This is the SAS code form the publication "Comparing the SAS GLM and MIXED
Procedures for Repeated Measures".  You can find the article immediately
with a google search for the remainder of the output as I have only
provided the end test for fixed effects.  This is the model I would like to
fit with R.  I truly appreciate any help in accomplishing this.

SAS
proc mixed data=formixed;
class gender age person;
model y = gender|age;
repeated / type=un sub=person;
run;

             Tests of Fixed Effects
Source          NDF DDF Type III F Pr > F
GENDER         1    25     9.29    0.0054
AGE                3    25    34.45   0.0001
GENDER*AGE 3    25     2.93    0.0532

On Thu, Jan 26, 2012 at 9:11 PM, Joshua Wiley <jwiley.psych@gmail.com>wrote:

> Hi Charles,
>
> Caveat emptor: I have not read John Maindonalds analysis of this data.
>  There may well be problems with this, but here are some of the things
> I would try with the data.
>
> By the way, if you want us to help you fit the same model as SAS, it
> would help to know what SAS is fitting.  If you could provide the
> formula for the model and covariance structure, that would help.  If
> you do not know, perhaps first try to replicate in SAS using something
> more explicit than the 'repeated' option.
>
> Cheers,
>
> Josh
>
> dat <- structure(list(distance = c(26, 25, 29, 31, 21.5, 22.5, 23, 26.5,
> 23, 22.5, 24, 27.5, 25.5, 27.5, 26.5, 27, 20, 23.5, 22.5, 26,
> 24.5, 25.5, 27, 28.5, 22, 22, 24.5, 26.5, 24, 21.5, 24.5, 25.5,
> 23, 20.5, 31, 26, 27.5, 28, 31, 31.5, 23, 23, 23.5, 25, 21.5,
> 23.5, 24, 28, 17, 24.5, 26, 29.5, 22.5, 25.5, 25.5, 26, 23, 24.5,
> 26, 30, 22, 21.5, 23.5, 25, 21, 20, 21.5, 23, 21, 21.5, 24, 25.5,
> 20.5, 24, 24.5, 26, 23.5, 24.5, 25, 26.5, 21.5, 23, 22.5, 23.5,
> 20, 21, 21, 22.5, 21.5, 22.5, 23, 25, 23, 23, 23.5, 24, 20, 21,
> 22, 21.5, 16.5, 19, 19, 19.5, 24.5, 25, 28, 28), age = c(8L,
> 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L,
> 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L,
> 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L,
> 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L,
> 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L,
> 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L,
> 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L,
> 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L, 10L, 12L, 14L, 8L,
> 10L, 12L, 14L), Subject = structure(c(12L, 12L, 12L, 12L, 13L,
> 13L, 13L, 13L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 16L, 16L,
> 16L, 16L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L, 19L, 19L, 19L,
> 19L, 20L, 20L, 20L, 20L, 21L, 21L, 21L, 21L, 22L, 22L, 22L, 22L,
> 23L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 25L, 25L, 25L, 25L, 26L,
> 26L, 26L, 26L, 27L, 27L, 27L, 27L, 1L, 1L, 1L, 1L, 2L, 2L, 2L,
> 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 6L, 6L, 6L,
> 6L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 10L, 10L,
> 10L, 10L, 11L, 11L, 11L, 11L), .Label = c("F01", "F02", "F03",
> "F04", "F05", "F06", "F07", "F08", "F09", "F10", "F11", "M01",
> "M02", "M03", "M04", "M05", "M06", "M07", "M08", "M09", "M10",
> "M11", "M12", "M13", "M14", "M15", "M16"), class = "factor"),
>    Sex = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
>    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
>    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
>    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
>    2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
>    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>    1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("Female", "Male"
>    ), class = "factor")), .Names = c("distance", "age", "Subject",
> "Sex"), class = "data.frame", row.names = c("1", "2", "3", "4",
> "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15",
> "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26",
> "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37",
> "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48",
> "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59",
> "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70",
