently of interest in epidemiology when the domains are large. For small domains, however, there are no exact methods except Fisher's exact test. A basic problem, therefore, is to compare two populations by assessing the difference between the proportions of individuals who possess a characteristic in the first and second populations. When there is prior information, we take the proportions to have independent conjugate beta distributions with known parameters, thereby facilitating a Bayesian analysis. We consider Bayesian inference on functions of the proportions, and the three most common scalar measures used in epidemiology and health services research, namely relative risk, odds ratio and attributable risk. We develop the highest density regions (both exact and approximate) for relative risk, odds ratio and attributable risk. In addition, we consider the Bayes factor for testing whether the model with a common proportion holds rather than one with distinct proportions. Using data from the population-based Worcester Heart Attack Study, we apply our methodology to study gender differences in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics. The Bayes factor, the approximate and exact intervals generally suggest that there are no substantial differences in the pharmacologic management of males and females hospitalized with AMI.
In the National Crime Survey (NCS), data on victimization can be poststrati ed into domains determined by urbanization, type of place, and poverty level. There is much dif culty in the analysis of binary data with substantial nonresponse. We consider three Bayesian hierarchical models for binary nonresponse data, like those from the NCS, which are clustered within a number of domains or areas. As in small area estimation, one key feature is that each model "borrows strength" across the areas through the selection approach to nonresponse. This is necessary to estimate the parameters with the least association to the observed data (i.e., weakly identi ed parameters). The rst model assumes that the nonresponse mechanism is ignorable, and the second model assumes that it is nonignorable. We argue that a discrete model expansion (a probabilistic mixture) may be inappropriate for modeling uncertainty about ignorability. Therefore, we propose a third model through a continuous model expansion on an odds ratio for each area. When the odds ratio is 1, we have the ignorable model; otherwise, the model is nonignorable. One important feature is that uncertainty about ignorability is incorporated by "centering" on the ignorable model. We analyze the poststrati ed data from the NCS to reveal latent features associated with nonresponse. The complexity of the posterior distributions of the parameters forces us to implement the methodology using Markov chain Monte Carlo methods. When the proportion of households with a characteristic (i.e., victimization in the NCS) and the response probability of a household in the population are estimated, we nd that the nonignorable model and the expansion model are similar but that they differ from the ignorable model. Although considerable prior information about the nonresponse mechanism is needed, the expansion model indicates that nonresponse for most of the areas is nonignorable. An analysis shows that inference is not very sensitive to an important distribution assumption, and a simulation exercise shows that the expansion model works very well.
Summary In 2011, the US Department of Agriculture's National Agricultural Statistics Service started the complete implementation of the County Agricultural Production Survey (CAPS). The CAPS is an annual survey to provide accurate county level acreage and production estimates of approved federal and state crop commodities. The current top down method of producing official county level estimates that satisfy the county–district–state benchmarking constraint is an expert assessment incorporating multiple sources of information. We propose a model‐based method that combines the CAPS acreage data with auxiliary data and improves county level survey estimation, while providing measures of uncertainty for the county level acreage estimates. Auxiliary sources of information include remote sensing data, weather data and planted acreage administrative data from other US agencies. A hierarchical Bayesian subarea level model is proposed and implemented, with an additional hierarchical level for the sampling variances. County level, model‐based acreage estimates have lower coefficients of variation than the corresponding county level survey acreage estimates. Top down benchmarking methods are investigated and the final acreage estimates satisfy the county–district–state benchmarking constraint.
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