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

[Paul Johnson]

Thanks to everybody for looking at the example. If that code can be
re-used in any way that helps lme4 development, I give permission to
re-use or edit it and put it to use. I'm happy to let everybody who
actually understands this debate it.  I don't (yet).

I need to explain to users why we have these warnings with lmer but
not SAS or Stata.  In the output I pasted in to the original email, it
reports convergence in a few steps of EM.  But lmer is going for a lot
more iterations.  How to explain that difference to students?

I'm reading through the papers that Doug has written in the last 10
years or so explaining the estimation process in PLS.   Bates and
Debroy makes this clear for LMM.  In comparison, the mainstream HLM
folks treated MLM a a GLS problem. Raudenbush & Bryk, for example, or
Snidjers & Bosker, describe calculation of predictions for the b's as
a posterior calculation, rather than an element of the optimization.

It appears to me Stata is written that GLS way.  Stata has a parameter
vector with fixed effects and variances of random effects (Beta,
Sigma).   In contrast, lmer i optimising over (Beta, Sigma, b).

Am I just making up a story here?

pj

On Fri, Oct 16, 2015 at 1:35 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
> 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
>



-- 
Paul E. Johnson
Professor, Political Science        Director
1541 Lilac Lane, Room 504      Center for Research Methods
University of Kansas                 University of Kansas
http://pj.freefaculty.org              http://crmda.ku.edu