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I am re-posting this from stackoverflow after someone's kind suggestion. That person also suggested that the main of the issue may be low number of virus positive samples n=12. Which I suspected. But I am also wandering if linear separation could be an issue, as all the virus positives occur in the low food group. Can these problems be resolved using GLMMs or should I think of other statistical tests?

Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),family=binomial,data=data,method = "ML")

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.001101 (tol = 0.001, component 3)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 4 negative eigenvalues

Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,family=binomial,control=glmerControl(optCtrl=list(maxfun=1e9)))

Food_Treatment.glmer <- glmer(Virus_DNA~Food*Treatment(1|Set),data=data,family=binomial,                            control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=1e9))) 

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00393532 (tol = 0.001, component 2)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 2 negative eigenvalues

Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment(1|Set),family=binomial,data=data)

Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment(1|Set),family=binomial,data=data,control=glmerControl(optCtrl=list(maxfun=1e9)))

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00248016 (tol = 0.001, component 2)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 1 negative eigenvalues

Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00139574 (tol = 0.001, component 2)

I am re-posting this from StackOverflow after someone's kind suggestion. That person also suggested that the main of the issue may be low number of virus positive samples n=12. Which I suspected. But I am also wandering if linear separation could be an issue, as all the virus positives occur in the low food group. Can these problems be resolved using GLMMs or should I think of other statistical tests?

Food_Treatment.glmer <- glmer(Virus_DNA~Food*Treatment+(1|Set),
                              family=binomial,data=data,method = "ML")

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
     Model failed to converge with max|grad| = 0.001101 (tol = 0.001, component 3)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
     Model failed to converge: degenerate Hessian with 4 negative eigenvalues

Food_Treatment.glmer <- glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,
                             family=binomial,control=glmerControl(optCtrl=list(maxfun=1e9)))

Food_Treatment.glmer <- glmer(Virus_DNA~Food*Treatment(1|Set),data=data,family=binomial, 
                          control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=1e9))) 

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
     Model failed to converge with max|grad| = 0.00393532 (tol = 0.001, component 2)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
     Model failed to converge: degenerate Hessian with 2 negative eigenvalues

Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment(1|Set),family=binomial,
                                 data=data)

Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment(1|Set),family=binomial,
                                 data=data,control=glmerControl(optCtrl=list(maxfun=1e9)))

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
     Model failed to converge with max|grad| = 0.00248016 (tol = 0.001, component 2)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
      Model failed to converge: degenerate Hessian with 1 negative eigenvalues

Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : 
    Model failed to converge with max|grad| = 0.00139574 (tol = 0.001, component 2)

I am re-posting this from stackoverflow after someone's kind suggestion. The suggesty also suggested that the main of the issue may be low number of virus positive samples n=12. Which I suspected. But I am also wandering if linear seperation could be an issue, as all the virus positives occur in the low food group. Can these problems be resolved using GLMMs or should I think of other statistical tests.

Tried fitting the model: Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),family=binomial,data=data,method = "ML")

to get the warning messages "Warning messages:

1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.001101 (tol = 0.001, component 3)

2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 4 negative eigenvalues"

After running code with more iterations of the model, I still get the same warning messages: Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,family=binomial,control=glmerControl(optCtrl=list(maxfun=1e9)))

I then looked on-line and that people had similar problems and tried the otmizer "bobyqa": Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,family=binomial, control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=1e9))) I then got the very similar warning messages:

"Warning messages:

1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00393532 (tol = 0.001, component 2)

2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 2 negative eigenvalues"

I then thought of simplifying the model and tried no interactions between explanatory variables, with the codes: Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment+(1|Set),family=binomial,data=data) and Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment+(1|Set),family=binomial,data=data,control=glmerControl(optCtrl=list(maxfun=1e9))) Only to get the warning messages :

"Warning messages:

1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00248016 (tol = 0.001, component 2)

2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 1 negative eigenvalues"

So I tried this simplified model with the opimizers "bobyqa" and "Nelder_Mead", as well as the otimzers "nlminb" and "L-BFGS-B" from the package optimx.

All but the "bobyqa" opimzers produce variations on the 2 warning messages. "bobyqa" otpimzer produces the 1 warning message:

"warning message:

In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00139574 (tol = 0.001, component 2)

I am re-posting this from stackoverflow after someone's kind suggestion. That person also suggested that the main of the issue may be low number of virus positive samples n=12. Which I suspected. But I am also wandering if linear separation could be an issue, as all the virus positives occur in the low food group. Can these problems be resolved using GLMMs or should I think of other statistical tests?

Tried fitting the model:

Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),family=binomial,data=data,method = "ML")

to get the warning messages

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.001101 (tol = 0.001, component 3)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 4 negative eigenvalues

After running code with more iterations of the model, I still get the same warning messages:

Food_Treatment.glmer<-glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,family=binomial,control=glmerControl(optCtrl=list(maxfun=1e9)))

I then looked on-line and that people had similar problems and tried the optmizer bobyqa:

Food_Treatment.glmer <- glmer(Virus_DNA~Food*Treatment(1|Set),data=data,family=binomial,                            control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=1e9))) 

I then got the very similar warning messages:

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00393532 (tol = 0.001, component 2)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 2 negative eigenvalues

I then thought of simplifying the model and tried no interactions between explanatory variables, with the code:

Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment(1|Set),family=binomial,data=data)

and

Food.Plus.Treatment.glmer<-glmer(Virus_DNA~Food+Treatment(1|Set),family=binomial,data=data,control=glmerControl(optCtrl=list(maxfun=1e9)))

Only to get the warning messages :

Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00248016 (tol = 0.001, component 2)
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge: degenerate Hessian with 1 negative eigenvalues

So I tried this simplified model with the optimizers bobyqa and Nelder_Mead, as well as the optimzers nlminb and L-BFGS-B from the package optimx.

All but the bobyqa optimizers produce variations on the 2 warning messages. The bobyqa optimizer produces the 1 warning message:

Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.00139574 (tol = 0.001, component 2)