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

[svm]

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

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