Hello,
 
I've been building models with lmer() and keep running into False Convergence warnings. I keep encountering cases where the addition of one parameter seems to lead to the warning, but then the subsequent addition of another remedies it.
 
> correction.0 <- lmer(correction ~ 1 + (1|speaker),data=units,family="binomial",verbose=T)
  0:     24706.538: 0.0335037 -4.13024
  1:     24432.859:  1.03340 -4.14431
  2:     24425.193: 0.963810 -4.34639
  3:     24408.935: 0.750125 -4.34192
  4:     24404.161: 0.675248 -4.33695
  5:     24398.878: 0.525983 -4.32131
  6:     24398.725: 0.519804 -4.29548
  7:     24398.724: 0.517406 -4.29419
  8:     24398.724: 0.518371 -4.29403
  9:     24398.724: 0.518344 -4.29415
 10:     24398.724: 0.518339 -4.29414
> correction.0
Generalized linear mixed model fit by the Laplace approximation 
Formula: correction ~ 1 + (1 | speaker) 
   Data: units 
   AIC   BIC logLik deviance
 24403 24423 -12199    24399
Random effects:
 Groups  Name        Variance Std.Dev.
 speaker (Intercept) 0.26868  0.51834 
Number of obs: 152042, groups: speaker, 64

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -4.29429    0.06943  -61.85   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> correction.1 <- lmer(correction ~ 1 + (1|speaker) + (1|conversation),data=units,family="binomial",verbose=T)
  0:     24682.764: 0.0473814 0.0335037 -4.13024
  1:     24335.241: 0.743581 0.750990 -4.15305
  2:     24311.324: 0.533599 0.810394 -4.33436
  3:     24293.262: 0.333266 0.610929 -4.35828
  4:     24287.547: 0.539771 0.424512 -4.41392
  5:     24285.122: 0.504311 0.419236 -4.40604
  6:     24282.703: 0.434515 0.412988 -4.38416
  7:     24282.407: 0.429242 0.427203 -4.35114
  8:     24282.390: 0.425712 0.421596 -4.34965
  9:     24282.388: 0.427588 0.420940 -4.34802
 10:     24282.387: 0.426838 0.420253 -4.34744
 11:     24282.387: 0.426838 0.420253 -4.34744
 12:     24282.387: 0.426838 0.420253 -4.34744
 13:     24282.387: 0.426838 0.420253 -4.34744
 14:     24282.387: 0.426838 0.420253 -4.34744
 15:     24282.387: 0.426838 0.420253 -4.34744
Warning message:
In mer_finalize(ans) : false convergence (8)
> correction.1
Generalized linear mixed model fit by the Laplace approximation 
Formula: correction ~ 1 + (1 | speaker) + (1 | conversation) 
   Data: units 
   AIC   BIC logLik deviance
 24288 24318 -12141    24282
Random effects:
 Groups       Name        Variance Std.Dev.
 conversation (Intercept) 0.18219  0.42684 
 speaker      (Intercept) 0.17661  0.42025 
Number of obs: 152042, groups: conversation, 128; speaker, 64

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -4.34744    0.06978   -62.3   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> correction.2 <- lmer(correction ~ 1 + (1|speaker) + (1|conversation) + utt.length,data=units,family="binomial",verbose=T)
  0:     24171.002: 0.0473814 0.0335037 -4.65347 0.0351006
  1:     24143.887: 0.0742134 0.0604685 -4.65399 0.0408817
  2:     23895.285: 0.334822 0.322766 -4.66060 0.0495873
  3:     23809.758: 0.335021 0.322992 -4.66088 0.0354429
  4:     23801.801: 0.340073 0.298202 -4.78160 0.0374430
  5:     23801.745: 0.340246 0.298372 -4.78167 0.0377880
  6:     23801.692: 0.340480 0.298603 -4.78178 0.0375365
  7:     23801.625: 0.341259 0.298540 -4.78185 0.0378764
  8:     23801.529: 0.342785 0.297844 -4.78185 0.0375345
  9:     23797.449: 0.338850 0.344340 -4.80326 0.0379412
 10:     23794.434: 0.389152 0.340197 -4.81267 0.0374290
 11:     23794.260: 0.389190 0.340253 -4.81270 0.0381288
 12:     23792.732: 0.375106 0.363181 -4.88431 0.0388161
 13:     23792.300: 0.403398 0.349532 -4.90578 0.0389408
 14:     23791.448: 0.413082 0.385301 -4.89715 0.0387158
 15:     23791.415: 0.414048 0.392737 -4.90049 0.0388527
 16:     23791.415: 0.414043 0.394087 -4.90087 0.0388451
 17:     23791.415: 0.414016 0.394129 -4.90090 0.0388453
> correction.2
Generalized linear mixed model fit by the Laplace approximation 
Formula: correction ~ 1 + (1 | speaker) + (1 | conversation) + utt.length 
   Data: units 
   AIC   BIC logLik deviance
 23799 23839 -11896    23791
Random effects:
 Groups       Name        Variance Std.Dev.
 conversation (Intercept) 0.17141  0.41402 
 speaker      (Intercept) 0.15534  0.39413 
Number of obs: 152042, groups: conversation, 128; speaker, 64

