Course detail

LCE5714 - Mixed Models and Variance Components


Credit hours

In-class work
per week
Practice
per week
Credits
Duration
Total
3
1
8
15 weeks
120 hours

Instructor
Clarice Garcia Borges Demetrio
Cristian Marcelo Villegas Lobos
Renata Alcarde Sermarini

Objective
Enable the student to use the mixed model methodology to analyse data from studies that include
random effects.

Content
To define mixed models, to estimate the parameters, to predict the random effects, to calculate the
expectation of mean squares or to use the Hasse diagrams to get them and to estimate the components
of variance. Enable the student to make applications of variance components, using R software.
Contents:1. Mixed model definition.
2. Parameter estimation and prediction of random effects
3. Expectation of mean squares
3.1 Completely randomized designs
3.2 Randomized complete block designs
3.3 Latin saquare designs
3.4 Factorial designs
3.5 Split-plot designs
3.6 Hierarchical designs
3.7 Series of experiments
3.8 Hasse Diagram
4. Estimation methods for variance components
4.1 Moment method
4.2 Maximum likelihood
4.3 Restricted maximum likelihood
5. Hypotheses testing
6. Confidence intervals for variance components
7. Aplications in sampling and breeding

Bibliography
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BARBIN, D. Componentes de Variância - Teoria e Aplicações. 3ª ed. FEALQ, Piracicaba, SP. 2019. 144p.
BIOMETRICS. Washington, Volume 7, nº 1. 1951.
COX, D.R.; SOLOMON, P.J. Components of Variance. Chapman & Hall/CRC, Londres. 2003.
DEMIDENKO, E. Mixed Models. Theory and Applications. John Wiley, Nova Iorque. 2004.
GALWEY, N.W. Introduction to Mixed Modelling. Beyond Regression and Analysis of Variance. John
Wiley, Sussex. 2008.
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Nova Iorque. 1999.
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McCULLOCH, C.E.; SEARLE, S.S.; NEUHAUS, J.M. Generalized, Linear and Mixed Models. John Wiley,
Nova Iorque. 2008.
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Wiley, Nova Iorque. 2006.
RAO, P.S.R.S. Variance Components Estimation. Mixed Models, Methodologies and Applications.
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SCHABENBERGER, O; PIERCE, F.J. Contemporary Statistical Models for the Plant and Soi Sciences.
Taylor & Francis, Londres. 2001.
SEARLE, S.R.; GRUBER, M.H.J. Linear Models. 2ª ed. Wiley, 2016.SEARLE, S.R.; CASELA, G.; McCULLOCH, C.E. Variance Components. 2ª ed. Wiley-Interscience. 2006.
WELHAM, S.J.; GEZAN, S.A.; CLARK, S.J.; MEAD, A. Statistical Methods in Biology. Design and Analysis
of Experiments and Regression. CRC Press, Londres. 2015.
WEST, B.; WELCH, K.B; GALECKI, A.T. Linear Mixed Models: A Practical Guide Using Statistical Software.
2ª ed. Chapman & Hall/CRC. 2014.