Introduction to Mixed Modelling: Beyond Regression and Analysis of Variance混合模型导论：回归与方差分析及其他问题

作者： N. W. Galwey著

出 版 社：

出版时间： 2006-11-1字数：版次： 1页数： 366印刷时间： 2006/11/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780470014967包装： 精装编辑推荐

作者简介

Nicholas W. Galwey, Principal Scientist, GlaxoSmithKline, Harlow, Essex. A respected consultant and researcher in the pharmaceutical industry with extensive teaching experience.

内容简介

Mixed modelling is one of the most promising and exciting areas of statistical analysis, enabling more powerful interpretation of data through the recognition of random effects. However, many perceive mixed modelling as an intimidating and specialized technique. This book introduces mixed modelling analysis in a simple and straightforward way, allowing the reader to apply the technique confidently in a wide range of situations.

Introduction to Mixed Modelling shows that mixed modelling is a natural extension of the more familiar statistical methods of regression analysis and analysis of variance. In doing so, it provides the ideal introduction to this important statistical technique for those engaged in the statistical analysis of data.

目录

Preface

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 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 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 more than one random-effect term

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 mixed modelling 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-effect 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-effect 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 Regarding a treatment term as a random-effect term. The use of mixed-model analysis to analyse an unbalanced data set

3.10 Comparison of a variance-component estimate with its standard error

3.11 An alternative significance test for variance components

3.12 Comparison among significance tests for variance components

3.13 Inspection of the residual values

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 SEs for regression coefficients in a mixed-model analysis

4.3 SEs 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 between treatment means

4.6 SEs for treatment means in designed experiments: a difference in approach between analysis of variance and mixed-model analysis

……

5 Estimation of random effects in mixed models:best linear unbiased

6 More advanced mixed models for more elaborate data sets

7 Two case studies

8 The use of mixed models for the analysis of unbalanced experimental designs

9 Beyond mixed modelling

10 Why is the criterion for fitting mixed models called residual maximum likelihood?

References

Index