[R-sig-ME] implicit nesting

[Douglas Bates]

On Tue, Jul 6, 2010 at 7:33 PM, array chip <arrayprofile at yahoo.com> wrote:
> Dear Dr. Bates,

> I am learning lmer() from lme4 package. I came across your article "Fitting linear mixed models in R" in R News (vol5, May 2005). I have 2 questions:

> 1. one is about the implicit nesting in the section "Specifying levels" where you gave an example dataset "Pixel" from MEMSS package. You said "If we wish to fit a model with random effects for "side within dog" we must first create a dog/side factor as
>      > Pixel$DS <- wirth(Pixel, Dog:Side)[drop=TRUE]
> ".
> I still don't quite understand why we have to create a new factor variable like the above. What is wrong if we simply specify a model like this (it runs and produces results):
>  > fm <- lmer(pixel~day + (day|Side) + (day|Dog), Pixel)

Because Side has only two levels, "L" and "R", and you want to define
random effects separately for each side of each dog.

> 2. the 2nd question is about the example you gave in the section "Nested and non-nested grouping factors" where you considered the dataset "star" from mlmRev package. In this example, the model specification is:
>   > fm4 <- lmer(math ~ gr + sx + eth + cltype + (yrs | id) + (yrs | sch), star)

When modeling the results of annual test scores like these, "year" and
"grade" are usually confounded or close to being confounded within
each student.  For defining per-student random effects we prefer to
use yr because the year should always change from one result to the
next but when a student has been retained the grade doesn't change.

> In this model, you didn't include "yrs" as a fixed effect. The how should we explain the random slope? When "yrs" is included as a fixed effect in the model, we can explain random slope as a random slope around a fixed common slope. But if "yrs" is not included as a fixed effect, does that mean the random slope is around a common fixed slope of 0?

> Actually, I tried to add "yrs" as a fixed effect:
>   > fm4 <- lmer(math ~ gr + sx + eth + cltype + yrs + (yrs | id) + (yrs | sch), star)
> But I got an error message "Error in mer_finalize(ans) : Downdated X'X is not positive definite, 13.", why is that?

When means that you have linearly dependent columns in the
fixed-effects model matrix.

> Thank you very much!
>
> John