Science Fair data
Hi, and thanks again. That makes sense with the 3 levels of division:
(Intercept) divisionJunior divisionSenior
80.306526 -3.252372 -2.694055
...so that the Junior and Senior levels are both slightly lower than
the Elementary level.
I'd love to really understand the summary of lmer and what ranef,
fixef, coef and fitted are extracting - so that probably means I don't
understand the basics and nomenclature of HLMing as I thought I might
have. I took a 1-week class on HLM, and I have the book you (Douglas
Bates) wrote... Maybe I just need to study up on things a little
better!
Anyway, I appreciate your help very much : )
Doug
On Wed, Jan 27, 2010 at 8:07 AM, Douglas Bates <bates at stat.wisc.edu> wrote:
On Tue, Jan 26, 2010 at 10:10 PM, Doug Adams <fog0 at gmx.com> wrote:
I appreciate that, both of you (& that's ok for the mistake Christopher) ? :)
So fixed factors as simply listed by themselves (no 1| notation) and random effects are listed with appropriate nesting... ?I do want to consider schools as random effects; that will give me the information I'd like to have about the variability (and reliability too?) of the schools as they fit into the big picture.
When I use fixef & ranef to extract estimates for division and schools (& maybe districts eventually too now), am I right in thinking that the 3 numbers given for each level of division (fixef) are the intercepts for each level -- as if there were individual OLS regressions performed for each?
Not quite. ?They should be labeled "(Intercept)" and something like division2 and division 3. ?(By the way, it helps if you quote the output when you want to discussion what particular values mean.) ?The (Intercept) coefficient represents the prediction at the first level of the division factor. ?The next two coefficients are the change from the first to the second level and from the first to the third level.
And are the random effects for the schools (ranef) are the slopes associated with those regression lines?