correlation of random intercepts and slopes

Dear list!

I have a situation where lmer reports much higher
correlations of random slopes and intercepts than I would
expect. ?I generated fake data for a fictitious experiment
using the function new.df shown below. ?The experiment has a
within-factor 'cond' with levels 1 and 2, a set of items and
subjects which are both measured repeatedly. ?There are
random intercepts and slopes for items and subjects. ?On top
there's sampling error. ?The dependent measure 'rt' is some
kind of reaction time. ?Example:

?> d <- new.df(cond1.rt=600, effect.size=10, sdev=10,
? ? ? ? ? ? ? ?nsubj=49, sdev.int.subj=10, sdev.slp.subj=10,
? ? ? ? ? ? ? ?nitems=16, sdev.int.items=10,
? ? ? ? ? ? ? ?sdev.slp.items=10)

cond1.rt is the average reaction time in condition 1.
cond1.rt+effect.size is the rt in condition 2, sdev
the sampling error, the rest concerns number of subjects and
items, and the sdevs of their random intercepts and slopes.
This is the head of the data frame:

?> head(d)
? ?subj item cond ? ? ? rt re.int.subj re.slp.subj re.int.item re.slp.item
?1 ? ?1 ? ?1 ? ?1 628.4764 ? ?12.15373 ? ?4.138659 ? -0.932447 ? ?6.619795
?2 ? ?1 ? ?1 ? ?2 603.1140 ? ?12.15373 ? -4.138659 ? -0.932447 ? -6.619795
?3 ? ?1 ? ?2 ? ?1 617.8467 ? ?12.15373 ? ?4.138659 ? -2.980553 ? ?2.471397
?4 ? ?1 ? ?2 ? ?2 606.5777 ? ?12.15373 ? -4.138659 ? -2.980553 ? -2.471397
?5 ? ?1 ? ?3 ? ?1 622.8397 ? ?12.15373 ? ?4.138659 ? -2.133049 ? ?5.101761
?6 ? ?1 ? ?3 ? ?2 616.4011 ? ?12.15373 ? -4.138659 ? -2.133049 ? -5.101761

The random intercepts and slopes have small correlations:

?> with(subset(d, cond==1), cor(re.int.subj, re.slp.subj))
?[1] 0.2650591
?> with(subset(d, cond==1), cor(re.int.item, re.slp.item))
?[1] -0.3144838

But when I roll an lmer model, I see much higher correlations
of slopes and intercepts:

?> lmer(rt~cond+(cond|item)+(cond|subj), d)
?Linear mixed model fit by REML
?Formula: rt ~ cond + (cond | item) + (cond | subj)
? ? Data: d
? ? AIC ? BIC logLik deviance REMLdev
? 12050 12098 ?-6016 ? ?12040 ? 12032
?Random effects:
? Groups ? Name ? ? ? ?Variance Std.Dev. Corr
? subj ? ? (Intercept) 349.735 ?18.7012
? ? ? ? ? ?cond ? ? ? ? 82.905 ? 9.1052 ?-0.839
? item ? ? (Intercept) 201.250 ?14.1863
? ? ? ? ? ?cond ? ? ? ? 81.835 9.0463 ?-0.732
? Residual ? ? ? ? ? ? ?98.758 ? 9.9377
?Number of obs: 1568, groups: subj, 49; item, 16

?Fixed effects:
? ? ? ? ? ? ?Estimate Std. Error t value
?(Intercept) ?594.053 ? ? ?4.511 ?131.70
?cond ? ? ? ? ? 8.120 ? ? ?2.657 ? ?3.06

?Correlation of Fixed Effects:
? ? ? (Intr)
?cond -0.765


When I xyplot the data, I can't see any correlation of
slopes and intercepts. ?Could anybody please enlighten
me as to why lmer reports these high correlations?

Many thanks!

?Titus


?new.df <- function(cond1.rt=600, effect.size=10, sdev=10,
? ? ? ? ? ? ? ? ? ? sdev.int.subj=10, sdev.slp.subj=10, nsubj=10,
? ? ? ? ? ? ? ? ? ? sdev.int.items=10, sdev.slp.items=10, nitems=10) {

? ?ncond <- 2

? ?subj <- rep(1:nsubj, each=nitems*ncond)
? ?item <- rep(1:nitems, nsubj, each=ncond)
? ?cond <- rep(0:1, nsubj*nitems)
? ?err ?<- rnorm(nsubj*nitems*ncond, 0, sdev)
? ?d ? ?<- data.frame(subj=subj, item=item, cond=cond+1, err=err)

? ?# Adding random intercepts and slopes for subjects:
? ?re.int.subj ? <- rnorm(nsubj, 0, sdev.int.subj)
? ?d$re.int.subj <- rep(re.int.subj, each=nitems*ncond)
? ?re.slp.subj ? <- rnorm(nsubj, 0, sdev.slp.subj)
? ?d$re.slp.subj <- rep(re.slp.subj, each=nitems*ncond) * (cond - 0.5)

? ?# Adding random intercepts and slopes for items:
? ?re.int.item ? <- rnorm(nitems, 0, sdev.int.items)
? ?d$re.int.item <- rep(re.int.item, nsubj, each=ncond)
? ?re.slp.item ? <- rnorm(nitems, 0, sdev.int.items)
? ?d$re.slp.item <- rep(re.slp.item, nsubj, each=ncond) * (cond - 0.5)

? ?d$rt <- (cond1.rt + cond*effect.size
? ? ? ? ? ? + d$re.int.subj + d$re.slp.subj
? ? ? ? ? ? + d$re.int.item + d$re.slp.item
? ? ? ? ? ? + d$err)

? ?d
?}