understanding I() in lmer formula
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))