What is the lmer/nlme equivalent of the REPEATED subcommand in SPSS's MIXED procedure?

On 22 March 2018 at 16:11, Maarten Jung
<Maarten.Jung at mailbox.tu-dresden.de> wrote:

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?

Yes, I'd say so. And Ben Pelzer's email from yesterday has a data+code
example of exactly that if I'm not mistaken.

If factor1 is 'time' this model is quite similar to the famous MMRM*
often used in pharma to model clinical trials (for purposes of
handling/'imputation' of missing values) in which measurements are
made on subjects at, say, a handful of timepoints over the trial
period. This model essentially specifies that each subject-profile
follows a multivariate normal distribution with the so-called
'unstructured' variance-covariance matrix with dimensions equal to the
number of timepoints, further, all the subject profiles are
independent. Differences between treatment groups are then estimated
at each timepoint and usually the differences at the last timepoint
are of primary interest. Long story short: Yes it makes sense and it's
done all the time in the pharmaceutical world.

Cheers
Rune

*The MMRM is a very specific model not just any 'mixed model for
repeated measurements', in fact, it is not really a mixed model (the
lack of random effects give it away...).

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>

    >     <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>>

    >     <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>

    >     <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>>>

    >     >>        <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>

    >     <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>>

    >     <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>

    >     <mailto:R-sig-mixed-models at r-project.org

    <mailto:R-sig-mixed-models at r-project.org>>>> mailing list

    >     >>