help with a cross-classified random effects model code in R.

Dear Dr. Bates,
You replied to a question by Violet(Shu) Xu on how to estimate
cross-classified (XC) models. In the DIGEST version however, no example
code is provided.
In general, how do we estimate XC models using lme4?

Is the following example for a null model for some dependent variable Y
for pupils who attended specific primary and secondary schools correct?
Or does lmer then estimate a nested model?

lmer(Y~(1|primaryschool)+(1|secondaryschool),data=dataname)

That will estimate the model with crossed random effects.  An example
of exactly this type is

data(ScotsSec, package = "mlmRev")
library(lme4)

Loading required package: Matrix
Loading required package: lattice

Attaching package: 'Matrix'


	The following object(s) are masked from package:stats :

	 xtabs

(fm1 <- lmer(attain ~ (1|primary) + (1|second), ScotsSec))

Linear mixed model fit by REML
Formula: attain ~ (1 | primary) + (1 | second)
   Data: ScotsSec
   AIC   BIC logLik deviance REMLdev
 17159 17183  -8575    17149   17151
Random effects:
 Groups   Name        Variance Std.Dev.
 primary  (Intercept) 1.13002  1.0630
 second   (Intercept) 0.37222  0.6101
 Residual             8.11069  2.8479
Number of obs: 3435, groups: primary, 148; second, 19

Fixed effects:
            Estimate Std. Error t value
(Intercept)   5.5017     0.1787   30.79

To see that the primary and secondary schools classifications are not
nested you can check the image of the cross classification of those
factors produced by

image(xtabs(~ primary + second, ScotsSec, sparse = TRUE))

I enclose a PDF file of that image.
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