Perfectly correlated random effects (when they shouldn't be)

On 15-07-15 12:52 PM, Paul Buerkner wrote:

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

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

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-- Steven V. Miller Assistant Professor Department of Political
Science Clemson University http://svmiller.com

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