[R-sig-ME] What is the lmer/nlme equivalent of the REPEATED subcommand in SPSS's MIXED procedure?
Maarten Jung
Maarten.Jung at mailbox.tu-dresden.de
Thu Mar 22 16:11:21 CET 2018
Dear Rune,
thanks for making clear what /REPEATED stands for!
Independently, does it make sense to fit a model via
gls(value ~ factor1, data, correlation = corSymm(form = ~ 1|person), weights
= varIdent(form = ~1|factor1))
when there is only one observation per subject-factor1-combination?
Regards,
Maarten
On Thu, Mar 22, 2018 at 11:38 AM, Rune Haubo <rune.haubo at gmail.com> wrote:
> On 22 March 2018 at 10:05, Maarten Jung
> <Maarten.Jung at mailbox.tu-dresden.de> wrote:
> > I think the problem is that there is only one observation per
> > subject-occasion-combination in this example.
> > In this case the random slopes are confounded with the residual variation
> > (see [1]).
>
> I agree.
>
> >
> > One *can* fit this model using lmer(test ~ 1 + occ2 + occ3 + (1 + occ2 +
> > occ3|person), data = mydata, control = lmerControl(check.nobs.vs.nRE =
> > "ignore")) or
> > lme(test ~ 1 + occ2 + occ3, mydata, random = ~ occ2 + occ3|person).
> >
> > However, I don't know if the gls() fit ist more trustworthy than the
> > lmer/lme fit here.
> > I would be grateful if somebody more experienced in mixed models could
> > comment on this.
>
> If you are trying to replicate a model that is specified with a
> 'repeated' statement (and 'repeated' in SPSS means the same as in SAS)
> then we are talking about specifying a structure in the residual
> variance-covariance matrix (cf.
> https://support.sas.com/documentation/cdl/en/statug/
> 63033/HTML/default/viewer.htm#statug_mixed_sect019.htm).
> If we write the model as y = X beta + Z b + e with b ~ N(0, G) and e ~
> N(0, R), then 'repeated' is specifying the structure in R. This is
> exactly what nlme::gls and nlme::lme do via the weights and
> correlation arguments; you need lme if you have 'true' random effects
> on top of the structure in R.
>
> If we write the marginal distribution of y as y ~ N(X beta, V), with V
> = ZGZ' + R then the structure in V can be obtained by appropriate
> specification of either Z and G or R, or both. This means that in some
> cases there is more than one 'natural' way to specify the same
> marginal model (compound symmetry is the classical example*). Now,
> lmer has the structure of R fixed at sigma^2 I, i.e. a multiple of the
> identity matrix, but with appropriate random-effect specification you
> can sometimes obtain the same (marginal) likelihood as if the
> structure was specified in the R matrix. My advice, is however, that
> if you want to fit a model with a particular structure in R, then
> don't use lmer; you really have to know all details of what is going
> to be sure that it works as intended.
>
> Cheers,
> Rune
>
> *Actually the compound symmetry and random intercept models are _not_
> the same (though often claimed to be) because the parameter spaces
> differ. This means that for some data sets the model fits are the same
> (i.e. same likelihood) and for other data sets the model fits are
> different.
>
> >
> > Best regards,
> > Maarten
> >
> > [1]
> > https://stackoverflow.com/questions/26465215/random-
> slope-for-time-in-subject-not-working-in-lme4?utm_medium=
> organic&utm_source=google_rich_qa&utm_campaign=google_rich_qa
> >
> > On Wed, Mar 21, 2018 at 9:27 PM, Ben Pelzer <b.pelzer at maw.ru.nl> wrote:
> >
> >> Hi Maarten,
> >>
> >> Here is an example which shows the unstructured model with gls and the
> >> not converging model with lmer. In this example, we have three occasions
> >> on which the dependent variable "test" was observed, for each of 20
> >> persons. In total then we have 60 observations, with the "occasion"
> >> variable taking values 1, 2, 3. The data also contain the person id
> >> variable "person" and dummy variables "occ1", "occ2", "occ3" as (0 or 1)
> >> indicators of the occasion. In the syntax below, a factor variable
> >> "factor1" is created also, to be in line with your question.
