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Doctoral thesis, 2022

Analysis of factorial experiments using mixed-effects models: options for estimation, prediction and inference

Al-Sarraj, Razaw


In linear mixed-effects modelling of experiments, estimation of variance components, prediction of random effects, and computation of denominator degrees of freedom associated with inference on fixed effects, are important elements of the analysis. This thesis investigates alternatives to the likelihoodbased procedures for analysis of factorial experiments with normally distributed observations. Consistent methods, such as the maximum likelihood method, can be disadvantageous in cases where only small samples are available. Moreover, the algorithms used in linear mixed-effects models can be computationally demanding in large datasets. In this thesis, Henderson’s method 3, a non-iterative variance component estimation method, was considered for estimation of the variance components in a two-way mixed linear model with three variance components. The variance component estimator corresponding to one of the random effects was improved by perturbing the standard unbiased estimator. The improved variance component estimator performed better in terms of mean square error. In an application on a quantitative trait loci (QTL) study, the modified estimator was compared to the restricted maximum likelihood estimator on data from European wild boar × domestic pig intercross. The modified estimator was shown to approximate the results obtained from the restricted maximum likelihood (REML) method very closely. For balanced and unbalanced data in two-way with and without interaction models, the generalized prediction intervals for the random effects were derived. The coverage probabilities of the proposed intervals were compared with those based on the REML method and the approximate methods of Satterthwaite (1946) and Kenward and Roger (1997). The coverage of the proposed intervals was closer to the chosen nominal level than coverage of prediction intervals based on the REML method. With focus on Type I error, the implications of the available options in the mixed procedure of SAS and the lmer function of R for the inference on the fixed effects were examined. With the default setting of SAS, the frequency of Type I error was higher than with R. The Type I error rate in SAS was close to the nominal value when negative estimates of the variance components were allowed. Both software packages occasionally produced inaccurate results.


generalized prediction intervals; Henderson’s method 3; mean square error; mixed-effects models; QTL; REML; variance components

Published in

Acta Universitatis Agriculturae Sueciae
2022, number: 2022:15
ISBN: 978-91-7760-905-6, eISBN: 978-91-7760-906-3
Publisher: Swedish University of Agricultural Sciences