[R-sig-ME] lme4, failure to converge with a range of optimisers, trust the fitted model anyway?

[Ken Beath]

One of the problems is that you have a relatively high random effects
variance. A standard deviation of the intercept of 3 is a huge amount, it
means that there is massive variation in the random effect value needed to
model each cluster, to the point that some clusters will be all zeros and
some will be all ones. In this situation the assumption of approximate
normality of the likelihood around the nodes which is required for using
Laplace's method is very far from met.

I would find a spare computer and increase nAGQ to say 5. It might take a
while to run but hopefully it will be enough to make it converge. Then
increase nAGQ until the logLikelihood doesn't change. I have a preference
for nlminb.

Programs that do random effects logistic with more than one random effect
are scarce. I can try Latent Gold with Syntax Module but I'm not certain
what limit it has on number of observations.


On 4 April 2015 at 20:29, Hans Ekbrand <hans.ekbrand at gmail.com> wrote:

> Dear list,
>
> I know, the failure to converge problem is boring, but still I would
> like your input on my situation.
>
> I have tried four optimizers/methods, and they all fail; glmer used.
>
> 1. Nelder_Mead: Model failed to converge with max|grad| = 0.00116526
>    (tol = 0.001, component 6)
>
> 2. bobyqa: Model failed to converge with max|grad| = 0.00117064 (tol =
>    0.001, component 7)
>
> 3. optimx, nlminb: Model failed to converge: degenerate Hessian with 4
>    negative eigenvalues
>
> 4. optimx, L-BFGS-B: Model failed to converge with max|grad| =
>    0.012963 (tol = 0.001, component 7)" "Model failed to converge:
>    degenerate Hessian with 3 negative eigenvalues
>
> The sample size is large: 1.833.793
>
> The estimates resulting from fitting the model to data with the
> different optimizers are similar:
>
>                                      NM     bobyqa      nlmin       BFGS
> (Intercept)                   4.9857379  3.7283744  4.9477121  3.2138480
> QoG                           0.7866227  0.5962816  0.7534208  0.5991817
> GDPLog                       -1.5161825 -1.3643422 -1.5111097 -1.2940261
> Ruralyes                      4.3436228  4.3422641  4.3419199  4.3415551
> KilledPerMillion5Log          0.6632158  0.6005677  0.6276264  0.5216984
> Ruralyes:KilledPerMillion5Log 0.7313136  0.7316543  0.7314746  0.7329137
>
> My theoretical focus is on the last two rows.
>
> 1. Is this likely to be a false positive? I'm willing to share data if
>    that can help the development of lme4.
>
> 2. If the fits are bad, then what are my alternatives? continue with
>    glmer and increase nAGQ? Other ideas? Or do I need to use other
>    packages? I really love lme4, so I hope this will not be necessary.
>
>
> Kind regards,
>
> Hans Ekbrand
>
>
>
>
>
>
>
> Postscript.
>
> Here is the output of summary for the Nelder_Mead fit:
>
> Generalized linear mixed model fit by maximum likelihood (Laplace
> Approximation) ['glmerMod']
>  Family: binomial  ( logit )
> Formula: SanitationDeprivation ~ (1 | Country) + (1 | ClusterID) + QoG +
>     GDPLog + Rural * KilledPerMillion5Log
>    Data: my.df.aid
>
>       AIC       BIC    logLik  deviance  df.resid
> 1013298.5 1013397.9 -506641.2 1013282.5   1833785
>
> Scaled residuals:
>     Min      1Q  Median      3Q     Max
> -9.6390 -0.2883 -0.0508  0.0666 14.6730
>
> Random effects:
>  Groups    Name        Variance Std.Dev.
>  ClusterID (Intercept)  9.675   3.110
>  Country   (Intercept) 11.115   3.334
> Number of obs: 1833793, groups:  ClusterID, 38177; Country, 65
>
> Fixed effects:
>                               Estimate Std. Error z value Pr(>|z|)
> (Intercept)                    4.98574    0.08764   56.89  < 2e-16 ***
> QoG                            0.78662    0.13190    5.96 2.46e-09 ***
> GDPLog                        -1.51618    0.04841  -31.32  < 2e-16 ***
> Ruralyes                       4.34362    0.04655   93.31  < 2e-16 ***
> KilledPerMillion5Log           0.66322    0.15070    4.40 1.08e-05 ***
> Ruralyes:KilledPerMillion5Log  0.73131    0.06059   12.07  < 2e-16 ***
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Correlation of Fixed Effects:
>             (Intr) QoG    GDPLog Rurlys KlPM5L
> QoG         -0.042
> GDPLog      -0.153  0.129
> Ruralyes    -0.020  0.067 -0.037
> KlldPrMll5L -0.081 -0.113 -0.091 -0.131
> Rrlys:KPM5L -0.007 -0.088 -0.044 -0.426  0.205
>
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>



-- 

*Ken Beath*
Lecturer
Statistics Department
MACQUARIE UNIVERSITY NSW 2109, Australia

Phone: +61 (0)2 9850 8516

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