[R-sig-ME] Crossed or random effects

[Ben Bolker]

Katrina Evans <katrina.evans at ...> writes:

> I have a set of telemetry data, which provides the foraging distances
> travelled by birds at different breeding stage.  My aim is to find out if
> birds are travelling different distances at different stages in the breeding
> season. Telemetry readings were taken from 30 birds over a period of 3
> months, producing around 100 records of distance travelled for each bird. I
> have included Bird_ID as a random factor in my mixed model. My model so far
> is as follows:
> 
> Mlmer1<-lmer(Distance~BreedingStatus +(Status|Bird_id), data=Distance)
> 

  Is there a difference between 'BreedingStatus' (in the fixed effects)
and 'Status' (effect varying among Bird_id -- you could think of
this as "Status crossed with Bird_id"), or are they supposed to be
the same bird?

> I have a few of queries -
> 
> 1) For one breeding stage eg. incubating female, the same bird, eg female
> 807, appears repeatedly. In addition, this bird will also be present
> in other breeding stage groups,
   
  (this is the same as "levels of the BreedingStatus variable", right?)

> eg provisioning and chicks fledged groups.
> Is it enough to have Bird_id in as a simple random effect in the model, or
> is it important to allow for the fact that the same bird also occurs in some
> (but not all) of the other breeding stage groups? I have been reading about
> crossed random effects but am struggling to find relevant ecology examples.
> I also don't think this is quite the same thing.

   Since BreedingStatus (as I understand it) is a fixed effect, 
you're essentially crossing BreedingStatus with Bird_id 
by specifying (BreedingStatus|Bird_id)) [which is what I wrote above]

> 2) Some of the birds were in pairs, so I am thinking of adding 'Pair' in as
> a second random effect. However, I'm not sure if I have a big enough sample
> size to create a valid model. And would this be crossed or nested??

   If any bird was observed in more than one pair, then it would
be crossed.  If birds were only ever observed in a single pair,
then it would be nested -- but I think you don't have to worry about
the distinction.  Since Status is relevant only to birds, and not
to pairs, and as long as birds are uniquely identified (and not
e.g. identified only as individual 1 and 2 within each pair) 
I think  that (1|Pair) + (Status|Bird_id) would be fine.  The only
way to be sure you have a big enough sample size is to try it --
variances estimated as zero, correlations among random effects
estimated as +/- 1, or convergence warnings/errors are the signs
that you may be overfitting.

> 
> 3) I have been trying mixed models in both R and SPSS. SPSS makes a point of
> asking the user to choose an induced correlation structure for the model. Is
> this something that should always be checked for? A lot of texts on this
> topic for R seem to gloss over this. As I have repeated measures on the same
> birds, it is likely that measurements for one bird will be more similar to
> each other than those for another bird. 

  That's incorporated in your model already, by specifying bird
as a random effect.

> Also measurements taken in June for
> one bird may all be similar, compared to those in August for the same bird.
> Any advice would be really useful.

  You could add 'month' as a fixed effect (adding it as a random
effect won't work very well with three months).  You could add
'day' as a random effect, probably crossed, since you probably
don't have multiple samples of birds per day [hence variation among
birds within days would be confounded with the residual variance].
There is an additional way to model correlation, which is to add
autocorrelation structures for the fact that birds are likely to
behave similarly on days that are close together in time.  You can
do this with lme (in the nlme package), but not (yet) with lmer.
If you don't end up wanting to do too much fancy stuff with crossed
random effects, you could switch to lme.