> "71", "72", "73", "74", "75", "76", "77", "78", "79", "80", "81",
> "82", "83", "84", "85", "86", "87", "88", "89", "90", "91", "92",
> "93", "94", "95", "96", "97", "98", "99", "100", "101", "102",
> "103", "104", "105", "106", "107", "108"))
>
> require(ggplot2)
> require(mgcv)
>
> ## intercepts and slopes seem different between sexes
> ## but there is no evidence of a nonlinear relationship between
> ## age and distance
> ggplot(dat, aes(x = age, y = distance, colour = Sex)) +
>  geom_point() +
>  stat_smooth(method = "gam", formula = y ~ s(x))
>
> ## reorder data by initial distance value
> dat$Subject <- with(dat, reorder(Subject,
>  distance[ifelse(age == min(age), TRUE, NA)],
>  FUN = mean, na.rm = TRUE))
>
> ## slight evidence that lower intercepts may be
> ## associated with more positive slopes
> ggplot(dat, aes(x = age, y = distance, colour = Sex)) +
>  geom_point() +
>  stat_smooth(method = "gam", formula = y ~ s(x)) +
>  facet_wrap(~ Subject)
>
> ## lme4 package for mixed effects models
> require(lme4)
>
> mnull <- lmer(distance ~ 1 + (1 | Subject), data = dat)
> m1 <- update(mnull, . ~ . + age * Sex)
> m2 <- update(m2, . ~ . + (0 + age | Subject))
> m3 <- lmer(distance ~ age * Sex + (1 + age | Subject), data = dat)
>
> ## compare different models, m1 seems good
> anova(mnull, m1, m2, m3)
>
> plot(dat$distance, fitted(m1))
>
> ## examine residuals and random effects
> qqnorm(resid(m1))
> plot(dat$age, resid(m1))
> qqnorm(ranef(m1)$Subject[,1])
>
> ## view the summary
> summary(m1)
> ## Linear mixed model fit by REML
> ## Formula: distance ~ (1 | Subject) + age + Sex + age:Sex
> ##    Data: dat
> ##    AIC   BIC logLik deviance REMLdev
> ##  445.8 461.9 -216.9    428.7   433.8
> ## Random effects:
> ##  Groups   Name        Variance Std.Dev.
> ##  Subject  (Intercept) 3.2986   1.8162
> ##  Residual             1.9221   1.3864
> ## Number of obs: 108, groups: Subject, 27
>
> ## Fixed effects:
> ##             Estimate Std. Error t value
> ## (Intercept) 17.37273    1.18349  14.679
> ## age          0.47955    0.09347   5.130
> ## SexMale     -1.03210    1.53740  -0.671
> ## age:SexMale  0.30483    0.12142   2.511
>
> ## Correlation of Fixed Effects:
> ##             (Intr) age    SexMal
> ## age         -0.869
> ## SexMale     -0.770  0.669
> ## age:SexMale  0.669 -0.770 -0.869
>
>
> On Thu, Jan 26, 2012 at 5:37 PM, Charles Determan Jr <deter088@umn.edu>
> wrote:
> > I see, thank you Steven for your response.  Perhaps I should start a new
> > question on here for what people would recommend currently in R for
> > analyzing a repeated measures data set.  Would that be an appropriate
> > request without infringing upon any possible legal ramifications?
>  Perhaps
> > there is a slightly different method that is built on 'sound statistical
> > first principles'.  Or does anyone currently following this thread know
> an
> > appropriate repeated measures analysis of this 'dental' data that would
> be
> > similar to the SAS results?
> >
> > Charles
> >
> > On Thu, Jan 26, 2012 at 7:20 PM, Steven McKinney <smckinney@bccrc.ca>
> wrote:
> >
> >> Here's a typical agreement that users of SAS must agree to:
> >>
> >>
> >> Subject to the provisions contained herein, EMPLOYEE may use the SAS
> >> copyrighted computer software products which LICENSEE has provided in
> >> accordance with its agreement with SAS.
> >>
> >> EMPLOYEE acknowledges that these products are copyrighted and that SAS
> >> retains all title and ownership rights to the products.  EMPLOYEE agrees
> >> not to copy or permit others to copy the products, in whole or in part.
> >>
> >> EMPLOYEE agrees to use the products under this agreement only on a
> >> computer which is owned or leased by LICENSEE and controlled by
> LICENSEE.
> >>  EMPLOYEE further agrees that the products must remain under EMPLOYEE's
> >> control, and that resale or other transfer is explicitly prohibited.
> >>
> >> EMPLOYEE agrees to use the products only for EMPLOYEE's or LICENSEE's
> own
> >> data processing requirements, and not for commercial time-sharing,
> rental
> >> or service bureau use.
