Linear Equality Constraints in the General Linear Mixed Model |
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Authors: | Lloyd J. Edwards Paul W. Stewart Keith E. Muller Ronald W. Helms |
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Affiliation: | Department of Biostatistics, School of Public Health, The University of North Carolina, Chapel Hill 27599-7420, USA. Lloyd_Edwards@unc.edu |
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Abstract: | Scientists may wish to analyze correlated outcome data with constraints among the responses. For example, piecewise linear regression in a longitudinal data analysis can require use of a general linear mixed model combined with linear parameter constraints. Although well developed for standard univariate models, there are no general results that allow a data analyst to specify a mixed model equation in conjunction with a set of constraints on the parameters. We resolve the difficulty by precisely describing conditions that allow specifying linear parameter constraints that insure the validity of estimates and tests in a general linear mixed model. The recommended approach requires only straightforward and noniterative calculations to implement. We illustrate the convenience and advantages of the methods with a comparison of cognitive developmental patterns in a study of individuals from infancy to early adulthood for children from low-income families. |
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Keywords: | Cognitive development Correlated outcomes IQ Longitudinal data analysis Parameter constraints Random effect models Singular-value decomposition Transformations |
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