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -4.900904   0.072100  -67.97   <2e-16 ***
utt.length   0.038842   0.001641   23.67   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Correlation of Fixed Effects:
           (Intr)
utt.length -0.379
 
>From looking at various other threads about False Convergence warnings, my first thought was the extreme intercept was the cause (only around 1.6% of my observations are 1's), but the intercept is lower in correction.2 without False Convergence, and I can model even less likely outcomes with the same structure and they converge without problems
 
> insertion <- lmer(insertion ~ 1 + (1|speaker) + (1|conversation),data=units,family="binomial",verbose=T)
  0:     10846.326: 0.0473814 0.0335037 -5.14276
  1:     10735.152: 0.735573 0.758552 -5.16914
  2:     10706.537: 0.408726 0.665376 -5.44506
  3:     10703.900: 0.409732 0.559300 -5.43978
  4:     10703.472: 0.452849 0.473842 -5.39375
  5:     10703.366: 0.441452 0.482908 -5.39861
  6:     10703.361: 0.438940 0.502765 -5.42190
  7:     10703.319: 0.432561 0.501455 -5.40800
  8:     10703.317: 0.431934 0.500723 -5.40593
  9:     10703.316: 0.431666 0.500301 -5.40483
 10:     10703.316: 0.431564 0.500099 -5.40437
 11:     10703.316: 0.431502 0.499951 -5.40406
 12:     10703.316: 0.431489 0.499910 -5.40398
 13:     10703.316: 0.431506 0.499792 -5.40385
 14:     10703.316: 0.431466 0.499824 -5.40384
 15:     10703.316: 0.431466 0.499824 -5.40384
> insertion
Generalized linear mixed model fit by the Laplace approximation 
Formula: insertion ~ 1 + (1 | speaker) + (1 | conversation) 
   Data: units 
   AIC   BIC logLik deviance
 10709 10739  -5352    10703
Random effects:
 Groups       Name        Variance Std.Dev.
 conversation (Intercept) 0.18616  0.43147 
 speaker      (Intercept) 0.24982  0.49982 
Number of obs: 152042, groups: conversation, 128; speaker, 64

Fixed effects:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -5.40383    0.08442  -64.01   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
 
Can anybody give me any idea of what the problem might be, or at least why it doesn't happen consistently? What's particularly alarming is that I ran the same analyses about 8 or 9 months ago without any problems.
 
Finally, here's my sessionInfo():
 
R version 2.12.2 (2011-02-25)
Platform: i386-pc-mingw32/i386 (32-bit)

locale:
[1] LC_COLLATE=English_United Kingdom.1252 
[2] LC_CTYPE=English_United Kingdom.1252   
[3] LC_MONETARY=English_United Kingdom.1252
[4] LC_NUMERIC=C                           
[5] LC_TIME=English_United Kingdom.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] lme4_0.999375-41   Matrix_0.9996875-1 lattice_0.19-17   
[4] geoR_1.6-35        sp_0.9-84          languageR_1.1     

loaded via a namespace (and not attached):
[1] grid_2.12.2   nlme_3.1-98   stats4_2.12.2 tools_2.12.2
 
Thanks in advance,
 
Ian

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