[R-sig-ME] Perfectly correlated random effects (when they shouldn't be)

Wed Jul 15 18:52:03 CEST 2015

if you look at the results from a baysian perspective, it seems to be a
typcial "problem" of ML-procedures estimating the mode.

The mode is nothing special, just the point where the density is maximal.
When you have skewed distribution (as usual for correlations) the mode will
often be close to the borders of the region of definition (-1 or 1 in this
case). The posterior distribution of the correlation, however, can still be
very wide ranging from strong negative correlation to strong positive
correlation, especially when the number of levels of a grouping factor is
not that large. In those cases, zero (i.e. insignificant) correlation is a
very likely value even if the mode itself is extreme.

I tried fitting your models with bayesian R packages (brms and MCMCglmm).
Unfortunately, because you have so many observations and quite a few random
effects, they run relatively slow so i am still waiting for the results.

2015-07-15 3:45 GMT+02:00 svm <steven.v.miller at gmail.com>:

> I considered that. I disaggregated the region random effect from 6 to 18
> (the latter of which approximates the World Bank's region classification).
> I'm still encountering the same curious issue.
>
> Random effects:
>  Groups       Name        Variance  Std.Dev. Corr
>  country:wave (Intercept) 0.1530052 0.39116
>  country      (Intercept) 0.3735876 0.61122
>  wbregion     (Intercept) 0.0137822 0.11740
>               x1        0.0009384 0.03063  -1.00
>               x2         0.0767387 0.27702  -1.00  1.00
> Number of obs: 212570, groups:  country:wave, 143; country, 82; wbregion,
> 18
>
>  For what it's worth: the model estimates fine. The results are intuitive
> and theoretically consistent. They also don't change if I were to remove
> that region random effect. I'd like to keep the region random effect (with
> varying slopes) in the model. I'm struggling with what I should think about
> the perfect correlations.
>
> On Tue, Jul 14, 2015 at 9:07 PM, Jake Westfall <jake987722 at hotmail.com>
> wrote:
>
> > Hi Steve,
> >
> >
> > I think the issue is that estimating 3 variances and 3 covariances for
> > regions is quite ambitious given that there are only 6 regions. I think
> > it's not surprising that the model has a hard time getting good estimates
> > of those parameters.
> >
> >
> > Jake
> >
> > > Date: Tue, 14 Jul 2015 20:53:01 -0400
> > > From: steven.v.miller at gmail.com
> > > To: r-sig-mixed-models at r-project.org
> > > Subject: [R-sig-ME] Perfectly correlated random effects (when they
> > shouldn't be)
> >
> > >
> > > Hi all,
> > >
> > > I'm a long-time reader and wanted to raise a question I've seen asked
> > here
> > > before about correlated random effects. Past answers I have encountered
> > on
> > > this listserv explain that perfectly correlated random effects suggest
> > > model overfitting and variances of random effects that are effectively
> > zero
> > > and can be omitted for a simpler model. In my case, I don't think
> that's
> > > what is happening here, though I could well be fitting a poor model in
> > > glmer.
> > >
> > > I'll describe the nature of the data first. I'm modeling
> individual-level
> > > survey data for countries across multiple waves and am estimating the
> > > region of the globe as a random effect as well. I have three random
> > effects
> > > (country, country-wave, and region). In the region random effect, I am
> > > allowing country-wave-level predictors to have varying slopes. My
> inquiry
> > > is whether some country-wave-level contextual indicator can have an
> > overall
> > > effect (as a fixed effect), the effect of which can vary by region. In
> > > other words: is the effect of some country-level indicator (e.g.
> > > unemployment) in a given year different for countries in Western Europe
> > > than for countries in Africa even if, on average, there is a positive
> or
> > > negative association at the individual-level? These country-wave-level
> > > predictors that I allow to vary by region are the ones reporting
> perfect
> > > correlation and I'm unsure how to interpret that (or if I'm estimating
> > the
> > > model correctly).
> > >
> > > I should also add that I have individual-level predictors as well as
> > > country-wave-level predictors, though it's the latter that concerns me.
> > > Further, every non-binary indicator in the model is standardized by two
> > > standard deviations.
> > >
> > > For those interested, I have a reproducible (if rather large) example
> > > below. Dropbox link to the data is here:
> > >
> >
> https://www.dropbox.com/s/t29jfwm98tsdr71/correlated-random-effects.csv?dl=0
> > >
> > > In this reproducible example, y is the outcome variable and x1 and x2
> are
> > > two country-wave-level predictors I allow to vary by region. Both x1
> and
> > x2
> > > are interval-level predictors that I standardized to have a mean of
> zero
> > > and a standard deviation of .5 (per Gelman's (2008) recommendation).
> > >
> > > I estimate the following model.
> > >
> > > summary(M1 <- glmer(y ~ x1 + x2 + (1 | country) + (1 | country:wave) +
> > (1 +
> > > x1 + x2 | region), data=subset(Data), family=binomial(link="logit")))
> > >
> > > The results are theoretically intuitive. I think they make sense.
> > However,
> > > I get a report of perfect correlation for the varying slopes of the
> > region
> > > random effect.
> > >
> > > Random effects:
> > > Groups Name Variance Std.Dev. Corr
> > > country:wave (Intercept) 0.15915 0.3989
> > > country (Intercept) 0.32945 0.5740
> > > region (Intercept) 0.01646 0.1283
> > > x1 0.02366 0.1538 1.00
> > > x2 0.13994 0.3741 -1.00 -1.00
> > > Number of obs: 212570, groups: country:wave, 143; country, 82; region,
> 6
> > >
> > > What should I make of this and am I estimating this model wrong? For
> what
> > > it's worth, the dotplot of the region random effect (with conditional
> > > variance) makes sense and is theoretically intuitive, given my data. (
> > > http://i.imgur.com/mrnaJ77.png)
> > >
> > > Any help would be greatly appreciated.
> > >
> > > Best regards,
> > > Steve
> > >
> > > [[alternative HTML version deleted]]
> > >
> > > _______________________________________________
> > > R-sig-mixed-models at r-project.org mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
>
>
> --
> Steven V. Miller
> Assistant Professor
> Department of Political Science
> Clemson University
> http://svmiller.com
>
>         [[alternative HTML version deleted]]
>
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