[R-sig-ME] Random slope does not improve hierarchical fitting across time

Sat Jul 30 11:38:23 CEST 2016

Dear Xavier,

Both of your issues speak towards insufficient data (power too low) or
a model specification not suited for the data. See Bates et al
Parsimonious Mixed Models (http://arxiv.org/abs/1506.04967) for a
discussion on some of these issues.

Bottom line: you can't estimate all of your parameters precisely enough
(large standard errors or inability to estimate them) with the data you
have (either because there's not enough or because it isn't well
described by your model specification) and so you fail to get to
achieve significance. 

Best,
Phillip

On Fri, 2016-07-29 at 20:32 +0000, xavier piulachs wrote:
> Dear Ben,
> 
> 
> First of all, many thanks for your quick response. Moreover, I'm
> aware that you are an expertise in this field, so I'm doubly happy of
> receiving your comments.
> 
> I have two doubts about what you say (the clue point is maybe the
> first):
> 
> 
> 1) The effect of time is in the model as fixed effect (and it is
> significant), ok. But I also would expect that each subject, i =
> 1,...,n, has:
> 
>    a) His underlying baseline level (ie, a subject-specific baseline
> effect = beta0 + random intercept = beta0 + ui0) ,and
> 
>    b) A particular trend-evolution across time (a subject especific
> slope = fixed effect of time + random slope = beta_t + uit).
> 
> It is indeed very common when dealing repeated measurements across
> time (a particular case of longitudinal models) to have these two
> significant
> 
> effects.  In fact, always I have fitted longitudinal measurements
> over time (with unstructure matrix correlation by default), I got
> that random intercept
> 
> and slope model improves the accuracy of considering a single random
> intercept. So I think this is compatible with the idea of an
> autoregressive model.
> 
> Is it correct?
> 
> 
>  2) I have fitted the GLMM with the option corStruct = "full":
> 
> glmmADMB.0.int.NB <- glmmadmb(claimyr ~ obstime + (1|ID), corStruct =
> "full", data = tr.j, family = "nbinom")
> 
> And I get the following R error message:
> 
> Parameters were estimated, but standard errors were not: the most
> likely problem is that the curvature at MLE was zero or negative
> 
> The function maximizer failed (couldn't find parameter file)
> 
> 
> Best,
> 
> 
> Xavier
> 
> 
> ________________________________
> De: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> en
> nombre de Ben Bolker <bbolker at gmail.com>
> Enviado: viernes, 29 de julio de 2016 19:48
> Para: r-sig-mixed-models at r-project.org
> Asunto: Re: [R-sig-ME] Random slope does not improve hierarchical
> fitting across time
> 
> 
> 
> On 16-07-29 03:09 PM, xavier piulachs wrote:
> > 
> > Dear members of mixed-models list,
> > 
> > 
> > I'm adressing you in order to ask a question about Hierarchical and
> > ZI counts measured over time.
> > To have preliminar results, I'm modeling longitudinal data with a
> > Negative Binomial GLMM, via
> > lme4 and glmmADBM packages (very similar results). I have
> > considered two possibilities:
> > 
> > 
> > 1) A single random intercept:
> > glmer.0.int.NB <- glmer.nb(counts ~ obstime + (1|id), data =
> > tr.j)    # lme4 package
> > 
> > tr.j$ID <- as.factor(tr.j$id)
> > glmmADMB.0.int.NB <- glmmadmb(claimyr ~ obstime + (1|ID), data =
> > tr.j, family = "nbinom")
> >             Estimate Std. Error z value Pr(>|z|)
> > (Intercept)  -0.9652     0.1222 -7.9005   0.0000
> > obstime       0.0238     0.0073  3.2735   0.0011
> > 
> > 
> > 2) Random intercept and random slope effects:
> > glmer.0.slp.NB <- glmer.nb(counts ~ obstime + (obstime|id), data =
> > tr.j)   #  lme4 package
> > 
> > glmmADMB.0.slp.NB <- glmmadmb(claimyr ~ obstime + (obstime|ID),
> > data = tr.j, family = "nbinom")
> >             Estimate Std. Error z value Pr(>|z|)
> > (Intercept)  -0.9401     0.1190 -7.9005   0.0000
> > obstime       0.0230     0.0075  3.0540   0.0023
> > 
> > 
> > Surprisingly, the anova test indicates non significant improvement
> > by fitting second model:
> > 
> > anova(glmer.0.int.NB, glmer.0.slp.NB)  # LRT: p-value = 0.2725 >
> > 0.05
> > anova(glmmADMB.0.int.NB, glmmADMB.0.slp.NB) # LRT: p-value = 0.1042
> > > 0.05
> > 
> > 
> > As far as I know, when dealing repeated measurements across time,
> > we expect that outcomes closer in time to be
> > more correlated (it is indeed a more realistic approach), so I'm
> > totally disconcerted by this result.
> > Can anyone explain what could be the reason?
>   A few comments:
> 
> - most important: just because an effect is 'really' in the model
> (e.g.,
> in this case, the effect of time really does vary among individuals)
> doesn't mean it will have a statistically significant effect. In most
> observational/complex fields (population biology, social sciences),
> *all* of the effects are really non-zero. The purpose of significance
> tests is to see which effects can be distinguished from noise.
> 
> - your explanation ("outcomes closer in time are more correlated")
> isn't
> a very precise description of what the (obstime|ID) term in the model
> is
> doing.  Your description is of an autoregressive model; the
> (obstime|ID)
> model is a random-slope model (slopes with respect to time vary among
> individuals).  You might want to check out the glmmTMB package for
> autoregressive models ...
> - glmmADMB's default correlation structure is diagonal, glmer.nb's is
> unstructured; if you use (obstime||ID) in glmer.nb
> or    corStruct="full"
> in glmmadmb you should get more similar results (I would generally
> recommend "full" as the default ...)
> - likelihood ratio tests (which is what anova() is doing) generally
> give
> conservative p-values when applied to random-effect variances
> (boundary
> issues -- see http://tinyurl.com/glmmFAQ.html or Bolker (2009) or
> Pinheiro and Bates 2000 for more discussion) -- so the p-values
> should
> probably be approximately halved
> 
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