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An example from proficiency testing of the application of principal components to the estimation of variance components in mixed models.

Shulman SA
Proc Ann Meet Am Stat Assoc, August 5-9, 2001, Atlanta, Georgia, 2001 Aug; :1-6
A common problem in lab proficiency testing is the estimation of measurement error and lab-to-lab variability, when duplicate samples are not available. Since measurement errors are often assumed to constitute a statistically independent set, the variance-covariance matrix should be the sum of a diagonal matrix (corresponding to measurement error) and a matrix different from an identity matrix (1). Multivariate statistical methods and mixed model methods provide tests that a variance-covariance matrix is of this form. In this paper, these methods are applied to data from an industrial hygiene laboratory proficiency testing program, the Proficiency Analytical Testing Program(PAT). Variances and covariances are assumed to be approximately proportional to an unknown power of the mean, and various possibilities for the form of the associated variance-covariance matrix are considered. The form depends on the scale on which the analyses are carried out, the possibility that the measurement error and non-measurement error have variances that are not proportional to the same power of the mean, and the dimensionality of the non-identity matrix. Examples are presented from PAT.
Models; Laboratories; Laboratory testing; Sampling; Sampling methods; Statistical analysis; Industrial hygiene programs; Analytical methods; Author Keywords: Variance Components; Interaction; Multivariate Methods
Stanley A. Shulman, National Institute for Occupational Safety and Health, 4676 Columbia Parkway, MS-R3, Cincinnati, OH 45233
Publication Date
Document Type
Conference/Symposia Proceedings
Fiscal Year
NIOSH Division
Source Name
Proceedings of the Annual Meeting of the American Statistical Association
Page last reviewed: June 15, 2021
Content source: National Institute for Occupational Safety and Health Education and Information Division