title: Linear equality constraints in the general linear mixed model.
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.
authors.affiliation: Department of Biostatistics, School of Public Health, The University of North Carolina, Chapel Hill 27599-7420, USA. Lloyd_Edwards@unc.edu
authors.forename: L J
authors.initials: LJ
authors.lastname: Edwards
authors.forename: P W
authors.initials: PW
authors.lastname: Stewart
authors.forename: K E
authors.initials: KE
authors.lastname: Muller
authors.forename: R W
authors.initials: RW
authors.lastname: Helms
mesh_terms: D000293:Adolescent; D000328:Adult; D001699:Biometry; D002648:Child; D002657:Child Development; D002675:Child, Preschool; D003071:Cognition; D006801:Humans; D007223:Infant; D016014:Linear Models; D008137:Longitudinal Studies; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data