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Strictly Positive Estimates of Variance Components for Measurement Systems Analysis Models

Laura Lancaster (LauraL@JMP​), PhD, JMP Principal Research Statistician Developer, SAS
Chris Gotwalt, PhD, JMP Director of Statistical Research and Development, SAS

Variance components for measurement systems analysis (MSA) models are typically estimated using one of three techniques: the average and range method, expected means squares (EMS), and restricted maximum likelihood (REML). Each of these methods often produce negative variance components estimates. Because negative variance component estimates do not make sense in MSA studies, these estimates are set to zero. Posterior mean estimates using standard noninformative priors, such as Jeffreys prior or a flat prior, generate strictly positive variance components but have unacceptably high mean squared errors. We have generalized an alternative noninformative prior method that was developed by Portnoy and Sahai in the 1970s to unbalanced data and have applied this method to MSA studies. We will explain this method and show results of simulation experiments that compare the ability of this method to estimate variance components for typical MSA models with REML.

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