Thank you, John.

Yes, your answers do help. For me it's mainly about getting familiar with
the "R" way of doing things.

Thus your response also confirms what I suspected, that there is no explicit
user-interface (at least one that is widely used) in terms of
functions/packages that represents an unbalanced design in the same way that
aov would represent a balanced one. Analyzing balanced and unbalanced data
are obviously possible, but with balanced designs via aov what has to be
done is intuitive within the language but unintuitive for unbalanced
designs.

I did notice that this question gets asked several times and in slightly
different ways, and I think the lack of an interface that represents an
unbalanced design in the same way aov represents balanced designs is why the
question will probably keep getting asked again.

I had mentioned nlme and lme4 because I saw in some of the discussions that
using those were recommended for working with unbalanced designs. And
specifying random effects with zero variance, for example, would probably
serve my purposes.

Thank you for your help.

Sincerely,

Krishna

On Sun, Apr 3, 2011 at 7:28 AM, John Fox <jfox@mcmaster.ca> wrote:

> Dear Krishna,
>
> Although it's difficult to explain briefly, I'd argue that balanced and
> unbalanced ANOVA are not fundamentally different, in that the focus should
> be on the hypotheses that are tested, and these are naturally expressed as
> functions of cell means and marginal means. For example, in a two-way
> ANOVA,
> the null hypotheses of no interaction is equivalent to parallel profiles of
> cell means for one factor across levels of the other. What is different,
> though, is that in a balanced ANOVA all common approaches to constructing
> an
> ANOVA table coincide.
>
> Without getting into the explanation in detail (which you can find in a
> text
> like my Applied Regression Analysis and Generalized Linear Models),
> so-called type-I (or sequential) tests, such as those performed by the
> standard anova() function in R, test hypotheses that are rarely of
> substantive interest, and, even when they are, are of interest only by
> accident. So-called type-II tests, such as those performed by default by
> the
> Anova() function in the car package, test hypotheses that are almost always
> of interest. Type-III tests, which the Anova() function in car can perform
> optionally, require careful formulation of the model for the hypotheses
> tested to be sensible, and even then have less power than corresponding
> type-II tests in the circumstances in which a test would be of interest.
>
> Since you're addressing fixed-effects models, I'm not sure why you
> introduced nlme and lme4 into the discussion, but I note that Anova() in
> the
> car package has methods that can produce type-II and -III Wald tests for
> the
> fixed effects in mixed models fit by lme() and lmer().
>
> Your question has been asked several times before on the r-help list. For
> example, if you enter terms like "type-II" or "unbalanced ANOVA" in the
> RSeek search engine and look under the "Support Lists" tab, you'll see many
> hits -- e.g.,
> <Mhttps://stat.ethz.ch/pipermail/r-help/2006-August/111927.html>.
>
> I hope this helps,
>  John
>
> --------------------------------
> John Fox
> Senator William McMaster
>  Professor of Social Statistics
> Department of Sociology
> McMaster University
> Hamilton, Ontario, Canada
> http://socserv.mcmaster.ca/jfox
>
>
>
> > -----Original Message-----
> > From: r-help-bounces@r-project.org [mailto:r-help-bounces@r-project.org]
> > On Behalf Of Krishna Kirti Das
> > Sent: April-03-11 3:25 AM
> > To: r-help@r-project.org
> > Subject: [R] Unbalanced Anova: What is the best approach?
> >
> > I have a three-way unbalanced ANOVA that I need to calculate (fixed
> > effects plus interactions, no random effects). But word has it that aov()
> > is good only for balanced designs. I have seen a number of different
> > recommendations for working with unbalanced designs, but they seem to
> > differ widely (car, nlme, lme4, etc.). So I would like to know what is
> the
> > best or most usual way to go about working with unbalanced designs and
> > extracting a reliable ANOVA table from them in R?
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
>

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