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Reml guide Reml CA Guide to REML in GenStat by Roger Payne Sue Welham and Simon Harding GenStat Release was developed by VSN International Ltd in collaboration with practising statisticians at Rothamsted and other organisations in Britain Australia and Ne

Reml CA Guide to REML in GenStat by Roger Payne Sue Welham and Simon Harding GenStat Release was developed by VSN International Ltd in collaboration with practising statisticians at Rothamsted and other organisations in Britain Australia and New Zealand Main authors R W Payne S A Harding D A Murray D M Soutar D B Baird A I Glaser S J Welham A R Gilmour R Thompson R Webster Other contributors A E Ainsley N G Alvey C F Ban ?eld R I Baxter K E Bicknell I C Channing B R Cullis P G N Digby A N Donev M F Franklin J C Gower T J Hastie S K Haywood A F Kane A Kobilinsky W J Krzanowski P W Lane S D Langton P J Laycock P K Leech J H Maindonald G W Morgan J A Nelder A Papritz H D Patterson D L Robinson G J S Ross P J Rowley H R Simpson R J Tibshirani A D Todd G Tunnicli ?e Wilson L G Underhill P J Verrier R W M Wedderburn R P White and G N Wilkinson Published by E-mail Website VSN International The Waterhouse Waterhouse Street Hemel Hempstead Hertfordshire HP ES UK info genstat co uk http www genstat co uk GenStat is a registered trade of VSN International All rights reserved ? VSN International CContents Introduction Linear mixed models Split-plot design Commands for REML analysis Practical Means plots Practical Predictions Practical A non-orthogonal design Practical Residual plots Practical Meta analysis with REML Example a series of fungicide trials Commands for meta analysis Practical Spatial analysis Traditional blocking Correlation modelling The VSTRUCTURE directive Practical The variogram Practical Repeated measurements Correlation models over time Practical Random coe ?cient regression Practical Index C CIntroduction The REML algorithm provides several important types of analysis that are useful in a wide range of application areas including biology medicine industry and ?nance In biology they are usually known as linear mixed models but in some application areas e g education they may be called multi-level models GenStat's REML facilities are powerful and comprehensive but nevertheless very straightforward and easy to use This book is designed to introduce you to these techniques and give you the knowledge and con ?dence to use them correctly and e ?ectively It has been written to provide the notes for VSN ? s course on the use of REML in GenStat but it can be used equally well as a self-learning tool One of the key features of REML is that it can analyse data that involve more than one source of error variation In this respect it is similar to the GenStat ANOVA algorithm and the similarities and di ?erences between the two methods are explored in detail in Chapter An important advantage of REML over ANOVA is that it can analyse unbalanced designs It also has a powerful prediction algorithm that extends the ideas in GenStat ? s regression prediction algorithm to cover random as well as ?xed