Crossed random effects in lmer?

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 
bootstrap. New York: Springer talk about this.

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   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v