> >>
> >> I used two different specifications for the unstructured model with gls,
> >> depending on whether dummies or factor1 was used. For lmer, I used these
> >> three different specifications, none of which converges.
> >>
> >> The lmer syntax was added only to show the problem which lmer has with
> >> estimating an unstructured correlation pattern.
> >>
> >>
> >> #-----------------------------------------------------------
> >> ------------------------------------------------------------
> >> -------------------------------------
> >> mydata <-
> >> read.table(url("https://surfdrive.surf.nl/files/index.
> >> php/s/XfE3mtbFCTUejIz/download"),
> >> header=TRUE)
> >>
> >>
> >> #------------------- unstructured correlation matrix
> >> -----------------------
> >>
> >>
> >> # Before applying a model, let's first examine the variances and
> >> correlations
> >> # for the three occasions. We have a strong violation of the assumptions
> >> # of homoscedasticity and compound symmetry.
> >> test1 <- mydata[mydata$occasion==1,"test"]
> >> test2 <- mydata[mydata$occasion==2,"test"]
> >> test3 <- mydata[mydata$occasion==3,"test"]
> >> cor(cbind(test1, test2, test3))
> >> var(cbind(test1, test2, test3))
> >>
> >> # Unstructured model using gls from package nlme and dummies for
> occasion.
> >> # This model exactly reproduces the observed correlations between
> >> occasions.
> >> unstruc.gls1 <- gls(test ~ 1+ occ2 + occ3,
> >> method="REML", data=mydata,
> >> correlation=corSymm(form = ~ 1 |person),
> >> weights = varIdent(form = ~1|occasion))
> >> summary(unstruc.gls1)
> >>
> >>
> >> # Unstructured model using factor1 for occasion instead of dummies.
> >> # The results are exactly the same as those above, as should be.
> >> mydata$factor1 <- as.factor(mydata$occasion)
> >> unstruc.gls2 <- gls(test ~ factor1,
> >> method="REML", data=mydata,
> >> correlation=corSymm(form = ~ 1|person),
> >> weights = varIdent(form = ~1|factor1))
> >> summary(unstruc.gls2)
> >>
> >>
> >> # Unstructured model using lmer and dummies for occasion: does not
> >> converge.
> >> unstruc.lmer <- lmer(test ~ 1+ occ2 + occ3 + (1+occ2+occ3|person),
> >> data=mydata, REML=TRUE)
> >> summary(unstruc.lmer)
> >>
> >>
> >> # Unstructured model using lmer and factor1 for occasion: does not
> >> converge.
> >> unstruc.lmer <- lmer(test ~ 1+ factor1 + (1+factor1|person),
> >> data=mydata, REML=TRUE)
> >> summary(unstruc.lmer)
> >>
> >>
> >> # Unstructured model using lmer and factor1 for occasion, no intercept
> >> specified: does not converge.
> >> unstruc.lmer <- lmer(test ~ factor1 + (factor1|person),
> >> data=mydata, REML=TRUE)
> >> summary(unstruc.lmer)
> >>
> >>
> >>
> >> On 21/03/2018 13:07, Maarten Jung wrote:
> >> > Dear Ben,
> >> >
> >> > I am a bit puzzled.
> >> >
> >> > Do you mean that
> >> >
> >> > m1 <- gls(value ~ factor1, data, correlation = corSymm(form = ~
> >> > 1|participant), weights = varIdent(form = ~ 1|factor))
> >> >
> >> > would be equivalent to
> >> >
> >> > m2 <- lmer(value ~ factor1 + (factor1|participant), data)
> >> >
> >> > and one should use gls() because it allows for the same covariance
> >> > structures as /REPEATED does?
> >> >
> >>
> >>
> >> the two specifications are not equivalent in the sense that lmer also
> >> tries to estimate residual variance. However, with the given lmer model
> >> specification, the random factor1 effects capture all variance there is
> >> and no residual variance remains.
> >>
> >>
> >> > And, if so, why should m2 cause an identification problem and m1
> doesn't?
> >> >
> >> > Regards,
> >> > Maarten
> >> >
> >> Regards, Ben.
