Problems with convergence

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-
project.org] On Behalf Of Ben Bolker
Sent: Monday, March 30, 2015 22:21
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Problems with convergence

Ken Beath <ken.beath at ...> writes:

Yes, I was demonstrating that it fails convergence and then as a
consequence fails to profile. I have my doubts about
convergence for the bobyqa
algorithm, I have other applications where it doesn't converge

properly.

For some of my own work I've used nlminb followed by Nelder-Mead if

there

is a convergence failure. Not optimal but it seems to work.

   I'm still not sure whether you expect it to converge (I think you
do), or whether you are just pointing out that the convergence warning
in this case is probably justified (in the face of so many convergence
warnings that turn out to be false positives, this is a useful piece
of information).

While it is fairly heavily parameterised it is a real model,
 a frequentist
implementation of Smith, T. C., Spiegelhalter, D. J., & Thomas, a.

(1995).

Bayesian approaches to random-effects meta-analysis: a comparative

study.

Statistics in Medicine, 14(24), 2685?99. The reason for having studies

as

fixed effects is probably philosophical, the overall success rates are

not

likely to be given by normally distributed random effects, and are in

many

cases specifically chosen.

  I can appreciate that, but I still think it's unrealistic to expect
to be able to fit 22 parameters to 40 observations except under very
special circumstances.  One point about switching from the Bayesian
to the frequentist world is that the Bayesians (by definition) put
priors on their parameters, which provides a degree of regularization
that is not by default available to frequentist methods.  What priors
did Smith et al. use?  It might be worth trying this in blme with
priors on the fixed effects ...

I did find that one of the data sets that I have also failed, but

fitted

with a commercial program that is based on the EM algorithm. For this

type

of problem it is actually faster, as any type of quasi-Newton needs to
calculate lots of derivatives.

  I could whine about the difficulty of finding globally robust,
reliable, and fast optimization algorithms, but I won't.  I can certainly
appreciate that there are more reliable methods for particular
sub-classes of problems.

Anyway, I'm going to keep looking at the methods, and eventually the

code

for glmer and may eventually have some suggestions.

  Would be happy to hear them.

  It's worth pointing out that lme4 is using a preliminary "nAGQ=0"
step, which ignores the terms contributed by the integrals over the
distributions of the conditional modes and as a result is able to
fit both the fixed-effect parameters and the conditional modes in
a single linear-algebra step, reducing the dimensionality of the
nonlinear optimization to the length of the variance-covariance
parameter vector ...

On 19 March 2015 at 14:45, Ben Bolker <bbolker <at> gmail.com> wrote:

Ken Beath <ken.beath <at> ...> writes:

The following code shows that there are convergence problem

messages

where there is a problem with convergence. The profiling shows that
the maximum found is not the correct one. This is simulated data

for

a binary meta-analysis with fixed effect for study and random

effect

for treatment.

 [paragraph snipped to try to make Gmane happy]

  However, may I comment that this is a slightly ridiculous scenario?
The data set here has 40 observations, and the model tries to fit 22
parameters.  The model that treats id as a random effect works much
better.  I can believe there are scenarios where you really do
want study as a fixed effect, but did you expect it to be practical
here?

But maybe you're just trying to show that this is a "true positive"
case for the convergence warnings.

Some random code I wrote while diagnosing what was going on:

library(ggplot2); theme_set(theme_bw())

## proportion + weights is a little easier to handle
thedata <- transform(thedata,prop=nEvents/total)

ggplot(thedata,aes(trt,prop))+geom_point(aes(size=total))+
    geom_line(aes(group=id),colour="gray")
glmer1 <- glmer(prop~trt+factor(id)+(0+trt|id),
                weights=total,data=thedata,family=binomial)

## id as RE
glmer2 <- glmer(prop~trt+(1|id)+(0+trt|id),
                weights=total,data=thedata,family=binomial)

dd <- update(glmer1,devFunOnly=TRUE)
pars <- unlist(getME(glmer1,c("theta","fixef")))
library("bbmle")
ss <- slice2D(pars,dd)
library("lattice")
plot(ss)
## too complex, but too much work to cut down significantly

library(lme4)

thedata <- structure(list(nEvents=c(10L,53L,17L,18L,22L,6L,16L,
14L,13L,18L,15L,19L,52L,19L,8L,16L,50L,8L,9L,4L,
26L,45L,18L,20L,5L,16L,18L,7L,3L,19L,30L,26L,66L,
23L,29L,18L,72L,25L,9L,2L),total=c(200,200,200,200,
200,200,200,200,200,200,200,200,200,200,200,200,200,
200,200,200,200,200,200,200,200,200,200,200,200,200,
200,200,200,200,200,200,200,200,200,200),trt=c(0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1),id=structure(c(1L,
2L,3L,4L,5L,6L,7L,8L,9L,10L,11L,12L,13L,14L,15L,
16L,17L,18L,19L,20L,1L,2L,3L,4L,5L,6L,7L,8L,9L,
10L,11L,12L,13L,14L,15L,16L,17L,18L,19L,20L),.Label=c("1",
"2","3","4","5","6","7","8","9","10","11","12","13",

"14","15","16","17","18","19","20"),class="factor")),.Names=c("nEvents",

"total","trt","id"),row.names=c(NA,40L),class="data.frame")

glmer1<-glmer(cbind(nEvents,total-nEvents)~trt+factor(id)+

##   (0+trt|id),data=thedata,family=binomial)

# while glmer has problems with component 9 it is 8 with a problem

profile

# I've use devtol so the discrepancy is printed
prof.glmer1<-profile(glmer1,which=8,devtol=1.0e-3)