[R-sig-ME] [R] understanding I() in lmer formula

[Ben Bolker]

On Sat, Jun 17, 2017 at 12:29 PM, Don Cohen <don-r-help at isis.cs3-inc.com> wrote:
> Ben Bolker writes:
>  > For the level of detail you're getting into, it would be a really good
>  > idea to read the paper that accompanies the lme4 package:
>  > vignette("lmer",package="lme4") .  This goes into a lot of detail
>  > about the theory and data structures ...
>
>  vignette("lmer",package="lme4")
> gives me
>  Warning message:
>  vignette 'lmer' not found

That's surprising ... what's packageVersion("lme4") ?
>
> Is this the same as
> https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf ?

  Yes.

>
> I think that's the same one that I was having trouble with before
> and gave up around eqn 15.
> Although, I had the impression that it (looks like eqn 14) was
> describing what I expected and asked about in a previous message,
> namely paying only once for each group and then once for each data
> point within the group.
>
> Are you saying that the vignette link above actually answers the
> questions in this last message about how to compute the loglik of
> the model?  It doesn't look to me like it will.
> I view my current line of questions (and I have many more, but am
> trying to resist bombarding you with all at once) as a way to get
> the background I'll need to get through that paper.

   I would also recommend checking out Pinheiro and Bates (2000),
which is a full (book-length) treatment of the same topic, so is a
tiny bit more discursive/friendlier ...

>
> In fact, one of my questions when I read that paper was what
> correlated vs uncorrelated intercept and slope meant - I didn't
> see any explanation.  I think that Emmanuel Curis has now explained
> that, but I'm still trying to check my understanding.
>
> Since I'm writing anyway, let me indulge in one more question about
> the formulas.  Since (x|g) means correlated intercept and slope for
> x, does (x+y|g) include a separate correlation between x slope and
> y slope?  That is, the cost of specifying a group would involve a
> 3 dimensional normal distribution over intercept,x,y ?

  Yes.    (So in particular this model are 3*(3+1)/2=6 parameters
(equivalent to s^2{1}, s^2(x),s^2(y), cov(1,x), cov(1,y), cov(x,y))