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|Subj),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:Culture+(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

 

 

 


	[[alternative HTML version deleted]]


