calculation max|grad value?

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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