[R-sig-ME] using lme for cov structures?
Ben Pelzer
b.pelzer at maw.ru.nl
Wed Jul 26 21:45:45 CEST 2017
Dear Thierry and Wolfgang,
Thanks for responding so quickly. Here is the reproducible example of
the two models that I'm interested in.
# Read data.
opposites <-
read.table("https://stats.idre.ucla.edu/stat/r/examples/alda/dat/opposites_pp.txt",header=TRUE,sep=",")
# Open library.
library(nlme)
# Define group "one" with value 1 for all cases.
one <- rep(1, 140)
#----- Model estimated with gls.
comsym.gls <- gls(opp~1,opposites,
correlation=corCompSymm(form = ~ 1 |id), method="REML")
summary(comsym.gls)
#----- Same model estimated with lme.
comsym.lme <- lme(opp~1,opposites,
random= ~1|one,
correlation=corCompSymm(form = ~ 1 |one/id),
method="REML")
summary(comsym.lme)
#----- Wolfgang's gls suggestion for heterogeneous CS.
summary(gls(opp ~ 1, opposites, correlation = corCompSymm(form = ~ 1 |
id), weights = varIdent(form = ~ 1 | wave)))
# Does not work with lme.
summary(hetercom <- lme(opp ~ 1,opposites,
correlation=corCompSymm(form = ~ 1 |id),
weights=varIdent(form = ~1|wave), method="REML"))
# But does work with the "one" trick.
summary(lme(opp ~ 1,opposites,
random = ~1|one,
correlation=corCompSymm(form = ~ 1 |one/id),
weights=varIdent(form = ~1|wave), method="REML"))
The main reason of my mailing to the list is this. I was wondering
whether with lme it is possible to also estimate models with the
individuals nested in higher levels like schools or hospitals etc and at
the same time letting the residuals correlate within individuals over
time with one of the nice covar structures. However, I do NOT have a
reproducible example of such more complex models at the moment. I only
hoped that if the lme version of the model presented above has no
further problems than a (slightly) different AIC, BIC and std. error of
the fixed intercept, it would be meaningful to proceed in this way, i.e.
using lme instead of gls, since lme provides the important possibility
of additional random effects in the model.
As to Wolfgang's suggestion for heretogeneous CS using:
gls(opp ~ 1, correlation = corCompSymm(form = ~ 1 | id), weights =
varIdent(form = ~ 1 | timepoint))
I didn't find a way to estimate such a model with lme, except for the
method with the "trick". Using:
lme(opp ~ 1,opposites,
correlation=corCompSymm(form = ~ 1 |id),
weights=varIdent(form = ~1|wave), method="REML")
leads to error-message:
Error in lme.formula(opp ~ 1, opposites, correlation = corCompSymm(form
= ~1 | : incompatible formulas for groups in 'random' and 'correlation'
whereas
lme(opp ~ 1,opposites,
random = ~1|one,
correlation=corCompSymm(form = ~ 1 |one/id),
weights=varIdent(form = ~1|wave), method="REML")
leads to similar results as your gls suggestion.
Best regards, Ben.
On 26-7-2017 14:44, Thierry Onkelinx wrote:
> Dear Ben,
>
> Please be more specific on the kind of model you want to fit. That
> would lead to a more relevant discussion that your potential misuse of
> lme. A reproducible example is always useful...
>
> Best regards,
>
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
> and Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
>
> To call in the statistician after the experiment is done may be no
> more than asking him to perform a post-mortem examination: he may be
> able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does
> not ensure that a reasonable answer can be extracted from a given body
> of data. ~ John Tukey
>
> 2017-07-26 13:36 GMT+02:00 Ben Pelzer <b.pelzer at maw.ru.nl
> <mailto:b.pelzer at maw.ru.nl>>:
>
> Dear list,
>
> With longitudinal data, the package nlme offers the possibility to
> specify particular covariance structures for the residuals. In the
> examples below I used data from 35 individuals measured at 4 time
> points, so we have 4 observations nested in each of 35 individuals.
> These data are discussed in Singer and Willett, Applied Longitudinal
> Data Analysis, chapter 7.
