Envelopes for multivariate linear regression with linearly constrained coefficients

R. D Cook, Liliana Forzani, Lan Liu

Research output: Contribution to journalArticlepeer-review


A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection.

Original languageEnglish (US)
Pages (from-to)429-446
Number of pages18
JournalScandinavian Journal of Statistics
Issue number2
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© 2023 The Board of the Foundation of the Scandinavian Journal of Statistics.


  • envelope models
  • growth curves
  • repeated measures


Dive into the research topics of 'Envelopes for multivariate linear regression with linearly constrained coefficients'. Together they form a unique fingerprint.

Cite this