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

Mon Apr 13 14:41:21 CEST 2015

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:
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> 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
>>
>>
>>
>>
>> [[alternative HTML version deleted]]
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org  mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
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