[R-sig-ME] Random slope models with nested random effects and multiple x variables

[ONKELINX, Thierry]

Dear Sam,

You could model lmer (behaviour ~ (1|bird:track) + (a+b+c|bird)) which allows covariates among all 4 random effects (the random intercept and 3 random slopes). Thus you get a 4x4 variance-covariance matrix.

The other extreme is lmer (behaviour ~ (1|bird:track) + (1|bird) + (0 + a|bird) + (0+b|bird) + (0+c|bird)) where all random effects are indepent. Hence one could write is as a diagonal 4x4 vraiance-covariance matrix.

Note that lme from the nlme package allows for more structures in the variance-covariance matrix. I would have a look at it unless you need generalised linear mixed models or crossed random effects.

Best regards,

Thierry

> -----Oorspronkelijk bericht-----
> Van: Samantha Patrick [mailto:samantha.patrick at plymouth.ac.uk]
> Verzonden: donderdag 6 oktober 2011 15:19
> Aan: ONKELINX, Thierry; r-sig-mixed-models at r-project.org
> Onderwerp: RE: [R-sig-ME] Random slope models with nested random effects
> and multiple x variables
> 
> Hi Thierry
> 
> Thank you for getting back to me.  Modelling
> 
> lmer (behaviour ~ (a|bird)  + (1|bird:track))
> 
> does exactly what I want.
> 
> 
> However I simplified the model (to make it easier to explain to the list) and in
> reality the model has 3 environmental variables (a, b and c) and I want to know
> how each birds responds to each variable.
> 
> I have run the three models separately, so fitting:
> (1) a|bird + (1|bird:track)
> (2) b|bird + (1|bird:track)
> (3) c|bird + (1|bird:track)
> 
> but was wondering if you can fit all three in one model and whether this is a
> good idea!
> 
> My code for this again results in multiple intercepts for bird.
> 
> lmer (behaviour ~ (1|bird:track) + (a|bird) + (b|bird) + (c|bird))
> 
> While you could remove the intercepts
> 
> e.g.
> 
> lmer (behaviour ~ (1|bird:track) + (a|bird) + (0+b|bird) + (0+c|bird))
> 
> this would again result in the covariance between the intercept and the slope b
> and c being 0, when ideally I would like all three slopes to be able to covary with
> the intercept (through a a symmetric variance-covariance matrix).  Otherwise
> the intercept will be driven by one but not all slopes.  This may not be possible to
> avoid but I am keen to understand exactly how the intercept is calculated to
> make sure my interpretation of the results is correct.
> 
> Thanks
> 
> Sam
> 
> 
> 
> 
> 
> Dr Samantha Patrick
> EU INTERREG Post Doc
> Davy 618
> Marine Biology & Ecology Research Centre University of Plymouth Plymouth
> PL4 8AA
> 
> T: 01752 586165
> M: 07740472719
> 
> 
> -----Original Message-----
> From: ONKELINX, Thierry [mailto:Thierry.ONKELINX at inbo.be]
> Sent: 06 October 2011 13:00
> To: Samantha Patrick; r-sig-mixed-models at r-project.org
> Subject: RE: [R-sig-ME] Random slope models with nested random effects and
> multiple x variables
> 
> Dear Sam,
> 
> Models a and b are identical.
> 
> Model c has the problem that you fit two random intercepts for bird (one from
> the 1|bird/track term and one from the a|bird term
> 
> You might want the model lmer (behaviour ~ (a|bird)  + (1|bird:track))
> 
> Best regards,
> 
> Thierry
> 
> > -----Oorspronkelijk bericht-----
> > Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-
> > bounces at r-project.org] Namens Samantha Patrick
> > Verzonden: donderdag 6 oktober 2011 12:20
> > Aan: r-sig-mixed-models at r-project.org
> > Onderwerp: [R-sig-ME] Random slope models with nested random effects and
> > multiple x variables
> >
> > Hi
> >
> > I am fitting random intercept and slope models on some GPS tracking data.  I
> > have data from 113 tracks from 31 individuals with about 400 behavioural
> > observations per track.
> >
> > I am interested in looking at how individuals change their behaviour in
> response
> > to an environmental variable (a) but want to control for the non-independence
> > of points from individual tracks.
> >
> > So I have these possible lmer models :
> >
> >
> > a)       lmer (behaviour ~ (1|bird/track) + (-1+a|bird))
> >
> > b)      lmer (behaviour ~ (1|bird/track) + (0+a|bird))
> >
> > c)       lmer (behaviour ~ (1|bird/track) + (a|bird))
> >
> >
> > I have two questions:
> >
> > 1)     Can you fit an intercept and slope with different random effect
> structures?
> > In theory I think this is ok but I have not see it done.
> >
> > 2)     I am interested in the differences in covariance structures in the three
> > models.  I thought that model (a) set the covariance between the slope and
> > intercept for bird to 0 but from looking at previous posts in the forum, it seems
> > that model (b) may do this?  In which case does model (a) set the covariance to
> -
> > 1?
> > My understanding is that model (c) allows a symmetric variance-covariance
> > matrix (which is what I want) but I am concerned that this model is fitting two
> > intercepts for bird?
> >
> > Ideally I want the intercept for bird to be allowed to covary with the slope for
> > bird (I don't want to constrain it  to 0 or 1) but I am unsure if my problem is in
> the
> > syntax or whether I don't fully understand how the model partitions the
> variance
> > in nested random effects and that maybe the model I want to fit is not
> possible.
> >
> > Any advice on creating the models would be much appreciated!
> >
> > Many Thanks
> >
> > Sam
> >
> > Dr Samantha Patrick
> > EU INTERREG Post Doc
> > Davy 618
> > Marine Biology & Ecology Research Centre University of Plymouth Plymouth
> > PL4 8AA
> >
> > T: 01752 586165
> > M: 07740472719
> >
> >
> > 	[[alternative HTML version deleted]]
> >
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