[R-sig-ME] What is the lmer/nlme equivalent of the REPEATED subcommand in SPSS's MIXED procedure?

[Rune Haubo]

On 20 March 2018 at 18:34, Douglas Bates <bates at stat.wisc.edu> wrote:
> Kind of looks like SPSS went for bug-for-bug compatibility with SAS on this
> one.  In SAS PROC MIXED, "REPEATED" and "RANDOM" are two ways of specifying
> the random effects variance structure but they often boil down to the same
> model.
>
> I believe the model can be specified in lme4 as
>
>     value ~ factor1 + (factor1 | participant)
>
> This is what the mis-named* "UNSTRUCTURED" covariance type means
>
> * Old-guy, get off my lawn rant about terminology *
> As a recovering mathematician I find the name "unstructured" being used to
> denote a positive-definite symmetric matrix to be, well, inaccurate.
>

The UN option (for "unstructured") in the SAS random statement is kind
of tricky as it actually does not restrict the variance-covariance
matrix to be positive definite (or even postive semidefinite). I have
previously obtained such "fits" and it took a while to figure out why
R and SAS gave different answers. I am quoting here because it is at
least debatable in what sense a negative definite symmetric matrix is
actually a valid variance-covariance matrix... There is another option
that you can use (if I recall correctly it is the FA option for factor
analysis) if you are so "picky" that you actually also want the
variance-covariance matrix to be positive (semi)definite. Intuitive,
right ;-)

Cheers
Rune