Random slope models with nested random effects and multiple x variables

-----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


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