[R-sig-ME] lmer nonconvergent: care to run and explain?

[Douglas Bates]

For those who may be interested, these are the results of timing the fits
of two models on these simulated data.  For consistency within the timings
I have renamed the grouping factor Mind to G and named the three continuous
covariates as S, T and U.  The optimizers whose names start with LN_ are
timings from the Julia MixedModels package using the NLopt package for
optimization.  Those whose names start with NLOPT_LN_ are the same
optimizer code accessed through the nloptr package for R.  The others are
from the optimx package, bobyqa from the minqa package (the default for
lmer) and the build-in Nelder_Mead optimizer, which is generally pretty bad
and I can say that because I wrote it.

dsname = "paulsim"
form = Formula: Y ~ 1 + S + T + U + (1 | G) + ((0 + S) | G)
-2log(likelihood) time(s) feval geval optimizer
   143232.6341     1.5120   606     0 bobyqa
   143564.1597     0.2770    70     0 Nelder_Mead
   143232.9465     0.2680    66     0 NLOPT_LN_BOBYQA
   143272.7444     0.2430    53     0 NLOPT_LN_COBYLA
   143803.9823     0.3420    40     0 NLOPT_LN_NELDERMEAD
   143232.6341     0.4570   147     0 NLOPT_LN_SBPLX
   143232.6582     0.6320    58     0 optimx:L-BFGS-B
   143232.6341     0.5480   104     0 optimx:nlminb
   143232.6341     6.7930    NA     0 optimx:spg
   143232.6341     1.6930    NA     0 optimx:bobyqa
   143232.6341     0.0489   107     0 LN_BOBYQA
   143232.6382     1.9885 69711     0 LN_COBYLA
   143803.9823     0.0474    56     0 LN_NELDERMEAD
   143232.6341     0.0527   147     0 LN_SBPLX
form = Formula: Y ~ 1 + S + T + U + ((0 + S) | G)
-2log(likelihood) time(s) feval geval optimizer
   143232.6341     0.1400    41     0 bobyqa
   143232.6341     0.1510    49     0 Nelder_Mead
   143232.6343     0.1360    36     0 NLOPT_LN_BOBYQA
   143232.6503     0.1170    24     0 NLOPT_LN_COBYLA
   143232.6341     0.1540    48     0 NLOPT_LN_NELDERMEAD
   143232.6341     0.1900    74     0 NLOPT_LN_SBPLX
   143232.6368     0.3560    70     0 optimx:L-BFGS-B
   143232.6341     0.2470    29     0 optimx:nlminb
   143232.6341     0.3660    NA     0 optimx:spg
   143232.6341     0.2650    NA     0 optimx:bobyqa
   143232.6341     0.0240    43     0 LN_BOBYQA
   143232.6341     0.0240    34     0 LN_COBYLA
   143232.6341     0.0242    52     0 LN_NELDERMEAD
   143232.6341     0.0246    81     0 LN_SBPLX

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