[R-sig-ME] Crossed random effects in lmer?

David Duffy davidD at qimr.edu.au
Thu Mar 24 01:35:43 CET 2011

On Wed, 23 Mar 2011, Julia Sommerfeld wrote:

> 1. If I want to test if BreedSuc1 influences SameMate and SameSite,
> shouldn't I account for the fact that the BreedSuc1 value of Bird E and F is
> exactly the same, since they are a pair?
>
> 2. Shall I use lmer with Pair as a random effect? What about the individual
> Bird? If I look at site-fidelity (and mate-fidelity?), I'm looking at the
> behaviour of the individual, rather than the behaviour of the pair. Could I
> use a lmer model including Pair and Bird? But how can I relate the random
> effect "Pair" to "BreedSuc1" and "Bird" to "SameMate", "SameSite"? Crossed
> random effects?

If you had enough data, then you would include a Pair effect as well as an
individual effect - I would imagine there are incompatibilities among
birds as in other species ie A+B, C+D less success than A+D, B+C. I'm
guessing that you don't have enough data, though.

Mechanistically, you are arguing that bird behaviour in season t+1 is a
direct response to actual success in season t, so paths from both the
latent variables (perceived mate fitness ?) and manifest variable
(success) have to appear in the model.

For the test of your specific hypotheses, all these random effects are
nuisances.  If it were me, I try to fit a simple marginal model as per
your glm() models, and assess significance by simulation.

A delete-d jackknife might be one way to give roughly correct standard
errors.  This is a method where you generate pseudosamples by deleting a
random set of observations.  Shao J, Tu D (1995): The jackknife and

SE=((n-d)/dm * Sum(r_i-mean(r_i, i=1, m))^2)^1/2

where d is the number of observations dropped for each pseudosample, ri is
the test statistic value for the ith pseudosample, m is the number of
pseudosamples, and n is the number of observations.  I only mention this
because it is not very difficult to do ;) and seems to work for
complicated covariance structures.

--
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
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