[R-sig-ME] calculation max|grad value?

[Ben Pelzer]

Dear list,

For a given model in glmer (lme4_1.1-7), I got the warning message:

3: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :

   Model failed to converge with max|grad| = 0.0601483 (tol = 0.001, 
component 17)

My model has 15 fixed effects and two (uncorrelated) random effects.

There has been a lot of correspondence about convergence issues in the 
recent lme4 version(s) lately, but I cannot easily find what measure the
"max|grad" is exactly pointing to.  If I'm right, it is the "relative 
gradient" of one of the model parameters, apparantly parameter 17. But 
how exactly is this max|grad calculated? I found a command (coming from 
Ben Bolker):

gg <- model7 at optinfo$derivs$grad

which produces gradients that are much larger than 0.0601483, probably 
since they are "absolute" gradients.

In the book of Schnabel et al. I found a definition of the relative 
gradient in their equation (7.2.3):

         Delta(f) * x  / f

which I believe must be now interpreted as

         gradient * parameters estimate by glmer /  loglikelihood


Is this indeed the formula that is used in lme4 to derive the max|grad 
and is my interpretation of it correct?
(I would like to reproduce the max|grad value 0.0601483).

And which of the parameters in my model is actually "component 17" 
(which the warning message refers to)?

Thanks for any help!

Ben Pelzer.


*--------------------------.

Below is part of the glmer output and also the result from "gg <- 
model7 at optinfo$derivs$grad"

Generalized linear mixed model fit by maximum likelihood (Laplace
   Approximation) [glmerMod]
  Family: binomial  ( logit )
Formula: bottom10readA ~ 1 + female2 + (-1 + female2 | Country33) + (1 |
     SCHOOLID2) + SES_mean_cen + age_cen + secondgen_mean + native_mean +
     Parliament2013_cen + WLMP_cen + HDI2012_cen + selage_cen +
     ce + ZSTAND2012C + Fselage2 + FCE2 + FZstand_pisa_cen2
Control:
glmerControl(optimizer = "nloptwrap", optCtrl = list(algorithm = 
"NLOPT_LN_BOBYQA"))

      AIC      BIC   logLik deviance df.resid
151434.4 151613.4 -75700.2 151400.4   276524

Scaled residuals:
     Min      1Q  Median      3Q     Max
-4.6982 -0.3104 -0.1819 -0.1126 10.6450

Random effects:
  Groups    Name        Variance Std.Dev.
  SCHOOLID2 (Intercept) 2.314767 1.52144
  Country33 female2     0.008527 0.09234
Number of obs: 276541, groups:  SCHOOLID2, 10643; Country33, 35

Fixed effects:
                      Estimate Std. Error z value Pr(>|z|)
(Intercept)        -2.1629201  0.1006349 -21.493  < 2e-16 ***
female2            -0.4316766  0.0523024  -8.253  < 2e-16 ***
SES_mean_cen       -0.3901277  0.0257537 -15.148  < 2e-16 ***
age_cen            -0.1685527  0.0256951  -6.560 5.39e-11 ***
secondgen_mean     -0.2462713  0.1269396  -1.940   0.0524 .
native_mean        -1.0927106  0.0844515 -12.939  < 2e-16 ***
Parliament2013_cen -0.0020840  0.0025656  -0.812   0.4166
WLMP_cen            0.0002831  0.0027028   0.105   0.9166
HDI2012_cen        -0.0338573  0.0600986  -0.563   0.5732
selage_cen          0.0525462  0.0119847   4.384 1.16e-05 ***
ce                 -0.0902947  0.0496913  -1.817   0.0692 .
ZSTAND2012C        -0.0457672  0.1760672  -0.260   0.7949
Fselage2           -0.0092435  0.0096429  -0.959   0.3378
FCE2               -0.0650998  0.0450328  -1.446   0.1483
FZstand_pisa_cen2  -0.4586711  0.1497851  -3.062   0.0022 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


And finally the 17 gradients:

  gg

  [1]  -2.3293884   4.3723284  -5.6278026   0.2851749 1.6813773  -8.3454128
  [7]   4.1930703  -5.1109944  49.0449769 207.5065300 20.8115773 -31.4621360
[13]  14.0848733  -3.2661238 -24.9956165   7.0817152 -5.9149812




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