>
> In several sources I found that e.g. compound symmetry can easily be
> obtained with gls from package nlme, by using the correlation
> structure
> corCompSymm, as in:
>
> comsym <- gls(opp~1,opposites,
> correlation=corCompSymm(form = ~ 1 |id),
> method="REML")
>
> where id is subject-identifier for the individual. With gls
> however one
> cannot specify random effects, as opposed to lme. To have lme estimate
> compound symmetry is simple, one would not even need have to specify a
> particular correlation structure, it would suffice to say
> "random=~1|id". However, for more complex covariance structures, e.g.
> heterogeneous compound symmetry, I was only able to find syntax
> for gls,
> but not for lme.
>
> Then I thought that tricking lme might be an option by having a
> kind of
> "fake" random effect. That is, I constructed a variable "one" which
> takes value 1 for all cases, and let the intercept be random
> across "all
> one groups". This led to the following lme model:
>
>
> comsym.lme <- lme(opp~1,opposites, random= ~1|one,
> correlation=corCompSymm(form = ~ 1 |one/id),
> method="REML")
>
> And actually to my surprise, the results of this lme are highly
> similar
> to those of the gls above.
> The output of both is attached below. The loglik's are identical, the
> AIC and BIC are not, which I can understand, as the lme has an extra
> variance to be estimated, compared to the gls. Also, the fixed
> intercept's standard error is different, the one of the lme being
> about
> twice as large.
>
> I added some independent variables (not shown below) but the
> similarities between gls and lme remain, with only the AIC and BIC and
> the standard error of the fixed intercept being different for the two
> models.
>
> My question is threefold.
> 1) Suppose the individuals (say pupils) would be nested in
> schools, then
> I assume that with lme I could add school as a random effect, and
> run a
> "usual" model, with pupils nested in schools and observations in
> pupils,
> and then use any of the possible residual covariance structures
> for the
> observations in pupils. Would you agree with this? (with gls one
> cannot
> use an additional random effect, like e.g. school)
> 2) Are the lme results indeed to be trusted when using this "fake"
> random effect, apart from the differences with gls mentioned?
> Could you
> imagine a situation where lme with this trick would produce wrong
> results?
> 3) I don't understand the variance of the intercept in the lme output.
> Even when I specify a very simple model: lme(opp ~ 1, random = ~1|one,
> opposites, method="REML")
> lme is able to estimate the intercept variance...but what is this
> variance estimate expressing?
>
> Thanks a lot for any help!!!
>
> Ben.
>
>
>
>
>
> *----------------- gls
> ---------------------------------------------------
>
> > comsym <- gls(opp~1,opposites,
> correlation=corCompSymm(form = ~ 1 |id),
> method="REML")
> > summary(comsym)
>
> Generalized least squares fit by REML
> Model: opp ~ 1
> Data: opposites
> AIC BIC logLik
> 1460.954 1469.757 -727.4769
>
> Correlation Structure: Compound symmetry
> Formula: ~1 | id
> Parameter estimate(s):
> Rho
> 0.2757052
>
> Coefficients:
> Value Std.Error t-value p-value
> (Intercept) 204.8143 5.341965 38.34063 0
>
> Standardized residuals:
> Min Q1 Med Q3 Max
> -2.75474868 -0.71244027 0.00397158 0.56533908 2.24944156
>
> Residual standard error: 46.76081
> Degrees of freedom: 140 total; 139 residual
>
>
> #------------------ lme
> ---------------------------------------------------
>
> > comsym.lme <- lme(opp~1,opposites, random= ~1|one,
> correlation=corCompSymm(form = ~ 1 |one/id),
> method="REML")
> > summary(comsym.lme)
>
> Linear mixed-effects model fit by REML
> Data: opposites
> AIC BIC logLik
> 1462.954 1474.692 -727.4769
>
> Random effects:
> Formula: ~1 | one
> (Intercept) Residual
> StdDev: 10.53875 46.76081
>
> Correlation Structure: Compound symmetry
> Formula: ~1 | one/id
> Parameter estimate(s):
> Rho
> 0.2757052
> Fixed effects: opp ~ 1
> Value Std.Error DF t-value p-value
> (Intercept) 204.8143 11.81532 139 17.33463 0
>
> Standardized Within-Group Residuals:
> Min Q1 Med Q3 Max
> -2.75474868 -0.71244027 0.00397158 0.56533908 2.24944156
>
> Number of Observations: 140
> Number of Groups: 1
>
>
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