[R-sig-ME] Trouble Replicating Unstructured Mixed Procedure in R
Joshua Wiley
jwiley.psych at gmail.com
Fri Jan 27 04:11:22 CET 2012
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 at 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 at 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 at umn.edu]
>> Sent: January-26-12 4:50 PM
>> To: Steven McKinney
>> Cc: r-sig-mixed-models at 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 at 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 at r-project.org [mailto:
>> r-sig-mixed-models-
>> > bounces at r-project.org] On Behalf Of Charles Determan Jr
>> > Sent: January-26-12 4:07 PM
>> > To: John Maindonald
>> > Cc: r-sig-mixed-models at 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 at 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 at 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 at r-project.org [mailto:
>> > > r-sig-mixed-models-bounces at r-project.org] On Behalf Of Luca Borger
>> > > > Sent: Thursday, January 26, 2012 9:03 AM
>> > > > To: r-sig-mixed-models at 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 at r-project.org [mailto:
>> > > r-sig-mixed-models-bounces at r-project.org] On Behalf Of John Maindonald
>> > > >> Sent: Wednesday, January 25, 2012 11:19 PM
>> > > >> To: David Duffy
>> > > >> Cc: r-sig-mixed-models at 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 at 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 at 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 at r-project.org mailing list
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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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