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Adding fixed effects to a model

Summary


This page illustrates how to add fixed effects, for example sex or population density, to a model and test their significance.

Table of contents


Definitions

Sample code in the following examples includes the following variables

Response variable: Size
Fixed effects: Intercept (mu), SIZE, SEX and AGE
Random effects: Additive genetic variance
Data containing phenotypic information: phenotypicdata
Data containing pedigree data:pedigreedata

Sample Code

ASReml

To add fixed effects to a univariate model, simply modify the model specification to include any additional fixed effects before the random effects structure. The data file must have a column for each fixed covariate to be fitted. Significance of fixed effects can be tested with conditional or incremental Wald tests.

ASReml analysis of size  
 ANIMAL       !P 
 SIZE
 SEX         !A  #denotes a factor
 AGE          #here treated as a linear effect

pedigreedata.ped      !skip 1   
phenotypicdata.dat    !skip 1    !DDF 1 !FCON #specifies method of sig testing
 
SIZE ~ mu  AGE SEX AGE.SEX !r ANIMAL


ASReml-R

model<-asreml(fixed=SIZE~1+SEX+AGE
           ,random=~ped(ANIMAL,var=T,init=1)
           ,data=phenotypicdata
           ,ginverse=list(ANIMAL=ainv), na.method.X="omit', na.method.Y="omit')

#test significance of fixed effects using
wald.asreml(model, ssType="conditional", denDF="numeric")

MCMCglmm


Addition of a fixed effect is most easily accomplished by simply adding it to the fixed effects (so far only occupied by the population mean) section of the model specification. In general, priors on fixed effects will not be necessary.

model1.2<-MCMCglmm(BWT~SEX,random=~animal,
                       pedigree=Ped,data=Data,prior=prior1.1,
                       nitt=65000,thin=50,burnin=15000,verbose=FALSE)

posterior.mode(model1.2$Sol[,"SEX2"])

HPDinterval(model1.2$Sol[,"SEX2"],0.95)

posterior.mode(model1.2$VCV)

posterior.heritability1.2<-model1.2$VCV[,"animal"]/
                (model1.2$VCV[,"animal"]+model1.2$VCV[,"units"])
posterior.mode(posterior.heritability1.2)

HPDinterval(posterior.heritability1.2,0.95)


WOMBAT

To add fixed effects to a univariate model, simply modify the model specification in the parameter file. For example we might know (or suspect) that size is a sexually dimorphic trait and therefore include the sex of the individual in the model as a fixed effect.
MODEL
  FIX SEX
  RAN ANIMAL NRM
  TRAIT SIZE
END

WOMBAT will not provide the significance of the fixed effects in your model. However, generalised least-squares solutions for all fixed effects fitted, together with means and the number of observations for each group, can be found in FixSolutions.out.

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