> >>
> >> EMPLOYEE agrees not to create, or attempt to create, or permit or help
> >> others to create, the source code from the products furnished under this
> >> agreement.  EMPLOYEE agrees that it will not reverse engineer or
> decompile
> >> the products.
> >>
> >>
> >> (source:
> >>
> http://www.mcmaster.ca/uts/software_downloads/docs/SAS/saslicendform.doc )
> >>
> >> Note that last paragraph.  You can find it in other SAS end user license
> >> agreements.
> >>
> >> So anyone who tries to "replicate PROC MIXED for repeated measures set
> as
> >> unstructured in R"
> >> is then subject to legal action by the largest wealthiest statistical
> >> software company ever in
> >> existence.  I personally am not up for that challenge, especially when
> the
> >> code has
> >> debateable merits.
> >>
> >> I'd rather write code from scratch using sound statistical first
> >> principles,
> >> which I can do thanks to the amazing amount of hard work by the R core
> >> group,
> >> none of whom have ever asked me to sign any agreement (though they do
> >> insist
> >> that I distribute source code and the GNU General Public License with
> any
> >> copies I modify and/or distribute).
> >>
> >>
> >> Steven McKinney
> >>
> >> Statistician
> >> Molecular Oncology and Breast Cancer Program
> >> British Columbia Cancer Research Centre
> >>
> >>
> >>
> >>
> >> From: Charles Determan Jr [mailto:deter088@umn.edu]
> >> Sent: January-26-12 4:50 PM
> >> To: Steven McKinney
> >> Cc: r-sig-mixed-models@r-project.org
> >> Subject: Re: [R-sig-ME] Trouble Replicating Unstructured Mixed Procedure
> >> in R
> >>
> >> So am I to assume that this implies that there isn't any known way to
> >> replicate PROC MIXED for repeated measures set as unstructured in R?
> >>
> >> Charles
> >> On Thu, Jan 26, 2012 at 6:36 PM, Steven McKinney <smckinney@bccrc.ca>
> >> wrote:
> >> Since SAS does not publish its source code,
> >> replicating SAS code is not always possible
> >> (nor always desirable).
> >>
> >> R code is completely open, so can be studied,
> >> debated and replicated or modified - very useful when
> >> people want to engage in scientific discussions
> >> of statistical issues.  Doing good science and
> >> data analysis is challenging when you are working with
> >> a black box of mysterious computer code.  That's
> >> why statisticians have worked so hard for years to
> >> set up open source computational tools such as R.
> >>
> >>
> >> Steven McKinney
> >> Statistician
> >> Molecular Oncology and Breast Cancer Program
> >> British Columbia Cancer Research Centre
> >>
> >> > -----Original Message-----
> >> > From: r-sig-mixed-models-bounces@r-project.org [mailto:
> >> r-sig-mixed-models-
> >> > bounces@r-project.org] On Behalf Of Charles Determan Jr
> >> > Sent: January-26-12 4:07 PM
> >> > To: John Maindonald
> >> > Cc: r-sig-mixed-models@r-project.org
> >> > Subject: Re: [R-sig-ME] Trouble Replicating Unstructured Mixed
> Procedure
> >> in
> >> > R
> >> >
> >> > The only thing I am looking for is the appropriate R code to replicate
> >> the
> >> > SAS analysis shown in the previously mentioned paper.  That is all I
> ask.
> >> > What should the code be in order to analyze this 'dental' data to
> >> replicate
> >> > the 'UN' or 'unstructured' analysis in the prior paper.
> >> >
> >> > Regards,
> >> >
> >> > Charles
> >> >
> >> > On Thu, Jan 26, 2012 at 4:37 PM, John Maindonald
> >> > <john.maindonald@anu.edu.au
> >> > > wrote:
> >> >
> >> > > It is not really a matter of computational accuracy.  One can get
> >> highly
> >> > > accurate values for an inappropriate statistic.
> >> > >
> >> > > Or if there is insistence on using the word, accuracy, what is the
> >> > > meaning?
> >> > >
> >> > > i) the wrong formula is used?  Then in what sense is it 'wrong'?
> >> > >
> >> > > ii) there is a numerical inaccuracy in the calculation?  This is
> almost
> >> > > never an issue in a relatively simple calculation such as this,
> given
> >> > > the care taken by the code writers in such matters.
