mixed-effect linear regression?
lars
I would like to predict vowel realizations. Ideally, combinations of
F1 and F2, but for starters I will be happy with frontness/backness,
i.e. F2.
The project is about the language of Jamaicans in North America, and
realizations of (in the case of one variable) the STRUT vowel. It is
central in North American English, but mid-back in Jamaican. There are
tons of intermediate realizations in my data.
Independent variables will include addressee competence (three
levels), 'referee' (three levels), rhetorical activity (between five
and ten levels), interview vs. observed speech (binary), audio vs.
video recording (two levels), and others.
The number of tokens for this variable will probably range between 200
and 800.
If I focus only on F2, is 'mixed-effect linear regression' the right
thing to look into? Does anyone have pointers on what to do and how to
do it?
And in theory, are there models that try to predict an outcome in two
dimensions, i.e. combinations of F1 and F2?
Thank you!!!
Lars
Austin Frank
> I would like to predict vowel realizations. Ideally, combinations of
> F1 and F2, but for starters I will be happy with frontness/backness,
> i.e. F2.
>
> Independent variables will include addressee competence (three
> levels), 'referee' (three levels), rhetorical activity (between five
> and ten levels), interview vs. observed speech (binary), audio vs.
> video recording (two levels), and others.
>
> The number of tokens for this variable will probably range between 200
> and 800.
>
> If I focus only on F2, is 'mixed-effect linear regression' the right
> thing to look into? Does anyone have pointers on what to do and how to
> do it?
It certainly could be. This depends in large part on whether you think
it is reasonable to model your dependent variable as a combination of
hierarchical levels of effects. In my view, the independent variables
that you described above all sound like fixed effects (limited number of
levels, generally under the experimenter's control). For a study like
this, a common example of a random effect would be an effect of
speaker. If you only model an intercept effect for each speaker, you're
allowing each speaker to have a different baseline value for F2. You
could also model slope effects for each speaker allowing, for example,
each speaker to have a different sensitivity to the rhetorical activity
they're participating in. I believe I'm correct in saying that the
latter type of effects (random slope effects) only make sense if you
observe a speaker at multiple levels of the same factor.
If you want to try out a mixed effects model, a reasonable call (with
names for predictors based on your description above) would be
--8<---------------cut here---------------start------------->8---
lmer(f2 ~ competence + referee + activity + is.interview + is.audio
+ (1 | speaker),
data = jamaican_vowels)
--8<---------------cut here---------------end--------------->8---
A few notes:
- you may end up transforming the dependent variable (using
the log of F2, for example).
- you should decide whether you want to use the default contrasts
(contr.treatment) or some other type of contrasts (contr.sum). This
is especially important if you plan to include interactions.
- if you have five to ten levels of activity, you should consider
whether you want to model this as a continuous (or at least ordered)
factor. It's possible that you could get more easily interpretable
results from this scheme. If there's no obvious interpretation of
this predictor on an ordered scale, then don't worry about this.
- since I assume "referee" refers to different listeners/experimenters,
it might make conceptual sense to treat referee as a random effect as
well. The textbook by Gelman & Hill (2007) suggests that if an effect
is best understood conceptually as a random effect, it should be
included that way in the model. Some posts on the mailing list for
lmer have taken a more pragmatic approach, pointing out that even if
something is conceptually a random effect, estimating the variance
components from a small number of samples can be difficult (only two
or three interviewers). By this light, referee may be best as a fixed
effect. You can try to fit both models and see what makes sense to
you.
> And in theory, are there models that try to predict an outcome in two
> dimensions, i.e. combinations of F1 and F2?
I believe that the package multinomRob has been suggested to me for this
purpose, though I have never used it. It does not allow random effects,
as far as I know. Another possibility would be to do dimensionality
reduction on the two measurements, so that you were predicting the
dimension of greatest variance between F1 and F2. Look at the
documentation of prcomp() for information on one good way of doing
dimensionality reduction. I also believe that there examples of using
PCA on factors in a regression model in Baayen's recent textbook. I
don't know that he ever shows PCA on the dependent variable, but the R
code works the same way for either case.
HTH,
/au
--
Austin Frank
http://aufrank.net
GPG Public Key (D7398C2F): http://aufrank.net/personal.asc