[R] how to get "lsmeans"?
Muenchen, Robert A (Bob)
muenchen at utk.edu
Thu Mar 22 14:35:57 CET 2007
Hi All,
Perhaps I'm stating the obvious, but to increase the use of R in places
where SAS & SPSS dominate, it's important to make getting the same
answers as easy as possible. That includes things like lsmeans and type
III sums of squares. I've read lots of discussions here on sums of
squares & I'm not advocating type III use, just looking at it from a
marketing perspective. Too many people look for excuses to not change.
The fewer excuses, the better.
Of course this is easy for me to say, as I'm not the one who does the
work! Much thanks to those who do.
Cheers,
Bob
=========================================================
Bob Muenchen (pronounced Min'-chen), Manager
Statistical Consulting Center
U of TN Office of Information Technology
200 Stokely Management Center, Knoxville, TN 37996-0520
Voice: (865) 974-5230
FAX: (865) 974-4810
Email: muenchen at utk.edu
Web: http://oit.utk.edu/scc,
News: http://listserv.utk.edu/archives/statnews.html
=========================================================
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
> bounces at stat.math.ethz.ch] On Behalf Of John Fox
> Sent: Wednesday, March 21, 2007 8:59 PM
> To: 'Prof Brian Ripley'
> Cc: 'r-help'; 'Chuck Cleland'
> Subject: Re: [R] how to get "lsmeans"?
>
> Dear Brian et al.,
>
> My apologies for chiming in late: It's been a busy day.
>
> First some general comments on "least-squares means" and "effect
> displays."
> The general idea behind the two is similar -- to examine fitted values
> corresponding to a term in a model while holding other terms to
typical
> values -- but the implementation is not identical. There are also
other
> similar ideas floating around as well. My formulation is more general
> in the
> sense that it applies to a wider variety of models, both linear and
> otherwise.
>
> "Least-squares means" (a horrible term, by the way: in a 1980 paper in
> the
> American Statistician, Searle, Speed, and Milliken suggested the more
> descriptive term "population marginal means") apply to factors and
> combinations of factors; covariates are set to mean values and the
> levels of
> other factors are averaged over, in effect applying equal weight to
> each
> level. (This is from memory, so it's possible that I'm not getting it
> quite
> right, but I believe that I am.) In my effect displays, each level of
a
> factor is weighted by its proportion in the data. In models in which
> least-squares means can be computed, they should differ from the
> corresponding effect display by a constant (if there are different
> numbers
> of observations in the different levels of the factors that are held
> constant).
>
> The obstacle to computing either least-squares means or effect
displays
> in R
> via predict() is that predict() wants factors in the "new data" to be
> set to
> particular levels. The effect() function in the effects package
> bypasses
> predict() and works directly with the model matrix, averaging over the
> columns that pertain to a factor (and reconstructing interactions as
> necessary). As mentioned, this has the effect of setting the factor to
> its
> proportional distribution in the data. This approach also has the
> advantage
> of being invariant with respect to the choice of contrasts for a
> factor.
>
> The only convenient way that I can think of to implement least-squares
> means
> in R would be to use deviation-coded regressors for a factor (that is,
> contr.sum) and then to set the columns of the model matrix for the
> factor(s)
> to be averaged over to 0. It may just be that I'm having a failure of
> imagination and that there's a better way to proceed. I've not
> implemented
> this solution because it is dependent upon the choice of contrasts and
> because I don't see a general advantage to it, but since the issue has
> come
> up several times now, maybe I should take a crack at it. Remember that
> I
> want this to work more generally, not just for levels of factors, and
> not
> just for linear models.
>
> Brian is quite right in mentioning that he suggested some time ago
that
> I
> use critical values of t rather than of the standard normal
> distribution for
> producing confidence intervals, and I agree that it makes sense to do
> so in
> models in which the dispersion is estimated. My only excuse for not
yet
> doing this is that I want to undertake a more general revision of the
> effects package, and haven't had time to do it. There are several
> changes
> that I'd like to make to the package. For example, I have results for
> multinomial and proportional odds logit models (described in a paper
by
> me
> and Bob Andersen in the 2006 issue of Sociological Methodology) that I
> want
> to incorporate, and I'd like to improve the appearance of the default
> graphs. But Brian's suggestion is very straightforward, and I guess
> that I
> shouldn't wait to implement it; I'll do so very soon.
>
> Regards,
> John
>
> --------------------------------
> John Fox
> Department of Sociology
> McMaster University
> Hamilton, Ontario
> Canada L8S 4M4
> 905-525-9140x23604
> http://socserv.mcmaster.ca/jfox
> --------------------------------
>
> > -----Original Message-----
> > From: r-help-bounces at stat.math.ethz.ch
> > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Prof
> > Brian Ripley
> > Sent: Wednesday, March 21, 2007 12:03 PM
> > To: Chuck Cleland
> > Cc: r-help
> > Subject: Re: [R] how to get "lsmeans"?
