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Linear Equality Constraints in the General Linear Mixed Model
Author(s) -
Edwards Lloyd J.,
Stewart Paul W.,
Muller Keith E.,
Helms Ronald W.
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.01185.x
Subject(s) - generalized linear mixed model , piecewise linear function , mixed model , linear model , general linear model , linear regression , computer science , univariate , set (abstract data type) , generalized linear model , proper linear model , longitudinal data , mathematics , mathematical optimization , econometrics , bayesian multivariate linear regression , data mining , machine learning , multivariate statistics , geometry , programming language
Summary. 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 univari‐ate 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.