Abstract
Hierarchical selection models are introduced and shown to be useful in meta-analysis. These models combine the use of hierarchical models, allowing investigation of variability both within and between studies, and weight functions, allowing modeling of nonrandomly selected studies. Markov chain Monte Carlo (MCMC) methods are used to estimate the hierarchical selection model. This is first illustrated for known weight functions, and then extended to allow for estimation of unknown weight functions. To investigate sensitivity of results to unobserved studies directly, which is shown to be different from modeling bias in the selection of observed studies, the hierarchical selection model is used in conjunction with data augmentation. Again, MCMC methods may be used to estimate the model. This is illustrated for an unknown weight function.
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