Proper analysis for the Machines dataset in lme4

Dear Michael,

My following statement was not correct:

On Mon, Apr 28, 2008 at 8:38 AM, Reinhold Kliegl
<reinhold.kliegl at gmail.com> wrote:

 The comparison of m1 and m2 (or m1r and m2r) is conceptually
 questionable. m1 assumes there are 6 Workers; m2 assumes that there
 are 18 Workers, that is different groups of 6 persons worked on each
 of the 3 machines. Presumably, the experimental design decides whether
 m1 (m1r) or m2 (m2r) is the correct choice.

After reading Douglas Bates's explanation of random effects for the
Machines data today, I must add the following correction:

mr1: score ~ Machine + (1 | Worker)
mr2: score ~ Machine + (1 | Worker/Machine) ==  score ~ Machine + (1 |
Worker) + (1 | Worker:Machine)
mr3: score ~ Machine + (Machine | Worker)

I wrongly assumed "(1 | Worker/Machine)" would force the six workers
to be nested within Machine, that the program would treat them as 3
groups of 6 workers although they are coded 1 to 6. Rather this syntax
is shorthand for:  "(1 | Worker) + (1 | Worker:Machine)".
Viewed this way, mr1 and mr2 can be compared, of course, as can mr1
and mr3; these are nested models;  I am not sure about mr2 and mr3.