{"product_id":"introduction-to-mixed-modelling-9781119945499","title":"Introduction to Mixed Modelling","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMixed modelling is very useful, and easier than you think!     Mixed modelling is now well established as a powerful approach to statistical data analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The need for more than one random-effect term when fitting a regression line 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 A data set with several observations of variable Y at each value of variable X 1\u003c\/p\u003e \u003cp\u003e1.2 Simple regression analysis: Use of the software GenStat to perform the analysis 2\u003c\/p\u003e \u003cp\u003e1.3 Regression analysis on the group means 9\u003c\/p\u003e \u003cp\u003e1.4 A regression model with a term for the groups 10\u003c\/p\u003e \u003cp\u003e1.5 Construction of the appropriate F test for the significance of the explanatory variable when groups are present 13\u003c\/p\u003e \u003cp\u003e1.6 The decision to specify a model term as random: A mixed model 14\u003c\/p\u003e \u003cp\u003e1.7 Comparison of the tests in a mixed model with a test of lack of fit 16\u003c\/p\u003e \u003cp\u003e1.8 The use of REsidual Maximum Likelihood (REML) to fit the mixed model 17\u003c\/p\u003e \u003cp\u003e1.9 Equivalence of the different analyses when the number of observations per group is constant 21\u003c\/p\u003e \u003cp\u003e1.10 Testing the assumptions of the analyses: Inspection of the residual values 26\u003c\/p\u003e \u003cp\u003e1.11 Use of the software R to perform the analyses 28\u003c\/p\u003e \u003cp\u003e1.12 Use of the software SAS to perform the analyses 33\u003c\/p\u003e \u003cp\u003e1.13 Fitting a mixed model using GenStat’s Graphical User Interface (GUI) 40\u003c\/p\u003e \u003cp\u003e1.14 Summary 46\u003c\/p\u003e \u003cp\u003e1.15 Exercises 47\u003c\/p\u003e \u003cp\u003eReferences 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The need for more than one random-effect term in a designed experiment 52\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The split plot design: A design with more than one random-effect term 52\u003c\/p\u003e \u003cp\u003e2.2 The analysis of variance of the split plot design: A random-effect term for the main plots 54\u003c\/p\u003e \u003cp\u003e2.3 Consequences of failure to recognize the main plots when analysing the split plot design 62\u003c\/p\u003e \u003cp\u003e2.4 The use of mixed modelling to analyse the split plot design 64\u003c\/p\u003e \u003cp\u003e2.5 A more conservative alternative to the F and Wald statistics 66\u003c\/p\u003e \u003cp\u003e2.6 Justification for regarding block effects as random 67\u003c\/p\u003e \u003cp\u003e2.7 Testing the assumptions of the analyses: Inspection of the residual values 68\u003c\/p\u003e \u003cp\u003e2.8 Use of R to perform the analyses 71\u003c\/p\u003e \u003cp\u003e2.9 Use of SAS to perform the analyses 77\u003c\/p\u003e \u003cp\u003e2.10 Summary 81\u003c\/p\u003e \u003cp\u003e2.11 Exercises 82\u003c\/p\u003e \u003cp\u003eReferences 86\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Estimation of the variances of random-effect terms 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The need to estimate variance components 87\u003c\/p\u003e \u003cp\u003e3.2 A hierarchical random-effects model for a three-stage assay process 87\u003c\/p\u003e \u003cp\u003e3.3 The relationship between variance components and stratum mean squares 91\u003c\/p\u003e \u003cp\u003e3.4 Estimation of the variance components in the hierarchical random-effects model 93\u003c\/p\u003e \u003cp\u003e3.5 Design of an optimum strategy for future sampling 95\u003c\/p\u003e \u003cp\u003e3.6 Use of R to analyse the hierarchical three-stage assay process 98\u003c\/p\u003e \u003cp\u003e3.7 Use of SAS to analyse the hierarchical three-stage assay process 100\u003c\/p\u003e \u003cp\u003e3.8 Genetic variation: A crop field trial with an unbalanced design 102\u003c\/p\u003e \u003cp\u003e3.9 Production of a balanced experimental design by ‘padding’ with missing values 106\u003c\/p\u003e \u003cp\u003e3.10 Specification of a treatment term as a random-effect term: The use of mixed-model analysis to analyse an unbalanced data set 110\u003c\/p\u003e \u003cp\u003e3.11 Comparison of a variance component estimate with its standard error 112\u003c\/p\u003e \u003cp\u003e3.12 An alternative significance test for variance components 113\u003c\/p\u003e \u003cp\u003e3.13 Comparison among significance tests for variance components 116\u003c\/p\u003e \u003cp\u003e3.14 Inspection of the residual values 117\u003c\/p\u003e \u003cp\u003e3.15 Heritability: The prediction of genetic advance under selection 117\u003c\/p\u003e \u003cp\u003e3.16 Use of R to analyse the unbalanced field trial 122\u003c\/p\u003e \u003cp\u003e3.17 Use of SAS to analyse the unbalanced field trial 125\u003c\/p\u003e \u003cp\u003e3.18 Estimation of variance components in the regression analysis on grouped data 128\u003c\/p\u003e \u003cp\u003e3.19 Estimation of variance components for block effects in the split-plot experimental design 130\u003c\/p\u003e \u003cp\u003e3.20 Summary 132\u003c\/p\u003e \u003cp\u003e3.21 Exercises 133\u003c\/p\u003e \u003cp\u003eReferences 136\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Interval estimates for fixed-effect terms in mixed models 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The concept of an interval estimate 137\u003c\/p\u003e \u003cp\u003e4.2 Standard errors for regression coefficients in a mixed-model analysis 138\u003c\/p\u003e \u003cp\u003e4.3 Standard errors for differences between treatment means in the split-plot design 142\u003c\/p\u003e \u003cp\u003e4.4 A significance test for the difference between treatment means 144\u003c\/p\u003e \u003cp\u003e4.5 The least significant difference (LSD) between treatment means 147\u003c\/p\u003e \u003cp\u003e4.6 Standard errors for treatment means in designed experiments: A difference in approach between analysis of variance and mixed-model analysis 151\u003c\/p\u003e \u003cp\u003e4.7 Use of R to obtain SEs of means in a designed experiment 157\u003c\/p\u003e \u003cp\u003e4.8 Use of SAS to obtain SEs of means in a designed experiment 159\u003c\/p\u003e \u003cp\u003e4.9 Summary 161\u003c\/p\u003e \u003cp\u003e4.10 Exercises 163\u003c\/p\u003e \u003cp\u003eReferences 164\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Estimation of random effects in mixed models: Best Linear Unbiased Predictors (BLUPs) 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The difference between the estimates of fixed and random effects 165\u003c\/p\u003e \u003cp\u003e5.2 The method for estimation of random effects: The best linear unbiased predictor (BLUP) or ‘shrunk estimate’ 168\u003c\/p\u003e \u003cp\u003e5.3 The relationship between the shrinkage of BLUPs and regression towards the mean 170\u003c\/p\u003e \u003cp\u003e5.4 Use of R for the estimation of fixed and random effects 176\u003c\/p\u003e \u003cp\u003e5.5 Use of SAS for the estimation of random effects 178\u003c\/p\u003e \u003cp\u003e5.6 The Bayesian interpretation of BLUPs: Justification of a random-effect term without invoking an underlying infinite population 182\u003c\/p\u003e \u003cp\u003e5.7 Summary 187\u003c\/p\u003e \u003cp\u003e5.8 Exercises 188\u003c\/p\u003e \u003cp\u003eReferences 