> >> > >
> >> > > iii) where an approximation is used, as in using an F-distribution
> >> > > approximation, is the best choice of degrees of freedom  made to
> >> > > for use of this approximation?  I judge that the degrees of freedom
> >> > > for lme's F-statistic for the interaction are not well chosen.
>  Users
> >> > > really have to sort this out for themselves, rather than relying on
> >> > > what may be a fairly wild approximation that appears in lm's
> >> > > output.  Using 75df rather than 25df does not however make the
> >> > > difference that a choice between (e.g.) 5df and 25df would.
> >> > >
> >> > > A further and more basic issue is whether the statistic that is
> >> > > provided is appropriate to the intended generalisation.  I'd take
> >> > > this to be generalisation to another sample of youths from the
> >> > > same population.  In order to understand why R and SAS are
> >> > > giving different F-statistics for the interaction, one needs to
> >> > > understand just what variance-covariance structure is assumed
> >> > > in each case.  One might extract the two estimates of the
> >> > > var-cov structure and compare them. Look for terms in one that
> >> > > do not appear, or maybe that are zero, in the other.
> >> > >
> >> > > Finally, it is not just that Venables does not like type III SS.
> >> > > He is saying that they almost never correspond to a null
> >> > > hypothesis that makes any sense.  Those who disagree try to
> >> > > write down the model to which the null hypothesis corresponds
> >> > > in testing for the main effect of factor1 with a factor1:factor2
> >> > > interaction.
> >> > >
> >> > > John Maindonald             email: john.maindonald@anu.edu.au
> >> > > phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
> >> > > Centre for Mathematics & Its Applications, Room 1194,
> >> > > John Dedman Mathematical Sciences Building (Building 27)
> >> > > Australian National University, Canberra ACT 0200.
> >> > > http://www.maths.anu.edu.au/~johnm
> >> > >
> >> > > On 27/01/2012, at 2:41 AM, Thompson,Paul wrote:
> >> > >
> >> > > > OK, I've looked at that reference.
> >> > > >
> >> > > > There are 2 aspects of an estimate like a SS. The first is the
> >> > stability
> >> > > of the estimate, and the second is the interpretation of the
> estimate.
> >> > The
> >> > > issues with the interpretation of the different estimates go back to
> >> > 1970,
> >> > > and they are simply a matter of interpretation. The point of the
> >> Venables
> >> > > discussion is that he does not like Type III SS, not that they are
> >> wrong.
> >> > > He does not agree with the interpretation.
> >> > > >
> >> > > > The issue here is the accuracy of the Type III or Type I or Type
> II
> >> or
> >> > > whatever. Accuracy comes before interpretation. If the r module and
> SAS
> >> > do
> >> > > not arrive at the same estimates, that is an important thing.
> >> > > >
> >> > > > Once we agree upon computation, we can argue about interpretation.
> >> > > Charles Determan is inquiring as to computational accuracy. The use
> and
> >> > > interpretation of the various Type I, II, III, IV, LVX SS are
> >> secondary.
> >> > > >
> >> > > > -----Original Message-----
> >> > > > From: r-sig-mixed-models-bounces@r-project.org [mailto:
> >> > > r-sig-mixed-models-bounces@r-project.org] On Behalf Of Luca Borger
> >> > > > Sent: Thursday, January 26, 2012 9:03 AM
> >> > > > To: r-sig-mixed-models@r-project.org
> >> > > > Subject: Re: [R-sig-ME] Trouble Replicating Unstructured Mixed
> >> > Procedure
> >> > > in R
> >> > > >
> >> > > > I think:
> >> > > >
> >> > > > http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf
> >> > > >
> >> > > > HTH
> >> > > > Luca
> >> > > >
> >> > > >
> >> > > >
> >> > > > Le 26/01/2012 15:52, Thompson,Paul a écrit :
> >> > > >> I am unfamiliar with this critique of Type III SS. Can you point
> me
> >> to
> >> > > a reference discussing the difficulties with Type III SS?
> >> > > >>
> >> > > >> -----Original Message-----
> >> > > >> From: r-sig-mixed-models-bounces@r-project.org [mailto:
> >> > > r-sig-mixed-models-bounces@r-project.org] On Behalf Of John
> Maindonald
> >> > > >> Sent: Wednesday, January 25, 2012 11:19 PM
> >> > > >> To: David Duffy
> >> > > >> Cc: r-sig-mixed-models@r-project.org
> >> > > >> Subject: Re: [R-sig-ME] Trouble Replicating Unstructured Mixed
> >> > > Procedure in R
> >> > > >>
> >> > > >> It is well to note that type III sums of squares are problematic.
