[R-sig-ME] Correlation of Fixed Effects in repeated cross-sectional data

[Malcolm Fairbrother]

Dear mixed modellers,

I am trying to use lmer to estimate a model with binary individual  
responses (N=27899, from repeated cross-sectional data) nested within  
state-years (N=748), in turn nested in states (N=49)--and potentially  
also in years (N=20). My independent variable of greatest interest  
("stateyearX") varies both across states and within them over time,  
and for most states it is trending upward over the period of study.

My issue is the value I'm getting for the correlation between the  
stateyearX and Intercept Fixed Effects (see below). This holds true  
irrespective of whether or not I interact stateyearX with time,  
whether or not I include year as an additional level, and whether or  
not I add other covariates (at various levels).

This value seems alarmingly high... and I'm not really sure how to  
interpret it. Can anyone advise me on whether I'm doing something  
wrong and/or what to do instead? What is this value telling me about  
the relationship between the overall (not random?) Intercept and the  
estimate I'm getting for stateyearX?

Sorry if this is ignorant. This is my first ever post here--thanks  
very much for the package, and for all the great information already  
in the archives.

Any help on this gratefully received.
- Malcolm


Malcolm Fairbrother
School of Geographical Sciences
University of Bristol



 > (wm96k <- lmer(Y ~ stateyearX + time + (1 | stateyear) + (1 |  
state), family=binomial(link="logit"), data=tdat))
Generalized linear mixed model fit by the Laplace approximation
Formula: Y ~ stateyearX + time + (1 | stateyear) + (1 | state)
    Data: tdat
    AIC   BIC logLik deviance
  36650 36691 -18320    36640
Random effects:
  Groups    Name        Variance Std.Dev.
  stateyear (Intercept) 0.043609 0.20883
  state     (Intercept) 0.132090 0.36344
Number of obs: 27899, groups: stateyear, 748; state, 49

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)
(Intercept)  0.773340   0.461232   1.677   0.0936 .
stateyearX  -2.661767   1.287316  -2.068   0.0387 *
time        -0.008745   0.003642  -2.401   0.0163 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) sttyrX
stateyearX -0.990
time        0.832 -0.871


 > sessionInfo()
R version 2.9.1 (2009-06-26)
i386-apple-darwin8.11.1

locale:
en_GB.UTF-8/en_GB.UTF-8/C/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] lme4_0.999375-31   Matrix_0.999375-30 lattice_0.17-25     
foreign_0.8-37

loaded via a namespace (and not attached):
[1] grid_2.9.1  tools_2.9.1