Post-Stratification: A Modeler's Perspective
01 Sep 1993-Journal of the American Statistical Association (Taylor & Francis Group)-Vol. 88, Iss: 423, pp 1001-1012
TL;DR: This article developed Bayesian model-based theory for post-stratification, which is a common technique in survey analysis for incorporating population distributions of variables into survey estimates, such as functions of means and totals.
Abstract: Post-stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates. The basic technique divides the sample into post-strata, and computes a post-stratification weight w ih = rP h /r h for each sample case in post-stratum h, where r h is the number of survey respondents in post-stratum h, P h is the population proportion from a census, and r is the respondent sample size. Survey estimates, such as functions of means and totals, then weight cases by w h . Variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions. Literature on post-stratification is limited and has mainly taken the randomization (or design-based) perspective, where inference is based on the sampling distribution with population values held fixed. This article develops Bayesian model-based theory for the method. A basic normal post-stratification mod...
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Journal Article•
TL;DR: In this paper, the authors discuss in the context of several ongoing public health and social surveys how to develop general families of multilevel probability models that yield reasonable Bayesian inferences.
Abstract: The general principles of Bayesian data analysis imply that models for survey responses should be constructed conditional on all variables that affect the probability of inclusion and nonresponse, which are also the variables used in survey weighting and clustering. However, such models can quickly become very complicated, with potentially thousands of poststratification cells. It is then a challenge to develop general families of multilevel probability models that yield reasonable Bayesian inferences. We discuss in the context of several ongoing public health and social surveys. This work is currently open-ended, and we conclude with thoughts on how research could proceed to solve these problems.
425 citations
Cites background from "Post-Stratification: A Modeler's Pe..."
...Any of these equivalent expressions can be viewed as the posterior variance of θ given a noninformative prior distribution on the regression coefficients, and ignoring posterior uncertainty in σy (Little, 1993)....
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...When cell means are estimated using certain linear regression models, poststratified estimates can be interpreted as weighted averages (Little, 1991, 1993)....
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...We now review the unified notation for poststratification and survey weighting of Little (1991, 1993) and Gelman and Carlin (2002); see also Holt and Smith (1979)....
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TL;DR: In this article, the authors discuss in the context of several ongoing public health and social surveys how to develop general families of multilevel probability models that yield reasonable Bayesian inferences.
Abstract: The general principles of Bayesian data analysis imply that models for survey responses should be constructed conditional on all variables that affect the probability of inclusion and nonresponse, which are also the variables used in survey weighting and clustering. However, such models can quickly become very complicated, with potentially thousands of poststratification cells. It is then a challenge to develop general families of multilevel probability models that yield reasonable Bayesian inferences. We discuss in the context of several ongoing public health and social surveys. This work is currently open-ended, and we conclude with thoughts on how research could proceed to solve these problems.
382 citations
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TL;DR: The authors discusses the central role of propensity scores and balancing scores in the analysis of observational studies and shows that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates.
Abstract: : The results of observational studies are often disputed because of nonrandom treatment assignment. For example, patients at greater risk may be overrepresented in some treatment group. This paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies. The propensity score is the (estimated) conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates. Applications include: matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching, multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations, and visual representation of multivariate adjustment by a two-dimensional plot. (Author)
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TL;DR: In this article, it was shown that ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are missing at random and the observed data are observed at random, and then such inferences are generally conditional on the observed pattern of missing data.
Abstract: Two results are presented concerning inference when data may be missing. First, ignoring the process that causes missing data when making sampling distribution inferences about the parameter of the data, θ, is generally appropriate if and only if the missing data are “missing at random” and the observed data are “observed at random,” and then such inferences are generally conditional on the observed pattern of missing data. Second, ignoring the process that causes missing data when making Bayesian inferences about θ is generally appropriate if and only if the missing data are missing at random and the parameter of the missing data is “independent” of θ. Examples and discussion indicating the implications of these results are included.
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TL;DR: In this paper, three types of Bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician, and they are discussed in detail.
Abstract: A common reaction among applied statisticians is that the Bayesian statistician's energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying Bayes's theorem to calculate conditional distributions of unknowns given knowns. I feel, however, that the applied Bayesian statistician's tool-kit should be more extensive and include tools that may be usefully labeled frequency calculations. Three types of Bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician.
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TL;DR: The representative method has attracted the attention of many statisticians in different countries as discussed by the authors, mainly due to the general crisis, to the scarcity of money and to the necessity of carrying out statistical investigations connected with social life in a somewhat hasty way.
Abstract: Owing to the work of the International Statistical Institute, * and perhaps still more to personal achievements of Professor A.L. Bowley, the theory and the possibility of practical applications of the representative method has attracted the attention of many statisticians in different countries. Very probably this popularity of the representative method is also partly due to the general crisis, to the scarcity of money and to the necessity of carrying out statistical investigations connected with social life in a somewhat hasty way. The results are wanted in some few months, sometimes in a few weeks after the beginning of the work, and there is neither time nor money for an exhaustive research. But I think that if practical statistics has acquired something valuable in the representative method, this is due primarily to Professor A.L. Bowley, who not only was one of the first to apply this method in practice,t but also wrote a very fundamental memoirt giving the theory of the method. Since then the representative method has been often applied in different countries a.'l.d for different purposes. My chief topic being the theory of the representative method, I shall not go into its history and shall not quote the examples of its practical application
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