[R] lsmeans

John Fox jfox at mcmaster.ca
Sun Jun 8 21:26:12 CEST 2008

Dear Hadley,

Unfortunately, the term "marginal" gets used in two quite different ways,
and Searle's "population marginal means" would, I believe, be more clearly
called "population conditional means" or "population partial means." This is
more or less alternative terminology for "least-squares means" (to which
Searle rightly objects).


John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox

> -----Original Message-----
> From: hadley wickham [mailto:h.wickham at gmail.com]
> Sent: June-08-08 2:52 PM
> To: Douglas Bates
> Cc: John Fox; Dieter Menne; r-help at stat.math.ethz.ch
> Subject: Re: [R] lsmeans
> On Sun, Jun 8, 2008 at 12:58 PM, Douglas Bates <bates at stat.wisc.edu>
> > On 6/7/08, John Fox <jfox at mcmaster.ca> wrote:
> >> Dear Dieter,
> >>
> >>  I don't know whether I qualify as a "master," but here's my brief take
> >>  the subject: First, I dislike the term "least-squares means," which
> to
> >>  me like nonsense. Second, what I prefer to call "effect displays" are
> just
> >>  judiciously chosen regions of the response surface of a model, meant
> >>  clarify effects in complex models. For example, a two-way interaction
> >>  displayed by absorbing the constant and main-effect terms in the
> interaction
> >>  (more generally, absorbing terms marginal to a particular term) and
> setting
> >>  other terms to typical values. A table or graph of the resulting
> >>  values is, I would argue, easier to grasp than the coefficients, the
> >>  interpretation of which can entail complicated mental arithmetic.
> >
> > I like that explanation, John.
> >
> > As I'm sure you are aware, the key phrase in what you wrote is
> > "setting other terms to typical values".  That is, these are
> > conditional cell means, yet they are almost universally misunderstood
> > - even by statisticians who should know better - to be marginal cell
> > means.  A more subtle aspect of that phrase is the interpretation of
> > "typical".  The user is not required to specify these typical values -
> > they are calculated from the observed data.
> >
> How does Searle's "population marginal means" fit in to this?  The
> paper describes a PMM as "expected value of an observed marginal mean
> as if there were one observation in every cell." - which was what I
> thought happened in the effects display.  Is this a subtly on the
> definition of typical, or is that PMM's are only described for pure
> ANOVA's (i.e. no continuous variables in model)?
> Hadley
> --
> http://had.co.nz/

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