title: After trying various optimzers, model simplification running more iterations, when fitting GLMMs, R still produces warning messages
body: <p>I am trying to fit GLMM's to my data using the glmer function available in R's lme4 package.
  The data is available at: 
  <a href="https://onedrive.live.com/redir?resid=1B727FC7180E87DF%21118" rel="nofollow noreferrer">https://onedrive.live.com/redir?resid=1B727FC7180E87DF%21118</a></p>
  
  <p>I keep getting warning messages. Can anybody help me get rid of them. </p>
  
  <p>Tried fitting the model:<code>
  Food_Treatment.glmer&lt;-glmer(Virus_DNA~Food*Treatment+(1|Set),family=binomial,data=data,method = "ML")
  </code></p>
  
  <p>to get the warning messages  </p>
  
  <pre><code>"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"
  </code></pre>
  
  <p>After running code with more iterations of the model, I still get the same warning messages:
  <code>Food_Treatment.glmer&lt;-glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,family=binomial,control=glmerControl(optCtrl=list(maxfun=1e9)))</code></p>
  
  <p>I then looked on-line and that people had similar problems and tried the otmizer "bobyqa":</p>
  
  <p>Food_Treatment.glmer&lt;-glmer(Virus_DNA~Food*Treatment+(1|Set),data=data,family=binomial,                            control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=1e9)))</p>
  
  <p>I then got the very similar warning messages:</p>
  
  <p>"Warning messages:</p>
  
  <pre><code>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"
  </code></pre>
  
  <p>I then thought of simplifying the model and tried no interactions between explanatory variables, with the codes:   </p>
  
  <pre><code>Food.Plus.Treatment.glmer&lt;-glmer(Virus_DNA~Food+Treatment+(1|Set),family=binomial,data=data)
  </code></pre>
  
  <p>and </p>
  
  <pre><code>Food.Plus.Treatment.glmer&lt;-glmer(Virus_DNA~Food+Treatment+(1|Set),family=binomial,data=data,control=glmerControl(optCtrl=list(maxfun=1e9)))
  </code></pre>
  
  <p>Only to get the warning messages :</p>
  
  <pre><code>"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"
  </code></pre>
  
  <p>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.</p>
  
  <p>All but the "bobyqa" opimzers produce variations on the 2 warning messages.
  "bobyqa" otpimzer produces the 1 warning message:</p>
  
  <pre><code>"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)
  </code></pre>
  
  <p>P.S. This is my first post on here I hope I have provided enough information without being verbose and it is correctly formatted.</p>