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I have found a number of posts about how worried one should be when they get convergence warnings from lme4 (such as: How scared should we be about convergence warnings in lme4). However, I have not been able to find equivalent postings about convergence warnings when using multiple imputation datasets, specifically if the warnings are only on some of the runs but not all.

I am running random intercept models over 30 imputed datasets (imputed with mice) with a count outcome, with participants nested in schools (I’m not getting convergence warnings for my equivalent lmer models). I am not sure how concerned I should be when a handful of my imputed datasets throw convergence warnings but the rest do not. I’ve copied an example of two of the runs below, where the convergence error shows up at the end of the first summary but not the second (my data is restricted so I am not able to post it for reproducing the warnings).

Code: 

RQ1fullODGX2m3 <- with(imp, glmer(ODGX2 ~ preginsch + S1cl +  S6Bcl + gpainsch 
+parentedimputed + delinq+ S62Ocl + noparentimputed +  (1|SSCHLCDE), 
family=poisson, 
control=glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun=100000)), 
subset (RQ1full==1 & (preginsch==1 | futurepreg ==1))))

Excerpt of summary():

## summary of imputation 26 :
Generalized linear mixed model fit by maximum likelihood (Laplace 
Approximation) ['glmerMod'] Family: poisson  ( log )

Formula: ODGX2 ~ preginsch + S1cl + S6Bcl + otherraceinsch + gpainsch +  
parentedimputed + delinq + S62Ocl + noparentimputed + (1 | SSCHLCDE)
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+05))
Subset: (RQ1full == 1 & (preginsch == 1 | futurepreg == 1))

 AIC      BIC   logLik deviance df.resid 
 3148.8   3197.8  -1563.4   3126.8      628 

Scaled residuals: 
Min      1Q  Median      3Q     Max 
-2.4388 -1.1207 -0.0159  0.8869  4.1627 

Random effects:
Groups   Name        Variance Std.Dev.
SSCHLCDE (Intercept) 0.09933  0.3152  
Number of obs: 639, groups:  SSCHLCDE, 100

Fixed effects:

                  Estimate Std. Error z value Pr(>|z|)    
 (Intercept)      2.282264   0.299715   7.615 2.64e-14 ***
 preginsch       -0.020990   0.045705  -0.459 0.646054    
 S1cl            -0.064696   0.017899  -3.615 0.000301 ***
 S6Bcl           -0.245133   0.062187  -3.942 8.08e-05 ***
 otherraceinsch  -0.357046   0.065428  -5.457 4.84e-08 ***
 gpainsch         0.068533   0.031757   2.158 0.030923 *  
 parentedimputed  0.070955   0.058575   1.211 0.225761    
 delinq          -0.007203   0.019503  -0.369 0.711867    
 S62Ocl          -0.164883   0.066465  -2.481 0.013110 *  
 noparentimputed -0.161624   0.083127  -1.944 0.051858 .  

 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Correlation of Fixed Effects:

             (Intr) prgnsc S1cl   S6Bcl  othrrc gpnsch prntdm delinq S62Ocl
 preginsch    0.119                                                        
 S1cl        -0.930 -0.209                                                 
 S6Bcl       -0.212 -0.026  0.098                                          
 otherrcnsch -0.221 -0.069  0.148  0.341                                   
 gpainsch    -0.270  0.070 -0.030  0.110  0.072                            
 parentdmptd  0.070 -0.021 -0.062 -0.116 -0.131 -0.120                     
 delinq      -0.263  0.004  0.115  0.231  0.098  0.132 -0.041              
 S62Ocl       0.006 -0.007 -0.041 -0.004 -0.015  0.052 -0.011 -0.078       
 noparntmptd -0.035 -0.041  0.010 -0.024  0.039  0.018  0.041  0.037 -0.023
 convergence code: 0
 Model failed to converge with max|grad| = 0.00109371 (tol = 0.001, component 1)

 ## summary of imputation 27 :

 Generalized linear mixed model fit by maximum likelihood (Laplace 
 Approximation) ['glmerMod'] Family: poisson  ( log )

 Formula: ODGX2 ~ preginsch + S1cl + S6Bcl + otherraceinsch + gpainsch +  
 parentedimputed + delinq + S62Ocl + noparentimputed + (1 |      SSCHLCDE)
 Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+05))
 Subset: (RQ1full == 1 & (preginsch == 1 | futurepreg == 1))

 AIC      BIC   logLik deviance df.resid 
 3147.5   3196.5  -1562.7   3125.5      628 

 Scaled residuals: 
 Min      1Q  Median      3Q     Max 
 -2.4233 -1.1163 -0.0248  0.8748  4.0993 

