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Restricted linear models of fixed-effects
Journal of the Korean Data & Information Science Society 2018;29:593-600
Published online May 31, 2018
© 2018 Korean Data and Information Science Society.

Jaesung Choi1

1Department of Statistics, Keimyung University
Correspondence to: Professor, Department of Statistics, Keimyung University, Daegu 704-701, Korea. E-mail:
Received March 12, 2018; Revised May 7, 2018; Accepted May 9, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper discusses two methods for estimating the parameters of a linear model with restrictions given as a set of estimatable functions of fixed effects. One method is to use Lagrange multipliers and the other is transformations of restricted models. Although the parameter estimates are different from two methods, they are producing the invariant estimates for the estimable functions. It shows a general procedure how to set up the transformed model from a linear model with restrictions. It deals with forming the projection matrix and ascertaining estimable functions of the transformed model. It discusses that the projection matrix can be used to check whether the restrictions are of estimable functions. It also deals with the degrees of freedom and the variation of the residuals when estimable functions are used as part of the model.
Keywords : Estimable fuction, Lagrange multipliers, projection, reduced restricted model, restricted model.