deterministic correlation of intercept and slope random effects

-----Original Message-----
From: S Ellison [mailto:S.Ellison at LGCGroup.com]
Sent: Wednesday, August 17, 2011 6:13 PM
To: Martin Schmettow
Subject: RE: [R-sig-ME] deterministic correlation of intercept and slope
random effects

Wiser heads may also contribute, but I encountered a ssuspiciously exact
correlation myself not long ago. Turned out that with a comparatively

data set the optimiser had run up against the outer limits of correlation

the data were insufficient to pull it back.

So the optimiser might have fallen down a hole it couldn;t dig itself out

If you can have a look at an MCMC run on the model, see if any parameter
distributions show unexpected second nodes near zero (or, in your case, -1

you can see the correlation terms in the MCMC).

Not sure there's a solution, though; if getting more data was easy, I'd

had it already.

S Ellison

-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Martin
Schmettow
Sent: 17 August 2011 10:28
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] deterministic correlation of intercept and slope
random effects

Dear group members,



Using lme4 for a poisson regression I found an odd effect:
the correlation between random intercept and random slope is exactly
-1.



Currently, I analyze a data set from an experiment on cultural
differences in describing navigational routes. The outcome variables
are counts of verbal descriptors (like left-right descriptors, e.g.
"turn right"). There are three dichotomous predictors: Culture,
Instruction and Perspective.
Each subject was tested once in each of both Perspective conditions.



I started by determining whether a slope random effect was needed in
addition to the random intercept. This was done by comparing the AIC
of the following two models:



mr1<-lmer(LR~Culture*Instruction*Perspective+(1|Subj),data=cardin,
family=poisson)
mr2<-lmer(LR~Culture*Instruction*Perspective+(1+Perspective|Su
bj),data=cardi
n, family=poisson)



It turned out that the random intercept improves model fit (lower
AIC).



Then I computed all possible combinations of the three fixed effects
and interactions with random slope and intercept and by lowest AIC
arrived at:



m4c<-lmer(LR~Culture+Instruction+Perspective+Perspective:Cultu
re+(1+Perspect
ive|Subj),data=cardin, family=poisson)



Now, what strikes me is the correlation of exactly -1 between random
intercept and slope. Indeed, the negative correlation has a straight
forward
interpretation: Subjects already using left-right terms a lot are less
stimulated by the Perspective condition. But how can there be a
complete determination between intercept and slope?



Thanks in advance,

Martin.



Generalized linear mixed model fit by the Laplace approximation

Formula: LR ~ Culture + Instruction + Perspective +
Perspective:Culture +
(1 + Perspective | Subj)

   Data: cardin

   AIC   BIC logLik deviance

709.3 740.5 -346.7    693.3

Random effects:

Groups Name             Variance Std.Dev. Corr

 Subj   (Intercept)      0.44923  0.67024

        PerspectiveRoute 0.41462  0.64391  -1.000 Number of obs: 362,
groups: Subj, 181



Fixed effects:

                              Estimate Std. Error z value Pr(>|z|)

(Intercept)                    1.78390    0.07249  24.608  < 2e-16 ***

CultureDutch                   0.49138    0.12595   3.901 9.56e-05 ***

InstructionCompass Rose       -0.01677    0.04247  -0.395  0.69283

PerspectiveRoute               0.63388    0.07205   8.797  < 2e-16 ***

CultureDutch:PerspectiveRoute -0.40283    0.13118  -3.071  0.00213 **

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1



Correlation of Fixed Effects:

            (Intr) CltrDt InstCR PrspcR

CultureDtch -0.534

InstrctnCmR -0.303  0.038

PerspectvRt -0.889  0.511  0.005

CltrDtch:PR  0.488 -0.929 -0.001 -0.549








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