Re: [R] Unbalanced Anova: What is the best approach?

From: John Fox <jfox_at_mcmaster.ca>
Date: Sun, 03 Apr 2011 09:28:29 -0400

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_at_r-project.org [mailto:r-help-bounces_at_r-project.org]
> On Behalf Of Krishna Kirti Das
> Sent: April-03-11 3:25 AM
> To: r-help_at_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]]
>
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