Update III [🇷 for BE/BA]

posted by ElMaestro  – Denmark, 2020-07-12 23:46 (1823 d 17:10 ago) – Posting: # 21678
Views: 32,117

Look at this baby:

rm(list=ls(all=TRUE))

###### par vector is c(varT, varBR, varWR)

######
######   Section 1: Household things
######



CreateX=function(D)
{
 ##first the two treatments
 TrtT=as.numeric(as.character(D$Trt)=="T")
 TrtR=as.numeric(as.character(D$Trt)=="R")
 X=cbind(TrtT, TrtR)
 R= qr(X)$rank

 ## subjects: in a mixed model with subj as random
 ## we do not do subjects also as fixed, therefore they are #'ed away here
 ## for (s in unique(D$Subj))
 ## {
 ## v=as.numeric(D$Subj==s)
 ## #print(v)
 ## XX=data.frame(X, v)
 ## names(XX)[ncol(XX)] = paste("S", s, sep="")
 ## rnk=qr(XX)$rank
 ## if (rnk>R)
  ##  {
  ##     X=XX
  ##     R=rnk
  ##  }
  ## }
 ##now the Pers
 for (p in unique(D$Per))
 {
  v=as.numeric(D$Per==p)
  #print(v)
  XX=data.frame(X, v)
  names(XX)[ncol(XX)] = paste("P", p, sep="")
  rnk=qr(XX)$rank
  if (rnk>R)
    {
       X=XX
       R=rnk
    }
 }

 for (q in unique(D$Seq))
 {
  v=as.numeric(D$Seq==q)
  #print(v)
  XX=data.frame(X, v)
  names(XX)[ncol(XX)] = paste("Q", q, sep="")
  rnk=qr(XX)$rank
  if (rnk>R)
    {
       X=XX
       R=rnk
    }
 }
 return(as.matrix(X))
}




Create.CovM=function(Params)
##block diagonal covariance matrix
{
  varT=Params[1]
  varBR=Params[2]
  varWR=Params[3]
  #varRT=Params[4]
  #cat("Vars:", varT, varBR, varWR,"\n")

  Nobs=length(D$Y)
  V=matrix(0,ncol=Nobs, nrow=Nobs)
  for (iRow in 1:Nobs)
  for (iCol in 1:Nobs)
  {
   
   ## the diagonal
   if (iCol==iRow)
    {
      if (D$Trt[iRow]=="T") V[iRow,iCol]=V[iRow,iCol]+varT
      if (D$Trt[iRow]=="R") V[iRow,iCol]=V[iRow,iCol]+varWR +varBR
    }

   ## off diagonal
   if (iCol!=iRow)
   if (D$Subj[iRow]==D$Subj[iCol])
    {
     if (D$Trt[iCol]==D$Trt[iRow]) V[iRow,iCol]= V[iRow,iCol]+varBR
     #if (D$Trt[iCol]!=D$Trt[iRow]) V[iRow,iCol]= V[iRow,iCol]+varRT
    }
  }
  return(as.matrix(V))
}

######
######   Section 2: Matrix things
######


Obj.F12=function(Pars)
##this is line 3 of page 10 of:
##http://people.csail.mit.edu/xiuming/docs/tutorials/reml.pdf
{
  CovM=Create.CovM(Pars)

  A= -0.5*log(det(CovM))
  B= -0.5*log(det(t(X) %*% solve(CovM) %*% X))
  est.b = solve(t(X) %*% solve(CovM) %*% X) %*% t(X) %*% solve(CovM) %*% y
  tmp= y - X %*% est.b
  C=-0.5 *(t(tmp) %*% solve(CovM) %*% tmp)
  return(A+B+C)
}



Some.Initial.Guesses=function(foo)
{
  #guess variance within R
  D1=subset(D, D$Trt=="R")
  m=lm(log(Y)~factor(Subj)+factor(Seq)+factor(Per) , data=D1)
  #print(anova(m))
  varWR= anova(m)["Residuals", "Mean Sq"]
  m=lm(log(Y)~factor(Subj)+factor(Seq)+factor(Per)+factor(Trt) , data=D)
  varBR= anova(m)["factor(Subj)", "Mean Sq"]
  ##total var T, cheaply
  ##actually, this may be much better: varT=varBR+varWR
  D2=subset(D, D$Trt=="T")
  varT=var(log(D2$Y))
  varT=varBR+varWR
  L=list(varT=varT, varBR=varBR, varWR=varWR)
  return(L)
}



####
#### section 3: execution
####



D=read.csv("EMAII.a.csv" , header=T, sep="\t") ##public = easier
X=CreateX(D) ##public = easier
y=log(D$Y) ##public = easier


MyREML=function(foo.bar)
{
  L=Some.Initial.Guesses(0)
  print(L)
  parIni=c(0.06, 0.032, 0.012)
  F=optim(par=parIni, fn=Obj.F12,
      #method="BFGS",
      #lower=c(0.003,0.003,0.003), upper=c(1,1,1),
      control=list(reltol=1e-11, trace=T, fnscale=-1))
  print(F)
}
MyREML(0)



On my machine it gives:
$par
[1] 0.06776119 0.03636979 0.01237020

:-)
—
Pass or fail!
ElMaestro

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