## Table of contents for Introduction to mixed modelling : beyond regression and analysis of variance / Nicholas W. Galwey.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding. ```Contents
Preface. Why you need mixed modelling.
1. The need for more than one random-effect term when fitting a regression line
1.1 A data set with several observations of variable Y at each value of variable X
1.2 Simple regression analysis. Use of the software GenStat to perform the analysis.
1.3 Regression analysis on the group means
1.4 A regression model with a term for the groups
1.5 Construction of the appropriate F test for the significance of the explanatory variable when groups are present
1.6 The decision to regard a model term as random: a mixed model
1.7 Comparison of the tests in a mixed model with a test of lack of fit
1.8 The use of REsidual Maximum Likelihood (REML) to fit the mixed model
1.9 Equivalence of the different analyses when the number of observations per group is constant
1.10 Testing the assumptions of the analyses: inspection of the residual values
1.11 Use of the software R to perform the analyses
1.12 Fitting a mixed model using GenStat?s Graphical User Interface (GUI)
1.13 Summary
1.14 Exercises
2. The need for more than one random-effect term in a designed experiment
2.1 The split plot design: a design with two random-effect terms
2.2 The analysis of variance of the split plot design: a random-effect term for the main plots
2.3 Consequences of failure to recognise the main plots when analysing the split plot design
2.4 The use of REML to analyse the split plot design
2.5 A more conservative alternative to the Wald statistic
2.6 Justification for regarding block effects as random
2.7 Testing the assumptions of the analyses: inspection of the residual values
2.8 Use of R to perform the analyses
2.9 Summary
2.10 Exercises
3. Estimation of the variances of random-effect terms
3.1 The need to estimate variance components
3.2 A hierarchical random-effects model for a three-stage assay process
3.3 The relationship between variance components and stratum mean squares
3.4 Estimation of the variance components in the hierarchical random-effects model
3.5 Design of an optimum strategy for future sampling
3.6. Use of R to analyse the hierarchical three-stage assay process
3.7 Genetic variation: a crop field trial with an unbalanced design
3.8 Production of a balanced experimental design by ?padding? with missing values
3.9 Inspection of the residual values
3.10 Regarding a treatment term as a random-effect term. The use of mixed-model analysis to analyse an unbalanced data set.
3.11 Comparison of a variance component estimate with its standard error
3.12 An alternative significance test for variance components
3.13 Comparison among significance tests for variance components
3.14 Heritability. The prediction of genetic advance under selection.
3.15 Use of R to analyse the unbalanced field trial
3.16 Estimation of variance components in the regression analysis on grouped data
3.17 Estimation of variance components for block effects in the split-plot experimental design
3.18 Summary
3.19 Exercises
4. Interval estimates for fixed-effect terms in mixed models
4.1 The concept of an interval estimate
4.2 Standard errors for regression coefficients in a mixed-model analysis
4.3 Standard errors for differences between treatment means in the split plot design
4.4 A significance test for the difference between treatment means
4.5 The Least Significant Difference (LSD) between treatment means
4.6 Standard errors for treatment means in designed experiments: a difference in approach between analysis of variance and mixed-model analysis
4.7 Use of R to obtain SEs of differences between means and of means in a designed experiment
4.8 Summary
4.9 Exercises
5. Estimation of random effects in mixed models: Best Linear Unbiased Predictors (BLUPs)
5.1 The difference between the estimates of fixed and random effects
5.2 The method for estimation of random effects. The Best Linear Unbiased Predictor (BLUP) or ?shrunk estimate?.
5.3 The relationship between the shrinkage of BLUPs and regression towards the mean
5.4 Use of R for the estimation of random effects
5.5 Summary
5.6 Exercises
6. More advanced mixed models for more elaborate data sets
6.1 Features of the models introduced so far: a review
6.2 Further combinations of model features
6.3 The choice of model terms to be regarded as random
6.4 Disagreement concerning the appropriate significance test when fixed- and random-effect terms interact
6.5 Arguments for regarding block effects as random
6.6 Examples of the choice of fixed- and random-effect terms
6.7 Summary
6.8 Exercises
7. Two case studies
7.1 Further development of mixed modelling concepts through the analysis of specific data sets
7.2 A fixed-effects model with several variates and factors
7.3 Use of R to fit the fixed-effects model with several variates and factors
7.4 A random-effects model with several factors
7.5 Use of R to fit the random-effects model with several factors
7.6 Summary
7.7 Exercises
8. The use of mixed models for the analysis of unbalanced experimental designs
8.1 A balanced incomplete block design
8.2 Imbalance due to a missing block. Mixed-model analysis of the incomplete block design.
8.3 Use of R to analyse the incomplete block design
8.4 Relaxation of the requirement for balance: alpha designs
8.5 Use of R to analyse the alphalpha design
8.6 Summary
8.7 Exercises
9. Beyond mixed modelling
9.1 Review of the uses of mixed models
9.2 The Generalised Linear Mixed Model (GLMM). Fitting a logistic (sigmoidal) curve to proportions of observations.
9.3 Fitting a GLMM to a contingency table. Trouble-shooting when the mixed modelling process fails.
9.4 The Hierarchical Generalised Linear Model (HGLM)
9.5 The role of the covariance matrix in the specification of a mixed model
9.6 A more general pattern in the covariance matrix. Analysis of pedigree data.
9.7 Estimation of parameters in the covariance matrix. Analysis of temporal and spatial variation.
9.8 Summary
9.9 Exercises
10. Why is the criterion for fitting mixed models called REsidual Maximum Likelihood?
10.1 Maximum likelihood and residual maximum likelihood
10.2 Estimation of the variance from a single observation using the maximum-likelihood criterion
10.3 Estimation of from more than one observation
10.4 The ?-effect axis as a dimension within the sample space
10.5 Simultaneous estimation of ? and using the maximum-likelihood criterion
10.6 An alternative estimate of using the REML criterion
10.7 Extension to the general linear model. The fixed-effect axes as a sub-space of the sample space.
10.8 Application of the REML criterion to the general linear model
10.9 Extension to models with more than one random-effect term
10.10 Summary
10.11 Exercises
References
```

Library of Congress Subject Headings for this publication:

Multilevel models (Statistics).
Experimental design.
Regression analysis.
Analysis of variance.