calculation max|grad value?

Hi Dan,

Thanks for pointing me to that formula. Am I right that in case of
only one parameter (say a fixed intercept only), this measure means
that the gradient of the intercept-estimate is divided by the
(estimated) variance of the intercept? Could you explain to me the
rationale behind this measure or to put it differently: why is it
meaningful to use it as a criterion to evaluate the quality of the
convergence?

In case of more than one parameter, it's even less clear to me what
the measure exactly expresses and thus why it is used by glmer.

Thanks again for any help/explanation,

Ben Pelzer.

On 11-4-2015 1:51, Daniel McCloy wrote: with a model called mod,
you can get the relative gradient with

relgrad <- with(mod at optinfo$derivs, solve(Hessian, gradient)) 
print(max(abs(relgrad))

-- dan

Daniel McCloy http://dan.mccloy.info/ Postdoctoral Research Fellow 
Institute for Learning and Brain Sciences University of Washington


On 04/10/2015 06:54 PM, Ben Pelzer wrote:

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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