ASReml-S reference manual - VSN International

More documents

Recommendations

Info

Table 3.2. Families and link functions3.14 Generalized Linear Mixed Models 32Link Function gaussian binomial poisson Gammaidentity η = µ D * *sqrt η = √ µ *log η = log(µ) * D *inverse η = 1/µ * Dlogit η = µ/(1 − µ) Dprobit η = Φ −1 (µ) *cloglog η = log(− log(1 − µ)) *where µ is the mean on the data scale, η = Xτ is the linear predictoron the underlying scale and D is the default.3.14 Generalized Linear Mixed ModelsThere is the capacity to fit a wider class of models which include additional random effectsfor non-normal error distributions. The inclusion of random terms in a GLM is usuallyreferred to as a Generalized Linear Mixed Model (GLMM). For GLMMs, asreml uses whatis commonly referred to as penalized quasi-likelihood or PQL [Breslow and Clayton, 1993].The technique is also known by other names, including Schall’s technique [Schall, 1991],pseudo-likelihood [Wolfinger and O’Connell, 1993] and joint maximisation [Harville andMee, 1984, Gilmour et al., 1985]. It is implemented in many statistical packages, forinstance, in the GLMM procedure [Welham, 2005] and the IRREML procedure of Genstat[Keen, 1994], in MLwiN [Goldstein et al., 1998], in the GLMMIXED macro in SAS and inthe GLMMPQL function in R, to name a few.The PQL technique is based on a first order Taylor series approximation to the likelihood.It has been shown to perform poorly for certain types of GLMMs. In particular, forbinary GLMMs where the number of random effects is large compared to the numberof observations, it can underestimate the variance components severely (up to 50%) (forexample, Breslow and Lin [1995], Goldstein and Rasbash [1996], Rodriguez and Goldman[2001], Waddington et al. [1994]). For other types of GLMMs, such as Poisson data withmany observations per random effect, it has been reported to perform quite well [Breslow,2003, for example]. As well as the above <strong>reference</strong>s, users can consult McCulloch andSearle [2001] for more information about GLMMs.Most studies investigating PQL have focussed on estimation bias. Much less attentionhas been given to the wider inferential issues such as hypothesis testing. In addition,the performance of this technique has only been assessed on a small set of relativelysimple GLMMs. Anecdotal evidence from users suggests that this technique can givevery misleading results in certain situations.Therefore, we cannot recommend the use of this technique for general use. It is includedin the current version of asreml for advanced users. It is highly recommended that itsuse be accompanied by some form of cross-validatory assessment for the specific datasetconcerned. For instance, one way of doing this would be by simulating data using thesame design and using parameter values similar to the parameter estimates achieved,such as used in Millar and Willis [1999].
3.15 Multivariate analysis 333.15 Multivariate analysisMultivariate analysis is used when we are interested in estimating the correlations betweendistinct traits (for example, fleece weight and fibre diameter in sheep) and forrepeated measures of a single trait. The term multivariate analysis is used here in thenarrow sense of a multivariate mixed model. There are many other multivariate analysistechniques which are not covered by asreml.3.15.1 Model specificationIf the response term specified in the fixed formula of a asreml call is a matrix then amultivariate analysis is automatically performed. That is, for response variates y 1, . . . , y kin the data frame, a multivariate analysis would be specified with the call> asreml(fixed = cbind(y 1 , . . . , y k ) ∼ trait, . . .)In this case, asreml creates a factor trait (the multivariate equivalent to the univariategeneral mean) with the names of the response variates as levels.A multivariate analysis in asreml can be specified in one of two ways:• specifying a matrix as the response in the fixed formula, as noted above. For thewether trial data, the term trait is a factor generated by asreml with ntr = 2 levelsgfw and fdiam. Internally, asreml expands the data frame by repeating each row ntrtimes such that traits are nested within experimental units,• specifying the as.multivariate =trait argument; this assumes that the data frame hasbeen expanded into a univariate form outside asreml. In this case the order need notnecessarily be traits within units but the order of terms