[R] MCA in R

John Fox jfox at mcmaster.ca
Fri Jun 13 13:08:42 CEST 2008

Dear Kimmo,

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> Behalf Of K. Elo
> Sent: June-13-08 1:43 AM
> To: r-help at r-project.org
> Subject: Re: [R] MCA in R
> Dear John,
> thanks for Your quick reply.
> > John Fox wrote:
> > Dear Kimmo,
> >
> > MCA is a rather old name (introduced, I think, in the 1960s by
> > Songuist and Morgan in the OSIRIS package) for a linear model
> > consisting entirely of factors and with only additive effects --
> > i.e., an ANOVA model will no interactions.
> It is true, that MCA is an old name, but the technique itself is still
> robust, I think. The problem I am facing is that I have a research
> project where I try to find out which factors affect measured knowledge
> of a specific issue. As predictors I have formal education, interest,
> gender and consumption of different medias (TV, newspapers etc.). Now,
> these are correlated predictors and running e.g. a simple anova
> (anova(lm(...)) as You suggested) won't - if I have understood correctly
> - consider the problem of correlated predictors. MCA would do this.

That's because anova() calculates sequential ("type-I") sums of squares; if
you use the Anova() function in the car package, for example, you'll get
so-called type-II sums of squares -- for each factor after the others. You
could also more tediously do these tests directly using the anova()
function, by contrasting alternative models: the full model and the model
deleting each factor in turn.

> A colleague of mine has run anova and MCA in SPSS and the results differ
> significantly.

Yes, see above.

>  Because I am more familiar with R, I just hoped that this
> marvelous statistical package could handle MCA, too :)
> > Typically, the results of
> > an MCA are reported using "adjusted means." You could compute these
> > manually, or via the effects package.
> Well, I am interested in the eta and beta values, too. 

Aren't the eta values just the square-roots of the R^2's from the individual
one-way ANOVAs? I don't remember how the betas are defined, but do recall
that they are a peculiar attempt to define standardized partial regression
coefficients for factors that combine all of the levels.

> I have tried to
> use the effects package but my attempts with all.effects resulted in
> errors. I have to figure out what's going wrong here :)

If you tell me what you did, ideally including an example that I can
reproduce, I can probably tell you what's wrong.


> Kind regards,
> Kimmo Elo
> --
> University of Turku, Finland
> Dep. of political science
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