2,646 research outputs found
Bayesian Inference under Cluster Sampling with Probability Proportional to Size
Cluster sampling is common in survey practice, and the corresponding
inference has been predominantly design-based. We develop a Bayesian framework
for cluster sampling and account for the design effect in the outcome modeling.
We consider a two-stage cluster sampling design where the clusters are first
selected with probability proportional to cluster size, and then units are
randomly sampled inside selected clusters. Challenges arise when the sizes of
nonsampled cluster are unknown. We propose nonparametric and parametric
Bayesian approaches for predicting the unknown cluster sizes, with this
inference performed simultaneously with the model for survey outcome.
Simulation studies show that the integrated Bayesian approach outperforms
classical methods with efficiency gains. We use Stan for computing and apply
the proposal to the Fragile Families and Child Wellbeing study as an
illustration of complex survey inference in health surveys
General Design Bayesian Generalized Linear Mixed Models
Linear mixed models are able to handle an extraordinary range of
complications in regression-type analyses. Their most common use is to account
for within-subject correlation in longitudinal data analysis. They are also the
standard vehicle for smoothing spatial count data. However, when treated in
full generality, mixed models can also handle spline-type smoothing and closely
approximate kriging. This allows for nonparametric regression models (e.g.,
additive models and varying coefficient models) to be handled within the mixed
model framework. The key is to allow the random effects design matrix to have
general structure; hence our label general design. For continuous response
data, particularly when Gaussianity of the response is reasonably assumed,
computation is now quite mature and supported by the R, SAS and S-PLUS
packages. Such is not the case for binary and count responses, where
generalized linear mixed models (GLMMs) are required, but are hindered by the
presence of intractable multivariate integrals. Software known to us supports
special cases of the GLMM (e.g., PROC NLMIXED in SAS or glmmML in R) or relies
on the sometimes crude Laplace-type approximation of integrals (e.g., the SAS
macro glimmix or glmmPQL in R). This paper describes the fitting of general
design generalized linear mixed models. A Bayesian approach is taken and Markov
chain Monte Carlo (MCMC) is used for estimation and inference. In this
generalized setting, MCMC requires sampling from nonstandard distributions. In
this article, we demonstrate that the MCMC package WinBUGS facilitates sound
fitting of general design Bayesian generalized linear mixed models in practice.Comment: Published at http://dx.doi.org/10.1214/088342306000000015 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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