> >
> > On Wed, 21 Mar 2007, Chuck Cleland wrote:
> >
> > > Liaw, Andy wrote:
> > >> I verified the result from the following with output from JMP 6
on
> > >> the same data (don't have SAS: don't need it):
> > >>
> > >> set.seed(631)
> > >> n <- 100
> > >> dat <- data.frame(y=rnorm(n), A=factor(sample(1:2, n,
> > replace=TRUE)),
> > >> B=factor(sample(1:2, n, replace=TRUE)),
> > >> C=factor(sample(1:2, n, replace=TRUE)),
> > >> d=rnorm(n))
> > >> fm <- lm(y ~ A + B + C + d, dat)
> > >> ## Form a data frame of points to predict: all
> > combinations of the ##
> > >> three factors and the mean of the covariate.
> > >> p <- data.frame(expand.grid(A=1:2, B=1:2, C=1:2)) p[] <-
lapply(p,
> > >> factor) p <- cbind(p, d=mean(dat$d)) p <-
> > cbind(yhat=predict(fm, p),
> > >> p) ## lsmeans for the three factors:
> > >> with(p, tapply(yhat, A, mean))
> > >> with(p, tapply(yhat, B, mean))
> > >> with(p, tapply(yhat, C, mean))
> > >
> > > Using Andy's example data, these are the LSMEANS and
> > intervals I get
> > > from SAS:
> > >
> > > A y LSMEAN 95% Confidence Limits
> > > 1 -0.071847 -0.387507 0.243813
> > > 2 -0.029621 -0.342358 0.283117
> > >
> > > B y LSMEAN 95% Confidence Limits
> > > 1 -0.104859 -0.397935 0.188216
> > > 2 0.003391 -0.333476 0.340258
> > >
> > > C y LSMEAN 95% Confidence Limits
> > > 1 -0.084679 -0.392343 0.222986
> > > 2 -0.016789 -0.336374 0.302795
> > >
> > > One way of reproducing the LSMEANS and intervals from SAS using
> > > predict() seems to be the following:
> > >
> > >> dat.lm <- lm(y ~ A + as.numeric(B) + as.numeric(C) + d,
> > data = dat)
> > >> newdat <- expand.grid(A=factor(c(1,2)),B=1.5,C=1.5,d=mean(dat$d))
> > >> cbind(newdat, predict(dat.lm, newdat, interval="confidence"))
> > > A B C d fit lwr upr
> > > 1 1 1.5 1.5 0.09838595 -0.07184709 -0.3875070 0.2438128
> > > 2 2 1.5 1.5 0.09838595 -0.02962086 -0.3423582 0.2831165
> > >
> > > However, another possibility seems to be:
> > >
> > >> dat.lm <- lm(y ~ A + as.numeric(B) + as.numeric(C) + d,
> > data = dat)
> > >> newdat <-
> > >
> >
> expand.grid(A=factor(c(1,2)),B=mean(as.numeric(dat$B)),C=mean(as.numer
> > > ic(dat$C)),d=mean(dat$d))
> > >> cbind(newdat, predict(dat.lm, newdat, interval="confidence"))
> > > A B C d fit lwr upr
> > > 1 1 1.43 1.48 0.09838595 -0.08078243 -0.3964661 0.2349012
> > > 2 2 1.43 1.48 0.09838595 -0.03855619 -0.3479589 0.2708465
> > >
> > > The predictions directly above match what effect() in the effects
> > > package by John Fox returns:
> > >
> > > library(effects)
> > >
> > >> effect("A", fm, xlevels=list(d = mean(dat$D)))
> > >
> > > A effect
> > > A
> > > 1 2
> > > -0.08078243 -0.03855619
> > >
> > > But for some reason the predict() and effect() intervals
> > are a little
> > > different:
> > >
> > >> effect("A", fm, xlevels=list(d = mean(dat$D)))$lower
> > > [,1]
> > > 101 -0.3924451
> > > 102 -0.3440179
> > >
> > >> effect("A", fm, xlevels=list(d = mean(dat$D)))$upper
> > > [,1]
> > > 101 0.2308802
> > > 102 0.2669055
> > >
> > > I would be interested in any comments on these different
> > approaches
> > > and on the difference in intervals returned by predict()
> > and effect().
> >
> > AFAIR, the effects packages uses normal-based confidence
> > intervals and predict.lm uses t-based ones, and I have
> > suggested to John Fox that t-based intervals would be
> > preferable, at least as an option.
> >
> >
> > --
> > Brian D. Ripley, ripley at stats.ox.ac.uk
> > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
> > University of Oxford, Tel: +44 1865 272861 (self)
> > 1 South Parks Road, +44 1865 272866 (PA)
> > Oxford OX1 3TG, UK Fax: +44 1865 272595
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch 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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> PLEASE do read the posting guide http://www.R-project.org/posting-
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> and provide commented, minimal, self-contained, reproducible code.
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