[R] lsmeans

[hadley wickham]

On Sun, Jun 8, 2008 at 12:58 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
> 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 on
>>  the subject: First, I dislike the term "least-squares means," which seems 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 to
>>  clarify effects in complex models. For example, a two-way interaction is
>>  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 fitted
>>  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

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