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

Wed, Jul 15, 2015 9:52 AM

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,

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

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