Thanks for the reply,
I take from your message that my interpretation of the x2 random effect is
correct - it is the variance of the deviation from the group mean with x2=1
compared with x2=0. So the total effect of group when x2=1 would be the sum
of both random effects, yes?
The model you suggest:
y ~ x1 + x2 + (1 +x2 | group);
is identical to:
y ~ x1 + x2 + (x2 | group),
right? It seems to be based on my testing and understanding of lmer
defaults. In any case that model does not improve model fit according to
AIC/BIC and LRT, so I went with the one I described in my first email.
My problem is that these variances should not be correlated (because there
is no covariance between them, right?), though the estimates (pulled from
ranef() ) seem to be meaningfully correlated. Is this just a chance
occurrence or artifact, like when factor scores from uncorrelated factors
are highly correlated? Should I not interpret the high observed correlation
due to the lack of formal modeling and nonsignificant improvement? Am I
just capitalizing on chance?
Thanks!
Andrew
On Sat, Dec 6, 2014 at 3:23 PM, Ken Beath <ken.beath at mq.edu.au> wrote:
The random effect for x2 is giving the variation in the effect of x2,
that is the difference in levels (from x2=0 to x2=1), with id.
I would first try the model, and see if it improves AIC.
y ~ x1 + x2 + (1 +x2 | group)
This now allows for the random effects for the intercept and x2 to be
correlated
On 7 December 2014 at 02:12, Andrew McAleavey <andrew.mcaleavey at gmail.com
Hi,
I have a lmer model of the form:
y ~ x1 + x2 + (1 | group) + (0 +x2 | group) ;
where x1 is continuous, x2 is dichotomous and dummy-coded, and group has
about 250 levels (each with minimum 3 observations in each x2 level, but
the average is more like 7 per x2 level, and over 15 observations per
group
on average, ignoring x2). My understanding is that this model separately
estimates variance components for each level of x2 across groups, and
does
not model any correlation between them.
This was a better fit to the data than the structure:
y ~ x1 + x2 + (x2 | group) ;
and I came to this model based on a series of threads on this list. Note
that under this model the correlation between random effects for x2 and
the
intercept was .67, and as far as I can tell convergence was not a problem
in either model as it might be in some cases with smaller group numbers.
However, I would like to interpret, at least tentatively, the random
effects, and especially the relationship between them. My central
substantive question is whether groups vary with respect to differential
effectiveness with x2 levels (e.g., some groups were effective with x2=0
but not x2=1 while others were highly effective with both). Extracting
the
random effects and plotting them suggests that even though the model does
not explicitly include correlations, the two random effects are
correlated
at about r = .56.
My questions are these:
a) is a significant correlation like r = .56 common under conditions of
my
model in which these effects were not modeled?
b) to interpret the random effects, I think I may need to treat them as
additive and correlate u1 with (u1 + u2), which leads to an even higher
correlation (r > .8). Am I correct in this? My thinking is that u2, as a
dummy coded variable, represents the deviation for x2 = 1 from x2 = 0,
but
is that incorrect?
Thanks very much,
Andrew
--
Andrew McAleavey, M.S.
Department of Psychology
The Pennsylvania State University
346 Moore Building
University Park, PA 16802
aam239 at psu.edu
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