 Random effects:
  Groups   Name        Variance Std.Dev.
 SSCHLCDE (Intercept) 0.1002   0.3166  
 Number of obs: 639, groups:  SSCHLCDE, 100

 Fixed effects:
                  Estimate Std. Error z value Pr(>|z|)    
 (Intercept)      2.152035   0.301166   7.146 8.96e-13 ***
 preginsch       -0.017517   0.045798  -0.382 0.702104    
 S1cl            -0.061575   0.017894  -3.441 0.000579 ***
 S6Bcl           -0.228671   0.062095  -3.683 0.000231 ***
 otherraceinsch  -0.349868   0.065269  -5.360 8.30e-08 ***
 gpainsch         0.091911   0.031648   2.904 0.003682 ** 
 parentedimputed  0.040349   0.057918   0.697 0.486018    
 delinq           0.004404   0.019675   0.224 0.822877    
 S62Ocl          -0.153198   0.066588  -2.301 0.021410 *  
 noparentimputed -0.161569   0.083140  -1.943 0.051977 .  

 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 Correlation of Fixed Effects:
             (Intr) prgnsc S1cl   S6Bcl  othrrc gpnsch prntdm delinq S62Ocl
 preginsch    0.109                                                        
 S1cl        -0.931 -0.207                                                 
 S6Bcl       -0.208 -0.020  0.098                                          
 otherrcnsch -0.213 -0.068  0.147  0.338                                   
 gpainsch    -0.286  0.086 -0.010  0.103  0.050                            
 parentdmptd  0.050 -0.025 -0.047 -0.100 -0.114 -0.113                     
 delinq      -0.260  0.032  0.109  0.227  0.091  0.133 -0.027              
 S62Ocl       0.016 -0.001 -0.053 -0.017 -0.021  0.045  0.009 -0.052       
 noparntmptd -0.033 -0.040  0.009 -0.025  0.040  0.019  0.036  0.031 -0.020

I have tried different optimizers (per posts like this: https://rstudio-pubs-static.s3.amazonaws.com/33653_57fc7b8e5d484c909b615d8633c01d51.html) and am getting the similar convergence warnings results.

This is being run on a subset of my participants (~600). However, when I run models on my full data (~7000) I actually get more (lots more!) convergence warnings, which seems a bit unexpected given the comment on this post (How scared should we be about convergence warnings in lme4) that says “that optimizers run into problems when there is too little data for the number of parameters, or the proposed model is really not suitable”). The subset is what is ultimately of interest to my research question but I’m also not sure what level of concern I should have about the marked increase in warnings when run over more data.

I also tried running single level models with glm - which work fine - but don’t take into my participants being clustered in schools. When I run glms with clustered fixed effects (with the glmmML package’s glmmboot function), it overfits my models (AIC is infinite) so that is why I landed on random intercept models.

Thanks for any perspective!

EDIT: here is the convergence warning (it's at the end of summary #26 but not summary #27 in the printout above: Model failed to converge with max|grad| = 0.00109371 (tol = 0.001, component 1)

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Elizabeth H
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  • Look at http://stats.stackexchange.com/a/270642/99274 for some of the problems. Only you can cause convergence, and, if you do not, the results are sometimes not worth the photons you are reading them with. – Carl Mar 29 '17 at 23:52
  • Thanks for the link, Carl. My main question is whether the red flags raised by convergence warnings are as concerning if they only happen to a few of the datasets within an imputation, when the rest of the imputation runs without any warnings. – Elizabeth H Mar 30 '17 at 00:37
  • As a purist (and grateful that I am, since it keeps me honest), I say yes. When something does not converge, there is a problem. Maybe varying your [imputation](https://en.wikipedia.org/wiki/Imputation_(statistics)) method would help. Maybe your model is inappropriate. Maybe your regression method is inappropriate. Maybe.... see the link and explore why because if you do not, you *may* be doing gibberish. As a purist, I wouldn't like to risk it. – Carl Mar 30 '17 at 01:00
  • BTW, I cannot see your error codes above. Would you point them out for us plebs, please? – Carl Mar 30 '17 at 01:02
  • Have you read what Doug Bates et al. say regarding (the possibility of) false convergence warnings in `help("convergence")`? – Roland Mar 30 '17 at 06:31
  • Hi Roland, I went through the convergence help from the lme4 authors on my non-imputed data (which suggests false positives). However, I wasn't sure if the results I got there would hold with my imputed datasets, which have more data. I think I'll spot check the same tests on some of the imputed datasets (since I am not sure how I'd do them pooled, which was my initial concern) – Elizabeth H Mar 30 '17 at 14:04

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