Convergence errors in parametric bootstraps (PBmodcomp) of lmer models I am using PBmodcomp from the pbkrtest to perform a parametric bootstrap model comparison. However, for some of the comparisons a warning message stating that the models failed to converge appear. A example of the R script for my lemr models can be found here: https://stackoverflow.com/questions/25111939/error-runnning-parametric-bootstrap-pbmodcomp-on-lmer-objects 
modelfit.04b[[1]] <- PBmodcomp(output.04b[[1]], output.04a[[1]])
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

modelfit.04b[[1]]
Parametric bootstrap test; time: 611.59 sec; samples: 1000 extremes: 156;
large : y ~ age_c + gender_R2 + ibphdtdep + iyeareducc + apoegeno + age_c * 
    apoegeno + ABCA7_carrier + age_c * ABCA7_carrier + ABCA7_carrier * 
    apoegeno + age_c * ABCA7_carrier * apoegeno + (age_c | pathid)
small : y ~ age_c + gender_R2 + ibphdtdep + iyeareducc + apoegeno + age_c * 
    apoegeno + ABCA7_carrier + age_c * ABCA7_carrier + (age_c | 
    pathid)
         stat df p.value
LRT    6.5422  4  0.1621
PBtest 6.5422     0.1568

My models have no issues with convergence outside of the bootstrap. 
So my question is does this affect the p.value I get from the PBmodcomp function? Is it still valid? 
Thanks
 A: Your p-values are meaningless. The methods in the package you are stating must be using a Newton method of sorts to solve an optimization problem. The Newton method involves finding the inverse of the matrix of second derivatives (Hessian). The error is saying that this matrix became singular at some point (degenerate eigenvalues) and hence could not complete. In any case, it is throwing up the values it got till the point of termination
A: My answer was getting too long so I put up a new post.
I do not think too much will change on re-running, you may need to reformulate the setup. I haven't looked into the details of the package as to what exactly is being optimized but here is an explanation of why things might not change too much. Hope this helps you make an informed decision/hope other people chip in.
This error suggests that at some point your second derivative is becoming +/- $\infty$. If I tell you I want to minimize f(x) with this property using a solver which iteratively does it, will my starting point matter? Not if my problem is convex! (as is the case in most problems). Eventually you will probably to get stuck in the pit which pulls the solution towards -$\infty$. As a simple example, suppose I ask you to minimize x where x is real the answer is -$\infty$
9/10 cases I will say restructure the problem to rid yourself of this singularity. I am not sure if your problem falls in the 1/10 case but the odds are pretty low it does
