[R-sig-ME] Proper analysis for the Machines dataset in lme4

[Reinhold Kliegl]

Dear Michael,

A few comments on your example from the Baayen book:

>  # pr2 is analogous to m2 and mr2
>  pr2 <- lmer(rt ~ soa + (1 | subj / soa) + (1 | item), sp)
It does not look like subjects are nested with soa. So why would you
want to specify this model?

>  # pr3 is analogous to m3 and mr3 This is how Baayen analyzes it
>  # (the results aren't identical to his; I don't know why):
>  pr3 <- lmer(rt ~ soa + (1 + soa | subj) + (1 | item), sp)
This is an appropriate model for this experiment. It tests the fixed
effects of soa. It allows for mean differences between subjects and
for mean differences between items (i.e., the variances of the two
intercepts) as well as for variance between subjects in the soa
effects.

Here is the current lmer (lme4_0.999375-13) fit:
Linear mixed model fit by REML
Random effects:
 Groups   Name        Variance Std.Dev. Corr
 subj     (Intercept) 855.94   29.256
          soaShort    491.81   22.177   -0.806
 item     (Intercept) 449.39   21.199
 Residual             100.21   10.011
Number of obs: 64, groups: subj, 8; item, 8

Fixed effects:
            Estimate Std. Error t value
(Intercept)   540.91      14.92   36.26
soaShort       22.41      17.10    1.31

And here are the results as reported in Baayen (2008):
Random effects:
 Groups   Name        Variance Std.Dev. Corr
 subj     (Intercept) 861.99   29.360
          soaShort    502.65   22.420   -0.813
 item     (Intercept) 448.29   21.173
 Residual             100.31   10.016
Number of obs: 64, groups: subj, 8; item, 8

Fixed effects:
            Estimate Std. Error t value
(Intercept)   540.91      14.93   36.23
soaShort       22.41      17.13    1.31

So you are correct: There are minor differences in the variance
estimates. The simple reason is that Baayen worked with a much earlier
version of lmer 0.9975-7. I am much more impressed by the stability of
the estimates than the differences, given the many changes lmer
underwent internally in the mean time.

Best
Reinhold