Dear Mr/Mrs,

I am writing to you because I have convergence problems with my analysis
using lmer function. I am trying to implement a multi-trait GWAS analysis
for physiological traits in wheat, with 18337 SNPs, 384 genotypes and 20
traits. When I use Naive model (no correction structure) I have no
problems. When I incorporate the first two PC in the model, I obtain 50
warnings like:

44: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
  Model is nearly unidentifiable: large eigenvalue ratio
 - Rescale variables?
45: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
46: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
   Hessian is numerically singular: parameters are not uniquely determined
47: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
  Model failed to converge: degenerate  Hessian with 2 negative eigenvalues
48: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
  Model failed to converge: degenerate  Hessian with 2 negative eigenvalues
49: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
50: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,
 ... :
  Model failed to converge: degenerate  Hessian with 2 negative eigenvalues

I have tried with different optimizers like you suggested to other
investigators but all of them gave me warnings like the one I showed you.

My model is

    out2=NULL
    for(i in 4:ncol(MT.data)){
      Marker=MT.data[,i]
      modelo=lmer(MEAN~TRAIT + Marker:TRAIT + (1|GEN) + (1|PC1) + (1|PC2),
data=MT.data2)

      out<-cbind(anova(modelo)[2,], as.character(rownames(b)[i-3]),
(t(b[i-3,1:2])))
      out2<-rbind(out2, out)
    }

MEAN: vector with BLUEs for each trait
TRAIT: vector that indicates the trait for each row
Marker: SNPs column, each SNPs is repeated the number of traits
GEN: vector that indicates id of each genotype, each is repeated the number
of traits
PC1 and PC2: are principal components, each is repeated the number of
traits

What should I do? Thank you in advanced
Sincerely,
Sofía Brandariz

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