[R-lang] Re: is it possible to use lmer function with a polytomous response variable?

[Antti Arppe]

Dear all,

On Thu, 8 Apr 2010, gurcanli@cogsci.jhu.edu wrote:
> In my data I have a polytomous response variable which has 4 levels (4
> different verb categories). I want to analyze the data by using lmer
> function with fixed and random effects. Is it possible? If not, what other
> package can I use? Since I am new to this type of analysis, I would
> appreciate if you could give the details of the R-code.

The four verb categories you mention cannot but remind me of the four
synonymous (Finnish) verbs that I modeled with logistic regression in
my doctoral dissertation - though strictly speaking in terms of
linguistic explananatory variables as fixed effects (with authors as
clusters in a bootstrap validation of the model masquerading as the
impact of random effects). As a prelude (for some possible solutions)
to your mixed effects logistic regression modeling, the various
different heuristics for implementing this are described on pp.
113-116 and 119-125 in the published dissertation (to a certaint
extent based on a paper by Eibe Frank and Stefan Kramer, 2004:
Ensembles of nested dichotomies for multi-class problems, ACM
International Conference Proceeding Series; Vol. 69), anyhow:

http://www.ling.helsinki.fi/~aarppe/Publications/Arppe_Dissertation_Final_Print.pdf
[the entire dissertation electronically published as:
http://urn.fi/URN:ISBN:978-952-10-5175-3]

A brief overview of these heuristics can be found in a recent
presentation:

http://www.ling.helsinki.fi/~aarppe/Publications/Alberta_PLR_Arppe_100226.pdf

On Fri, 9 Apr 2010, T. Florian Jaeger wrote:
> Btw, Agresti (2002: Section 7.2 to 7.3) contains a pretty readable
> and concise introduction to the differences between cumulative
> logit, probit, and other cumulative link models for ordinal
> responses.

With respect to your question concerning including random effects as
well, my understanding of Agresti would seem to imply that applying
e.g. the one-vs-rest heuristic (with random effects for each outcome)
might be one possible solution, to cite:

Agresti 2002: 515 (Section 12.4.4 Baseline-Category Logit Models with
Random [Mixed] Effects): "... This requires using a vector or
cluster-specific random effects u(j,j), one for each logit [model].
... With nominal responses there is not reason to expect effects to be
similar for different [outcomes] j.

Nonetheless, an alternative solution is presented by the fact that a
polytomous/multinomial outcome model with multinomial (nominal)
predictors has an equivalent Poisson/count/log-linear model, which was
suggested to me by Harald Baayen (based on an observation he had
uncovered in Faraway 2006, and which is also inferable from the
already mentioned work by Agresti 2002). Then, most importantly, one
is able to apply the 'lmer' function in the 'lme4' package, as it is
implemented in R, to a polytomous outcome setting as yours. A recent
description presenting preliminary comparisons of the multinomial and
corresponding Poisson-count models for fixed effects as well as random
effects (with empirical evidence reassuring of their equivalence) can
be found at:

http://www.ling.helsinki.fi/~aarppe/Publications/Alberta_PMLR_Arppe_100313.pdf

So, with a Poisson-equivalent model for polytomous outcomes one is
indeed able to mesh the random effects for the various outcomes into
one and the same model with the fixed effects.

Were I to learn more of the specifics of your mixed effects modeling
problem, we could work out a way of applying the above to technique to
it.

My best wishes from this side of the Atlantic,

	-Antti
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Antti Arppe - Ph.D (General Linguistics), M.Sc. (Engineering)
Post-Doctoral Research Fellow (General Linguistics, Univ. of Helsinki)
E-mail: antti.arppe@helsinki.fi
WWW: http://www.ling.helsinki.fi/~aarppe
Maanahtu ina reedûti ihza ummânuuti ihannaq - dulum ugulak úmun ingul
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