in the rcov formula mustreflect the data order. Note that in this case trait refers to the factor in the dataframe that defines the traits but is not necessarily named trait.The following examples illustrate the specification of multivariate models in asreml, somecomponents of the returned object and the wald() method.A repeated measures exampleWolfinger [1996] summarises a range of variance structures that can be fitted to repeatedmeasures data, demonstrating the models using the rat dataset described in Section 1.3.2.The asreml function call for an analysis of the five repeated measures is:> wolfinger.asr summary(wolfinger.asr)$varcompgamma component std.error z.ratio constraintR!variance 1.00000 1.00000 NA NA FixedR!trait_wt0:wt0 21.57560 21.57560 6.228322 3.464110 UnconstrainedR!trait_wt1:wt0 33.01964 33.01964 10.354376 3.188955 UnconstrainedR!trait_wt1:wt1 68.72738 68.72738 19.839816 3.464114 Unconstrained
Page 1 and 2: Analysis of mixed modelsfor S langu
Page 3 and 4: D.G. ButlerQueensland Department of
Page 6: ContentsPreface . . . . . . . . . .
Page 10 and 11: ContentsviiB Available variance mod
Page 12 and 13: List of Figures1.1 Weekly body weig
Page 14 and 15: 1.3 Data sets used 21.2.2 Help and
Page 16 and 17: 1.3 Data sets used 41.3.2 Repeated
Page 18 and 19: 1.3 Data sets used 6101 Sire 1 0102
Page 20 and 21: 2.1 The linear mixed model 8Direct
Page 22 and 23: 2.2 Estimation 10There is a corresp
Page 24 and 25: 2.2 Estimation 12where H ij = ∂ 2
Page 26 and 27: 2.5 Inference for random effects 14
Page 28 and 29: 2.6 Inference for fixed effects 16T
Page 30 and 31: 2.6 Inference for fixed effects 18t
Page 32 and 33: 3Fitting the mixed model3.1 Introdu
Page 34 and 35: 3.3 Introducing the asreml function
Page 36 and 37: 3.6 Getting help3.7 The asreml func
Page 38 and 39: 3.8 Fixed terms 26na.method.Xkeep.o
Page 40 and 41: 3.8 Fixed terms 28Summary of reserv
Page 42 and 43: 3.10 Conditional factors: the at()
Page 46 and 47: 3.15 Multivariate analysis 34R!trai
Page 48 and 49: Source df F_inc F_con MSource df dd
Page 50 and 51: 4.1.1 Specifying variance models in
Page 52 and 53: 4.2 A sequence of structures for th
Page 54 and 55: Σ = [σ ij ] :{σii = σ 2 , ∀i
Page 56 and 57: 4.4 Variance model functions 44init
Page 58 and 59: The Matérn class4.4 Variance model
Page 60 and 61: 4.4 Variance model functions 48Chol
Page 62 and 63: Required argumentsobj4.5 Rules for
Page 64 and 65: 4.7 Constraining variance parameter
Page 66 and 67: 5Genetic analysis5.1 IntroductionIn
Page 68 and 69: 5.2 Pedigree, G-inverse objects and
Page 70 and 71: 5.4 Using Pedigree and G-inverse ob
Page 72 and 73: 6Prediction from the linear model6.
Page 74 and 75: Optional argumentslevels6.2 The pre
Page 76 and 77: 6.2 The predict method 64The predic
Page 78 and 79: 6.4 Complicated weighting 666.4 Com
Page 80 and 81: 7The asreml class and related metho
Page 82 and 83: maxiter maximum number of iteration
Page 84 and 85: 7.3 Methods and related functions 7
Page 88 and 89: pedigree7.3 Methods and related fun
Page 92 and 93: 8Examples8.1 IntroductionThis secti
Page 94 and 95:
8.2 Split Plot Design 82In this exa
Page 96 and 97:
8.3 Unbalanced nested design 84[4,]
Page 98 and 99:
8.3 Unbalanced nested design 86adju
Page 100 and 101:
8.4 Sources of variability in unbal
Page 102 and 103:
8.5 Balanced repeated measures 902
Page 104 and 105:
8.5 Balanced repeated measures 92Ta
Page 106 and 107:
8.5 Balanced repeated measures 94wh
Page 108 and 109:
8.6 Spatial analysis of a field exp
Page 110 and 111:
8.6 Spatial analysis of a field exp
Page 112 and 113:
Variety predicted.value standard.er
Page 114 and 115:
8.7 Unreplicated early generation v
Page 116 and 117:
8.7 Unreplicated early generation v
Page 118 and 119:
8.8 Paired Case-Control Study 106Th
Page 120 and 121:
Terms added sequentially; adjusted
Page 122 and 123:
8.8 Paired Case-Control Study 110[
Page 124 and 125:
8.8 Paired Case-Control Study 112..
Page 126 and 127:
8.9 Balanced longitudinal data - Ra
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
A.3 Aliasing and singularities 122W
Page 136 and 137:
Table B.1: Details of the available
Page 138 and 139:
B Available variance models 126Deta
Page 140 and 141:
ReferencesG. E. P. Box. Analysis of
Page 142 and 143:
References 130W. W. Stroup, P. S. B
Page 144 and 145:
Index 132F statistics, 17fa(,k), 49
show all

ASReml-S reference manual - VSN International

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?