Using data augmentation via the Gibbs Sampler to incorporate missing covariate structure in linear models for ecological assessments |
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Authors: | Edward L Boone Keying Ye Eric P Smith |
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Institution: | (1) Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284, USA;(2) Department of Management Science and Statistics, University of Texas at San Antonio, 6900 N Loop 1604 W, San Antonio, TX 78249, USA;(3) Department of Statistics, Virginia Tech, Blacksburg, VA 24061, USA |
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Abstract: | Missing covariate values in linear regression models can be an important problem facing environmental researchers. Existing
missing value treatment methods such as Multiple Imputation (MI), the EM algorithm and Data Augmentation (DA) have the assumption that both observed and unobserved data come from the same distribution,
most commonly a multivariate normal or a conditionally multivariate normal family. These methods do try to incorporate the
missing data mechanism and rely on the assumption of Missing At Random (MAR). We present a DA method which does not rely on
the MAR assumption and can model missing data mechanisms and covariate structure. This method utilizes the Gibbs Sampler as
a tool for incorporating these structures and mechanisms. We apply this method to an ecological data set that relates fish
condition to environmental variables. Notice that the presented DA method detects relationships that are not detected when
other missing data methods are employed.
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Keywords: | Bayesian methods Biological monitoring Data augmentation Ecological health Gibbs sampler Stressor-response Missing data |
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