Peter Visscher's answers to questions obtained during the StatGen seminar (Visscher et al. 
2006, PLoS Genetics 2(3):e41):

1. Why not compare unrelated twins from different pairs to get pi's near 0 when trying 
to fit the regression line?

The 2006 study was based upon a limited number of microsatellite markers, so we had 
little power to estimate pi near zero from unrelated individuals. Also, we deliberately 
wanted all information on genetic variance to come from within-family contrasts, i.e. 
to quantify the correlation between phenotypic and genotypic similarity within families. 
One of the topics of my talk today is to look at much more distant ('unrelated') 
relatives using SNP data to estimate IBD.

2. Why did you estimate pi at 1cM intervals? You had only sparse genotype data and 
could have estimated pi at 5cM intervals...

True, and that would have been computationally faster. One of my colleagues had done the 
1cM IBD scan so I just used those data. As long as the estimate of genome-wide IBD is 
unbiased the actual spacing for IBD estimation doesn't matter so much.

3. If I am interested in only one region of the genome (linkage already points to the 
area, for instance), why not estimate pi only for that region and maybe increase Var(pi)?

Agreed. In my follow-up 2007 paper (Am J Hum Genet) we partitioned genetic variance 
across chromosomes, taking advantage of the fact that var(pi) is larger for chroms. I 
wanted to avoid doing a linkage analysis because of the multiple testing problem and 
because linkage analysis for height had been done. Goldgar (1990? Am J Hum Genet) was 
one of the first to propose this kind of method for chromosome segments.

4. Is it sensible to assume f^2 = 0 for a trait like height?

I don't think we assumed this - it was our ML estimate. In our 2007 paper (for which 
we had more data), we estimate f^2 ~ 0.03.

5. Why does bias increase if f=0 under both simulation and theory (Table 1)?

I have to look at the theory again, but I think that this is because of the constraints 
imposed by the (RE)ML estimation, i.e. that variance componenets cannot be negative. A 
regression approach, e.g. Haseman-Elston applied to genome-wide IBD, may be unbiased.

6. Why not provide Monte Carlo error for the estimates of heritability?

Not sure what would we gain by doing that? We estimate the CI from the curvature of the 
likelihood profile, which is a fairly standard way to my knowledge. It does of course 
rely on asymptotia.

7. Could you tell me more about model misspecification and goodness-of-fit?

Not sure what you have in mind. We deliberate fitted an additive model because we wanted 
to estimate additive genetic variance. In the 2007 paper we tried to estimate AxA variance 
but we don't really have much power to do that because the pi coefficient are all so close 
to 0.5.