[R-sig-ME] Random intercept/slopes on two correlated outcomes

[Thierry Onkelinx]

Dear Theodore,

I missing the random slope of age. Use (0 + trait:age | id). The 0.98 is
the correlation between the random intercepts, not the outcomes. Likewise
the 0.925 is the correlation between the fixed intercepts, not the
outcomes. IMHO you should look at the trait:age and trait:X interactions.
These interactions model how strong the slopes of age and X differ between
the traits. Small differences suggest strong correlation. I'm not sure if
you can express that into a single correlation measurement.

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

2017-02-01 10:39 GMT+01:00 Theodore Lytras <thlytras op gmail.com>:

> Dear Thierry,
>
> Thank you, this helps indeed.
> However, are you sure that this models the random slopes (age | id) as
> well?
>
> I tried it on my data, I indeed get very similar results as with the two
> separate models, both for the fixed and for the random part.
> For the random part, I got:
>
> Random effects:
>  Groups   Name    Variance Std.Dev. Corr
>  id       traitY1 0.56144  0.7493
>           traitY2 0.93665  0.9678   0.98
>  Residual         0.06432  0.2536
>
> The variances for traitY1 and traitY2 are very close to the random
> intercept
> variances for the two separate models. But where are the variances for the
> random slopes??
>
> Also, the 0.98 above, is it the correlation between the outcomes? Or
> should I
> look at the "Correlation of Fixed Effects" part in the summary() output,
> where
> the correlation between traitY1 and traitY2 is reported as 0.925 ??
>
> A minor detail: the first "trait" in your formula, the one after the 0,
> isn't
> it redundant? [ Y ~ 0 + trait + trait * (age+X) + (0+trait|id)  ]
>
> Thank you again,
>
> Theodore
>
>
> Στις Τετάρτη, 1 Φεβρουαρίου 2017 9:49:58 Π.Μ. EET Thierry Onkelinx έγραψε:
> > Dear Theodore,
> >
> > You can do this is you convert the dataset into long format.
> >
> > untested
> >
> > library(lme4)
> > library(tidyr)
> > long <- gather(dat, key = "trait", value = "Y", Y1, Y2)
> > lmer(Y ~ 0 + trait + trait * (age + X) + (0 + trait | id), data = long)
> >
> > 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
> >
> > 2017-02-01 9:37 GMT+01:00 Theodore Lytras <thlytras op gmail.com>:
> > > Hi all,
> > >
> > > I have repeated measures on individuals, and I'm fitting two LMMs with
> > > random
> > > intercepts and slopes per participant, on two outcomes (Y1, Y2) as
> > > follows:
> > >
> > > library(lme4)
> > > m1 <- lmer(Y1 ~ age + X + (age | id), data=dat)
> > > m2 <- lmer(Y2 ~ age + X + (age | id), data=dat)
> > >
> > > Fixed covariates for the two outcomes are the same, and id =
> participant
> > > ID.
> > >
> > > However, my two continuous outcomes Y1 and Y2 are correlated (highly),
> > > thus I
> > > would like to jointly model them (including estimating their
> correlation).
> > >
> > > What is the appropriate way to do so in this case? Can lme4 do it, or
> do I
> > > have to resort to MCMCglmm or JAGS? Could someone point me in the right
> > > direction (for either lme4, MCMCglmm or JAGS), including any helpful
> > > papers,
> > > guides, etc ??
> > >
> > > Thank you,
> > >
> > > Theodore Lytras
> > >
> > > Epidemiologist, PhD student
> > > Hellenic Centre for Disease Control and Prevention
> > >
> > > _______________________________________________
> > > R-sig-mixed-models op r-project.org mailing list
> > > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>

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