Non-Negative Variance Component Estimation for Mixed- Effects Models

Volume 2 - Issue 3

Jaesung Choi*

Received: February 27, 2020;   Published: March 11, 2020

DOI: 10.26717/CTBB.MS.ID.000140

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Abstract

This paper discusses projection methods to find nonnegative estimates for variance components of random effects in mixed models. The proposed methods are based on the concepts of projections, which are called projection method I, II and III. These three methods produce the same nonnegative estimates for the same data. Even though each method uses orthogonal projections in its own way, the results are the same for the variance components regardless of which method is used. It is shown that quadratic forms of an observation vector are constructed differently in each method. All sums of squares in quadratic forms of the observation vector can be expressed as squared distances of corresponding projections. A projection model is defined and used to evaluate expected values of quadratic forms of observations that are associated with variance components. Hartley’s synthesis is used as a method for finding the coefficients of variance components.

Keywords:Mixed model; projections; quadratic forms; random effects; synthesis

x Abstract| Introduction| Mixed Models| Projection method| Projection model| Examples| Conclusion| Funding| References|