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Abstract 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.
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Mixed effects envelope models
When multiple measures are collected repeatedly over time, redundancy typically exists among responses. The envelope method was recently proposed to reduce the dimension of responses without loss of information in regression with multivariate responses. It can gain substantial efficiency over the standard least squares estimator. In this paper, we generalize the envelope method to mixed effects models for longitudinal data with possibly unbalanced design and time‐varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Improved accuracy and efficiency of the proposed method over the standard mixed effects model estimator are observed in both the simulations and the Action to Control Cardiovascular Risk in Diabetes (ACCORD) study.
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- Award ID(s):
- 1916013
- PAR ID:
- 10453340
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Stat
- Volume:
- 9
- Issue:
- 1
- ISSN:
- 2049-1573
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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