Linear mixed models

An introduction with applications in veterinary research


Table of Contents


Luc Duchateau

Biometrics Unit
International Livestock Research Institute (ILRI)
Nairobi, Kenya

Paul Janssen

Center for Statistics
Limburgs University Center (LUC)
Diepenbeek, Belgium

John Rowlands

Biometrics Unit
International Livestock Research Institute (ILRI)
Nairobi, Kenya

International Livestock Research Institute
P.O. Box 30709, Nairobi, Kenya

Center for Statistics, Limburgs University Center
Universitaire Campus, B-3590 Diepenbeek, Belgium

To Pascale: who fills my life with joy
Luc Duchateau

The International Livestock Research Institute (ILRI) began operations on 1 January 1995. ILRI is one of 16 centres in a worldwide agricultural research networks sponsored by the Consultative Group on Agricultural Research (CGIAR). ILRI conducts strategic research in the biological, animal and social sciences to improve livestock productivity in sustainable agricultural systems throughout the developing world. The objectives of the institute's research programmes are to improve animal health, nutrition and productivity (milk, meat, traction) in ways that are sustainable over the long term, to characterise and conserve the genetic diversity of indigenous tropical forage species and livestock breeds, to promote sound and equitable national policies for animal agricultural and natural resource management, and to strengthen the animal husbandry research programmes of developing countries.

The Limburgs University Center (LUC, Belgium), founded in 1973, offers education in medicine, economy and science. The Center for Statistics operates within the Faculty of Sciences. The three main activities of the centre are teaching, research and consultancy. One of the important activities is the organization of the international course programme 'Master of Science in Biostatistics'. This advanced study programme offers a solid education in statistics in general and biostatistics in particular. Completion of the full programme provides qualifications for positions in research centres, governmental services and industry. This programme is also ideally suited for students who want to pursue research towards a doctoral degree in statistics or in biostatistics. The Belgian Administration for Developmental Cooperation (BADC, Brussels) provides a number of scholarships to students from developing countries who want to take part in this biostatistics programme (a preparatory programme of three months, followed by the regular programme of twelve months).

This publication was printed by ILRI, P.O. Box 5689, Addis Ababa, Ethiopia

ISBN 92–9146–038–9

Correct citation: Duchateau L., Janssen P. and Rowlands G.J. 1998. Linear mixed models. An introduction with applications in veterinary research. ILRI (International Livestock Research Institute), Nairobi, Kenya. 159 pp.

Table of Contents


1 Introduction

2 The mixed model methodology

2.4.3 Estimating variance components

3  Into the realm of mixed models

Appendix A Data sets

Appendix B SAS programs

Appendix C Linear algebra useful for linear models

Appendix D The normal distribution

Appendix E Variances of linear combinations

Appendix F Denominator degree of freedom

Appendix G Expected mean squares