> >>
> >>
> >>
> >> >
> >> > On Wed, Mar 21, 2018 at 12:03 PM, Ben Pelzer <b.pelzer at maw.ru.nl
> >> > <mailto:b.pelzer at maw.ru.nl>> wrote:
> >> >
> >> > Dear all,
> >> >
> >> > As far as I know, the specification for lmer using
> >> >
> >> > value ~ factor1 + (factor1 | participant)
> >> >
> >> > causes an identification problem, because the residual variance is
> >> not
> >> > excluded from the estimations. It would indeed work (e.g. in MlWin
> >> > this
> >> > can be done) if we could constrain that residual variance to zero.
> >> > There
> >> > have been some mails in this list about whether or not
> constraining
> >> > residual variance to zero is possible in lmer, but I believe this
> >> > is not
> >> > possible. Would be nice if we could do this in lmer!
> >> >
> >> > Best regards, Ben.
> >> >
> >> >
> >> > On 20-3-2018 18:34, Douglas Bates wrote:
> >> > > Kind of looks like SPSS went for bug-for-bug compatibility with
> >> > SAS on
> >> > > this one. In SAS PROC MIXED, "REPEATED" and "RANDOM" are two
> >> > ways of
> >> > > specifying the random effects variance structure but they often
> >> boil
> >> > > down to the same model.
> >> > >
> >> > > I believe the model can be specified in lme4 as
> >> > >
> >> > > value ~ factor1 + (factor1 | participant)
> >> > >
> >> > > This is what the mis-named* "UNSTRUCTURED" covariance type means
> >> > >
> >> > > * Old-guy, get off my lawn rant about terminology *
> >> > > As a recovering mathematician I find the name "unstructured"
> being
> >> > > used to denote a positive-definite symmetric matrix to be, well,
> >> > > inaccurate.
> >> > >
> >> > > On Tue, Mar 20, 2018 at 12:19 PM Mollie Brooks
> >> > > <mollieebrooks at gmail.com <mailto:mollieebrooks at gmail.com>
> >> > <mailto:mollieebrooks at gmail.com <mailto:mollieebrooks at gmail.com
> >>>
> >> > wrote:
> >> > >
> >> > > I don’t know anything about spss, but if you basically want
> >> lme4
> >> > > with more correlation structures, you could look at the
> >> > structures
> >> > > available with glmmTMB.
> >> > >
> >> > https://cran.r-project.org/web/packages/glmmTMB/
> >> vignettes/covstruct.html
> >> > <https://cran.r-project.org/web/packages/glmmTMB/
> >> vignettes/covstruct.html>
> >> > >
> >> > > cheers,
> >> > > Mollie
> >> > >
> >> > > > On 20Mar 2018, at 18:11, Ben Pelzer <b.pelzer at maw.ru.nl
> >> > <mailto:b.pelzer at maw.ru.nl>
> >> > > <mailto:b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>>>
> >> wrote:
> >> > > >
> >> > > > Hi Maarten,
> >> > > >
> >> > > > You are right: you need nlme and NOT lme4 to specify
> >> > particular
> >> > > > correlation structures. Also, in nlme you would need gls
> >> > to make it
> >> > > > similar to mixed in spss. The repeated command in spss
> >> > gives the
> >> > > same
> >> > > > results as gls does for any of the covariance structures.
> >> > > >
> >> > > > Regards, Ben.
> >> > > >
> >> > > >
> >> > > > On 20/03/2018 17:30, Maarten Jung wrote:
> >> > > >> Dear Ben, dear Phillip,
> >> > > >>
> >> > > >> comparing [1] with [2] I think the /REPEATED command
> >> > specifies
> >> > > >> the error (co)variance structure of the model. Would you
> >> > agree
> >> > > with that?
> >> > > >> If so, AFAIK this is not possible with lmer and thus the
> >> > answer on
> >> > > >> Stack Overflow [3] would be wrong.
