lmer formula specification

Gjalt-Jorn,

You might want to check out the Model specification section of 
http://glmm.wikidot.com/faq

Between this and the Nieuwenhuis link you probably have everything you 
need...

HTH

Alan

--------------------------------------------------
Email: aghaynes at gmail.com <mailto:aghaynes at gmail.com>
Mobile: +41794385586
Skype: aghaynes


On 5 November 2012 16:03, Gjalt-Jorn Peters 
<gjalt-jorn at behaviorchange.eu <mailto:gjalt-jorn at behaviorchange.eu>> 
wrote:

    Dear all,

    I posted a question last week, but I haven't received any replies
    - I'm not sure why (because there were no replies :-)), but hereby
    I try again, this time taking it one question at a time.

    I don't manage to find a clear explanation of the lmer model
    specification syntax. I haven't been able to find a webpage
    explaining this. I did find some archived posts of this list, and
    a variety of webpages, but some resources seem outdated, and
    explanations often seem to assume proficiency with mixed models
    and/or prior knowledge of some parts of the specification. Which
    is a bit of an obstacle when you're new to both R and lmer :-)

    Did I just overlook a resource, or does nothing exist yet and is
    this knowledge indeed kind of fragmented over the internet? I've
    been struggling with this for a few weeks now (not full-time
    though :-)), but perhaps I'm missing crucial search terms or
    something.

    If no source like this exists yet, could somebody perhaps correct
    my inferences? If one or more of you are willing to provide some
    feedback, I can hopefully write a tutorial/webpage thing (similar
    to, e.g.
    http://www.rensenieuwenhuis.nl/r-sessions-16-multilevel-model-specification-lme4/,
    but a bit more complete, and similar to Douglas Bates' article at
    http://cran.r-project.org/doc/Rnews/Rnews_2005-1.pdf, but a bit
    more geared towards relative lay people). From a variety of
    sources, I pieced together the following.

    The basic form is 'criterion ~ formula', where formula specifies
    the model you use to predict the criterion. This model consists of
    one or more terms separated by plusses (+). A term can be:
    -- 1 -> specifies that the intercept should be estimated. Is in
    fact optional as the intercept is always estimated;
    -- a variable name >- specifies that coefficient of that variable
    should be estimated (i.e. its slope);
    -- an interaction term, consisting of two or more variable names
    separated by colons -> specifies that the interactions between all
    those variables should be estimated, as well as their regular
    coefficients;
    -- a specification of random effects, which can take a number of
    forms:
    ---- (1 | variable name) -> for each level of variable name,
    random intercepts are estimated
    ---- (variable name 1 | variable name 2) -> for each level of
    variable name 2, random slopes are estimated for variable name 1,
    and random intercepts are estimated (note: '1 + ' implicit, see
    first bullet);
    ---- (0 + variable name 1 | variable name 2) -> for each level of
    variable name 2, random slopes are estimated for variable name 1,
    but only one (fixed) intercept is estimated;
    ---- (variable name 1 + variable 2 | variable name 3) -> for each
    level of variable name 3, random slopes are estimated for variable
    name 1 and variable name 2, and random intercepts are estimated;
    ---- (variable name 1 | variable name 3 : variable name 2) -> for
    each unique combination of levels of variable name 2 and variable
    name 3 (where variable name 3 is the higher level), random slopes
    are estimated for variable name 1;
    ---- (variable name 1 | variable name 2 / variable name 3) -> for
    each level of variable name 2, which is nested within variable
    name 3, random slopes are estimated for variable name 1;

    The next step would be to generate a series of potential scenarios
    and providing syntax for each scenario, like Rense Nieuwenhuis
    does at
    http://www.rensenieuwenhuis.nl/r-sessions-16-multilevel-model-specification-lme4/.

    I hope somebody either knows a resource that roughly does this, or
    thinks it may be nice to help make something like this!

    Kind regards, and thank you in advance,

    Gjalt-Jorn Peters