191\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 More advanced mixed models for more elaborate data sets 192\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Features of the models introduced so far: A review 192\u003c\/p\u003e \u003cp\u003e6.2 Further combinations of model features 192\u003c\/p\u003e \u003cp\u003e6.3 The choice of model terms to be specified as random 195\u003c\/p\u003e \u003cp\u003e6.4 Disagreement concerning the appropriate significance test when fixed and random-effect terms interact: ‘The great mixed-model muddle’ 197\u003c\/p\u003e \u003cp\u003e6.5 Arguments for specifying block effects as random 204\u003c\/p\u003e \u003cp\u003e6.6 Examples of the choice of fixed- and random-effect specification of terms 209\u003c\/p\u003e \u003cp\u003e6.7 Summary 213\u003c\/p\u003e \u003cp\u003e6.8 Exercises 215\u003c\/p\u003e \u003cp\u003eReferences 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Three case studies 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Further development of mixed modelling concepts through the analysis of specific data sets 217\u003c\/p\u003e \u003cp\u003e7.2 A fixed-effects model with several variates and factors 218\u003c\/p\u003e \u003cp\u003e7.3 Use of R to fit the fixed-effects model with several variates and factors 233\u003c\/p\u003e \u003cp\u003e7.4 Use of SAS to fit the fixed-effects model with several variates and factors 237\u003c\/p\u003e \u003cp\u003e7.5 A random coefficient regression model 242\u003c\/p\u003e \u003cp\u003e7.6 Use of R to fit the random coefficients model 246\u003c\/p\u003e \u003cp\u003e7.7 Use of SAS to fit the random coefficients model 247\u003c\/p\u003e \u003cp\u003e7.8 A random-effects model with several factors 249\u003c\/p\u003e \u003cp\u003e7.9 Use of R to fit the random-effects model with several factors 266\u003c\/p\u003e \u003cp\u003e7.10 Use of SAS to fit the random-effects model with several factors 274\u003c\/p\u003e \u003cp\u003e7.11 Summary 282\u003c\/p\u003e \u003cp\u003e7.12 Exercises 282\u003c\/p\u003e \u003cp\u003eReferences 294\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Meta-analysis and the multiple testing problem 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Meta-analysis: Combined analysis of a set of studies 295\u003c\/p\u003e \u003cp\u003e8.2 Fixed-effect meta-analysis with estimation only of the main effect of treatment 296\u003cbr\u003e \u003cbr\u003e 8.3 Random-effects meta-analysis with estimation of study × treatment interaction effects 301\u003cbr\u003e \u003cbr\u003e 8.4 A random-effect interaction between two fixed-effect terms 303\u003c\/p\u003e \u003cp\u003e8.5 Meta-analysis of individual-subject data using R 307\u003c\/p\u003e \u003cp\u003e8.6 Meta-analysis of individual-subject data using SAS 312\u003c\/p\u003e \u003cp\u003e8.7 Meta-analysis when only summary data are available 318\u003c\/p\u003e \u003cp\u003e8.8 The multiple testing problem: Shrinkage of BLUPs as a defence against the Winner’s Curse 326\u003c\/p\u003e \u003cp\u003e8.9 Fitting of multiple models using R 338\u003c\/p\u003e \u003cp\u003e8.10 Fitting of multiple models using SAS 340\u003c\/p\u003e \u003cp\u003e8.11 Summary 342\u003c\/p\u003e \u003cp\u003e8.12 Exercises 343\u003c\/p\u003e \u003cp\u003eReferences 348\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 The use of mixed models for the analysis of unbalanced experimental designs 350\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 A balanced incomplete block design 350\u003c\/p\u003e \u003cp\u003e9.2 Imbalance due to a missing block: Mixed-model analysis of the incomplete block design 354\u003c\/p\u003e \u003cp\u003e9.3 Use of R to analyse the incomplete block design 358\u003c\/p\u003e \u003cp\u003e9.4 