SRMS
Session Slot: 10:30-12:20 Tuesday
Estimated Audience Size: 90
AudioVisual Request: xxx
Session Title: The Application of Logistic Models with Mixed Effects to Sample
Survey Datasets
In recent years, there has been tremendous progress
in developing the algorithms and software to fit models of this type.
At least two distinct methodologies have evolved, one frequentist,
the other Bayesian. The frequentist approach most favored is the
PQL (penalized quasi-likelihood) of Breslow and Clayton. This method
has been incorporated into two packages for analysis of multi-level
data, HLM and MLn. The Bayesian approach uses Monte Carlo Markov Chain
methods such as Gibbs sampling, data augmentation, and the
Metropolis-Hastings algorithm. Both methods are very computationally
intensive, but the Bayesian methods are more so than the
frequentist methods. The disadvantage of the frequentist methods is
that they tend to underestimate the variance of predicted random effects.
In this session, there will be speakers from both schools.
The idea will be for each to present a brief description of the
methodology (preferably, accessible to a wider audience), to contrast
their methodology with other available methodology, and to present
any evaluation results that are available. The most common applications
of these methods to sample survey datasets involve small area estimation
and imputation. Given the tradition of design-based inference of
datasets for public policy purposes, a critical question for the
proponents of these new methodologies is how to present their estimates
to journalists and politicians. The discussant was chosen specifically
to focus on this issue from the randomization-based perspective.
Theme Session: No
Applied Session: Yes
Session Organizer: Judkins, David R. Westat
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Email: jundkind1@westat.com
Session Timing: 110 minutes total (Sorry about format):
110 minutes total...please allocate Opening Remarks by Chair - 5 minutes First Speaker - 25 minutes Second Speaker - 25 minutes Third Speaker - 25 minutes Discussant - 15 minutes Floor Discussion - 15 minutes
Session Chair: Judkins, David R. Westat
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1. Bayesian Model Averaging for Small Area Estimation with Binary Data
Ghosh, Malay, University of Florida
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Email: ghoshm@stat.ufl.edu
Natarajan, Kannan, Bristol-Myers Squibb PRI
Abstract: Hierararchical Bayesian methods are now being widely used for the analysis of generalized mixed linear models (GLMM). One of the advantages of this approach is that it accounts for the uncertainty in the variance components by modeling rather than simple point estimation. These methods have proved to be very useful for small area estimation where one needs estimates simultaneously for several local areas. Sample sizes being small for the individual areas, one needs to ``borrow strength'' from similar neighboring areas.Often there are situations when there is no clearcut choice among several models. In such situations, one can find the posterior probabilities of the different models, pick the one with the highest posterior probability, and find small area estimates and standard errors based on that model. Another option is not to report estimates and standard errors based on a single model, but report estimates which are weighted averages of estimates based on different contemplated models, the respective weights being proportional to the poterior probabilities of these models.
We will illustrate the Bayesian model averaging idea with respect to a dataset pertaining to job satisfaction. There are 84 local areas classified according to seven geographic regions and 12 demographic categories. The responses are binary. The analysis is provided by using several hierarchical Bayes GLMM's, and then using the model averaging idea.
2. Model-Based Approaches to Small Area Estimation with Binary Data
McCulloch, Charles E., Cornell University
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Email: cem1@cornell.edu
Abstract: Small area estimation in sample surveys can be addressed using mixed models for binary data. Methods and software for model-based, frequentist analysis are much more prevalent than a decade ago. I will illustrate the use of mixed models and best predicted values for small area estimation and compare and contrast the various methods available for fitting such models. Several readily-available methods perform poorly for binary data and should be avoided.
3. Estimation by the Method of Generalized Zero Functions for Mixed Nonlinear Models
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Email: singhavi@statcan.ca
Wu., S., Statistics Canada
Abstract: There has been considerable development in recent years in the area of Bayesian and Frequentist approaches to estimation of parameters for mixed nonlinear models. Bayesian methods do provide optimal estimates for all parameters (fixed and random) but the assumptions about the priors are hard to verify. Frequentist methods, on the other hand, are based on much less restrictive distributional assumptions (e.g., up to second moments in a semiparametric framework) but may not give rise to consistent estimates of fixed (first and second order) parameters. In this paper we propose a frequentist solution termed method of generalized zero functions(GZF) which does give consistent estimates of all fixed parameters for a fairly general class of mixed nonlinear models, and optimal estimates of first order parameters (fixed and random). The GZF method can be viewed as a natural generalization of the familiar maximum quasi-likelihood method (or more generally the method of estimating functions) for fixed nonlinear models. This is similar to the way the best linear unbiased prediction for mixed linear models generalizes the method of linear zero functions of C.R. Rao (this is equivalent to BLUE) for fixed linear models. For survey data the GZF method adapts easily the Godambe-Thompson approach for optimal (jointly under design-model) estimation of superpopulation parameters. Illustrative examples for estimation with survey and nonsurvey data will be presented.
Discussant: Folsom, Ralph Research Triangle Institute
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List of speakers who are nonmembers: None