> >> > > >> For testing the effects of a main effect, the null model is
> >> > constraining
> >> > > >> the main effect in a manner that depends on the parameterisation.
> >> > > >>
> >> > > >> There are situations where it makes sense to fit interactions
> >> without
> >> > > >> main effects, and it is clear what constraint on the main effect
> is
> >> > the
> >> > > >> relevant null (with an interaction between a factor and a
> variable,
> >> > > >> does one want all lines to go though the same point, or through
> >> > > >> perhaps the origin?), but that situation is unusual.  For lines
> that
> >> > > >> are separate or all through the one point, one does not need
> >> > > >> type III sums of squares.
> >> > > >>
> >> > > >> Analyses often or frequently have enough genuine complications
> >> > > >> worrying (unless it is blindingly obvious that one ought to worry
> >> > > >> about it) without the rarely relevant complication of attending
> to a
> >> > > >> type III sum of squares.
> >> > > >>
> >> > > >> I'd guess that SAS and lme are, effectively, making different
> >> > > >> assumptions about the intended generalisation.  They are
> >> > > >> clearly using different denominator degrees of freedom for F.
> >> > > >> As one is looking for consistency across the 27 different youths,
> >> > > >> SAS's denominator degrees of freedom for the interaction seem
> >> > > >> more or less right, pretty much equivalent to calculating slopes
> >> > > >> for females and slopes for males and using a t-test to compare
> >> > > >> them.  (Sure, in the analyses presented, age has been treated
> >> > > >> as a categorical variable, but the comment still applies.)
> >> > > >>
> >> > > >> John Maindonald             email: john.maindonald@anu.edu.au
> >> > > >> phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
> >> > > >> Centre for Mathematics&  Its Applications, Room 1194,
> >> > > >> John Dedman Mathematical Sciences Building (Building 27)
> >> > > >> Australian National University, Canberra ACT 0200.
> >> > > >> http://www.maths.anu.edu.au/~johnm
> >> > > >>
> >> > > >> On 26/01/2012, at 1:54 PM, David Duffy wrote:
> >> > > >>
> >> > > >>> On Tue, 24 Jan 2012, Charles Determan Jr wrote:
> >> > > >>>
> >> > > >>>> Greetings,
> >> > > >>>>
> >> > > >>>> I have been working on R for some time now and I have begun the
> >> > > endeavor of
> >> > > >>>> trying to replicate some SAS code in R.  I have scoured the
> forums
> >> > but
> >> > > >>>>
> >> > > >>> This is also the Orthodont dataset, distributed with nlme.
> >> > > >>>
> >> > > >>> As David Atkins pointed out, R defaults to Type I SS. so you
> would
> >> > > need to use, for example, the Anova() command from the car package.
> >>  The
> >> > > other thing is that the SAS F statistics are only approximate,
> >> depending
> >> > on
> >> > > which covariance structure is chosen (perhaps John Maindonald or
> >> someone
> >> > > clever could comment), so SAS offers different possibilities for
> ddf eg
> >> > > >>>
> >> > > >>> http://www2.sas.com/proceedings/sugi26/p262-26.pdf
> >> > > >>>
> >> > > >>> while lme and lmer offer one or none.
> >> > > >>>
> >> > > >>> --
> >> > > >>> | David Duffy (MBBS PhD)
>   ,-
> >> > _|\
> >> > > >>> | email: davidD@qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101
>  /
> >> > > *
> >> > > >>> | Epidemiology Unit, Queensland Institute of Medical Research
> >> \_,-
> >> > ._/
> >> > > >>> | 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG
> >> 4D0B994A
> >> > v
> >> > > >>>
> >> > > >>> _______________________________________________
> >> > > >>> R-sig-mixed-models@r-project.org mailing list
> >> > > >>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >> > > >> _______________________________________________
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> >> > > >>
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> --
> Joshua Wiley
> Ph.D. Student, Health Psychology
> Programmer Analyst II, Statistical Consulting Group
> University of California, Los Angeles
> https://joshuawiley.com/
>

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