Use of SAS to analyse the incomplete block design 360\u003c\/p\u003e \u003cp\u003e9.5 Relaxation of the requirement for balance: Alpha designs 362\u003c\/p\u003e \u003cp\u003e9.6 Approximate balance in two directions: The alphalpha design 368\u003c\/p\u003e \u003cp\u003e9.7 Use of R to analyse the alphalpha design 373\u003c\/p\u003e \u003cp\u003e9.8 Use of SAS to analyse the alphalpha design 374\u003c\/p\u003e \u003cp\u003e9.9 Summary 376\u003c\/p\u003e \u003cp\u003e9.10 Exercises 377\u003c\/p\u003e \u003cp\u003eReferences 378\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Beyond mixed modelling 379\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Review of the uses of mixed models 379\u003c\/p\u003e \u003cp\u003e10.2 The generalized linear mixed model (GLMM): Fitting a logistic (sigmoidal) curve to proportions of observations 380\u003c\/p\u003e \u003cp\u003e10.3 Use of R to fit the logistic curve 388\u003c\/p\u003e \u003cp\u003e10.4 Use of SAS to fit the logistic curve 390\u003c\/p\u003e \u003cp\u003e10.5 Fitting a GLMM to a contingency table: Trouble-shooting when the mixed modelling process fails 392\u003c\/p\u003e \u003cp\u003e10.6 The hierarchical generalized linear model (HGLM) 403\u003c\/p\u003e \u003cp\u003e10.7 Use of R to fit a GLMM and a HGLM to a contingency table 410\u003c\/p\u003e \u003cp\u003e10.8 Use of SAS to fit a GLMM to a contingency table 415\u003c\/p\u003e \u003cp\u003e10.9 The role of the covariance matrix in the specification of a mixed model 418\u003c\/p\u003e \u003cp\u003e10.10 A more general pattern in the covariance matrix: Analysis of pedigrees and genetic data 421\u003c\/p\u003e \u003cp\u003e10.11 Estimation of parameters in the covariance matrix: Analysis of temporal and spatial variation 431\u003c\/p\u003e \u003cp\u003e10.12 Use of R to model spatial variation 441\u003c\/p\u003e \u003cp\u003e10.13 Use of SAS to model spatial variation 444\u003c\/p\u003e \u003cp\u003e10.14 Summary 447\u003c\/p\u003e \u003cp\u003e10.15 Exercises 447\u003c\/p\u003e \u003cp\u003eReferences 452\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Why is the criterion for fitting mixed models called REsidual Maximum Likelihood? 454\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Maximum likelihood and residual maximum likelihood 454\u003c\/p\u003e \u003cp\u003e11.2 Estimation of the variance 2 from a single observation using the maximum-likelihood criterion 455\u003c\/p\u003e \u003cp\u003e11.3 Estimation of 2 from more than one observation 455\u003c\/p\u003e \u003cp\u003e11.4 The -effect axis as a dimension within the sample space 457\u003c\/p\u003e \u003cp\u003e11.5 Simultaneous estimation of  and 2 using the maximum-likelihood criterion 460\u003c\/p\u003e \u003cp\u003e11.6 An alternative estimate of 2 using the REML criterion 462\u003c\/p\u003e \u003cp\u003e11.7 Bayesian justification of the REML criterion 465\u003c\/p\u003e \u003cp\u003e11.8 Extension to the general linear model: The fixed-effect axes as a sub-space of the sample space 465\u003c\/p\u003e \u003cp\u003e11.9 Application of the REML criterion to the general linear model 470\u003c\/p\u003e \u003cp\u003e11.10 Extension to models with more than one random-effect term 472\u003c\/p\u003e \u003cp\u003e11.11 Summary 473\u003c\/p\u003e \u003cp\u003e11.12 Exercises 474\u003c\/p\u003e \u003cp\u003eReferences 476\u003c\/p\u003e \u003cp\u003eIndex 477\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528867488087,"sku":"9781119945499","price":69.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119945499.jpg?v=1731873336","url":"https:\/\/bookcurl.com\/products\/introduction-to-mixed-modelling-9781119945499","provider":"Book Curl","version":"1.0","type":"link"}