[R-sig-ME] using lme4 to model regression with non-independent(nested?) data

[David Duffy]

On Fri, 17 Jan 2014, Louis wrote:

> Dear lme4 list,
> I am having trouble modelling regression with seemingly non-independent,
> nested observations and I think a mixed model approach (using *lme4* for
> example) is required. I am examining the effect of genetic relatedness
> of males on the proportion of offspring sired in cases of multiple
> paternity (multiple males contributing to a brood of eggs from one
> female). I have estimates of the genetic relatedness of each male and
> the female it mated with, as well as the proportion of offspring that
> male sired in the female's brood of eggs. There are 3-5 males
> contributing to a brood, and 9 separate broods sampled for paternity.
>
> *My questions are: *1)Should observations be nested within a female,
> 2)and/or should female be treated as a random effect (9 broods from 9
> females) or both? 3) should relatedness remain a fixed effect? Again, I
> am concerned that I have not adequately dealt with the non-independence
> of male proportion values.
> ID Female   Relat.   Prop.
> 1    A      .12      .3
> 2    A      .03      .02
> 4    A      .23      .68

Heavens! I don't think lme4 is the right tool, though I think you could 
get an approximately right model (negative covariance between males within 
each clutch). The female only comes into the multinomial bit, setting 
total clutch size, as I see it, so I don't see the point of a RE there. 
Personally, I would permute males within clutches, with a correlation 
coefficient as the measure of association.

Female Male N_Sired relatedness 
A      A1   3       0.12 
A      A2   1       0.03 
A      A3   6       0.68 
B      B1   2       0.05
...


| David Duffy (MBBS PhD)
| email: David.Duffy at qimrberghofer.edu.au  ph: INT+61+7+3362-0217 fax: -0101
| Genetic Epidemiology, QIMR Berghofer Institute of Medical Research
| 300 Herston Rd, Brisbane, Queensland 4006, Australia  GPG 4D0B994A