more fragile extreme-parameter GLMMs

[bbolker]

Both of these examples "work" in lme4.0, albeit with extreme parameter estimates and with a convergence warning in one case.

Case 1 (from the polytomous package):

## from
## library(polytomous)
## data(think)
## polytomous(Lexeme ~ Agent + Patient + (1|Register),
##      data=think, heuristic="poisson.reformulation")

load(system.file("testdata","polytom2.RData",package="lme4"))
library(lme4)
## library(lme4.0)
g1 <- glmer(formula=formula.poisson,data=data.poisson,family=poisson)
## from lme4.0:
## does work, but we get fixed effect parameters with abs > 18 ...
load(system.file("testdata","polytom3.RData",package="lme4"))
g2 <- glmer(formula=formula.poisson,data=data.poisson,family=poisson)
## Error: PIRLS step-halving failed to reduce deviance in pwrssUpdate
## In addition: Warning messages:
## 1: In pwrssUpdate(pp, resp, tolPwrss, GQmat, compDev, fac, verbose) :
##   Cholmod warning 'not positive definite' at file:../Cholesky/t_cholmod_rowfac.c, line 431
## 2: In pwrssUpdate(pp, resp, tolPwrss, GQmat, compDev, fac, verbose) :
##  Cholmod warning 'not positive definite' at file:../Cholesky/t_cholmod_rowfac.c, line 431

case 2: from http://stackoverflow.com/questions/18999329/control-maximum-number-of-iterations-in-lme4-1-0

load(system.file("testdata","SO_sep25.RData",package="lme4"))
library(lme4)
(logit.full <-
 glmer(event ~ 
       + V12 * I(V1 - 2)
       + V13
       + V9 * I(V5 - 2)
       + V11
       + V10
       + V2
       + V3
       + V4
       + V6 + V7 + V8
       + (1 + V6 + V7 + V8 | V14),
       family=binomial("logit"), data=dataset,
       verbose=10))

[bbolker]

I think this is now fixed: the two examples above, plus another one set by Johannes Radinger, now complete (more or less) succesfully, but they're (1) very slow (2) give warning messages about failure to converge in 10,000 evaluations. Need to:

• write some tests (preferably ones that run quickly)
• test against lme4.0 results
• try with bobyqa?
• examine convergence criteria?