> >> > > >>
> >> > > >> [1]
> >> > > >>
> >> > >
> >> > https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/>
> >> > > >> [2]
> >> > > >>
> >> > >
> >> > https://stats.idre.ucla.edu/spss/examples/alda/chapter7/
> >> applied-longitudinal-data-analysis-modeling-change-and-
> >> event-occurrenceby-judith-d-singer-and-john-b-willett-
> >> chapter-7-examining-the-multilevel-model-s-erro/
> >> > <https://stats.idre.ucla.edu/spss/examples/alda/chapter7/
> >> applied-longitudinal-data-analysis-modeling-change-and-
> >> event-occurrenceby-judith-d-singer-and-john-b-willett-
> >> chapter-7-examining-the-multilevel-model-s-erro/>
> >> > > >> [3]
> >> > > >>
> >> > >
> >> > https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-spsss-mixed-proc
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-
> spsss-mixed-proc>
> >> > > >>
> >> > > >> Regards,
> >> > > >> Maarten
> >> > > >>
> >> > > >> On Tue, Mar 20, 2018 at 2:10 PM, Ben Pelzer
> >> > <b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>
> >> > > <mailto:b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>>
> >> > > >> <mailto:b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>
> >> > <mailto:b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>>
> >> > > <mailto:b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>
> >> > <mailto:b.pelzer at maw.ru.nl <mailto:b.pelzer at maw.ru.nl>>>>> wrote:
> >> > > >>
> >> > > >> Dear Maarten,
> >> > > >>
> >> > > >> Take a look at
> >> > > >>
> >> > > >>
> >> > >
> >> > https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/>
> >> > >
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/>>
> >> > > >>
> >> > >
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/>
> >> > >
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/
> >> > <https://stats.idre.ucla.edu/r/examples/alda/r-applied-
> >> longitudinal-data-analysis-ch-7/>>>
> >> > > >>
> >> > > >> which shows you a number of covariance structures,
> among
> >> > > which is
> >> > > >> the unstructured matrix, for repeated measures in R
> >> > with lme. It
> >> > > >> refers to chapter 7 of Singer and Willett where they
> >> > discuss all
> >> > > >> these different structures and how to choose among
> them.
> >> > > Regards,
> >> > > >>
> >> > > >> Ben.
> >> > > >>
> >> > > >> On 20-3-2018 9:00, Maarten Jung wrote:
> >> > > >>
> >> > > >> Dear list,
> >> > > >> I came across a SPSS syntax like this
> >> > > >>
> >> > > >> MIXED value BY factor1
> >> > > >> /CRITERIA=CIN(95) MXITER(100) MXSTEP(10)
> >> > SCORING(1)
> >> > > >> SINGULAR(0.000000000001)
> >> > > >> HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE)
> >> > > >> PCONVERGE(0.000001,
> >> > > >> ABSOLUTE)
> >> > > >> /FIXED=factor1 | SSTYPE(3)
> >> > > >> /METHOD=REML
> >> > > >> /REPEATED=factor1 | SUBJECT(participant)
> >> > COVTYPE(UN).
> >> > > >>
> >> > > >> and struggle to find an equivalent lmer/nlme (or
> R in
> >> > > general)
> >> > > >> formulation
> >> > > >> for this kind of models.
> >> > > >> Does anybody know how to convert the REPEATED
> >> > subcommand
> >> > > into
> >> > > >> R code?
> >> > > >>
> >> > > >> Please note that I asked the question on Stack
> >> > Overflow
> >> > > about
> >> > > >> two month ago:
> >> > > >>
> >> > >
> >> > https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-spsss-mixed-proc
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-
> spsss-mixed-proc>
> >> > >
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-spsss-mixed-proc
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-
> spsss-mixed-proc>>
> >> > > >>
> >> > >
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-spsss-mixed-proc
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-
> spsss-mixed-proc>
> >> > >
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-spsss-mixed-proc
> >> > <https://stackoverflow.com/questions/48518514/what-is-
> >> the-lmer-nlme-equivalent-of-the-repeated-subcommand-in-
> spsss-mixed-proc>>>
> >> > > >>
> >> > > >> Best regards,
> >> > > >> Maarten
> >> > > >>
> >> > > >> [[alternative HTML version deleted]]
> >> > > >>
> >> > > >> _______________________________________________
> >> > > >> R-sig-mixed-models at r-project.org
> >> > <mailto:R-sig-mixed-models at r-project.org>
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> >> > <mailto:R-sig-mixed-models at r-project.org>>>
> >> > > >> <mailto:R-sig-mixed-models at r-project.org
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> >> > <mailto:R-sig-mixed-models at r-project.org>>
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> >> > > >>
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> >> > > >
> >> > > > [[alternative HTML version deleted]]
> >> > > >
> >> > > > _______________________________________________
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