Dear Arthur and ASREML members,
I am new to this list so my apologies if the following questions have
been already discussed. I have two questions: One about transformation
and other about convergence problem.
1. Since Hugo used logit (default) link function, I wonder if zz/pq
transformation is still correct. Isn't this formula used for converting
estimates on the underlying Normal scale to the observed probability
scales or vice versa?
Please correct me if I am wrong or if I missed something in the earlier
Factor, pi / sqrt(3), seems to approximate logistic and normal
distributions. Do we use this factor to convert estimates on logit scale
to normal scale first (both on the underlying scale) and then use zz/pq
to transform Normal estimates (transformed) to observed prob.scale ?
If the later was the right approach, how to transform parameter
estimates (h2, rg or rp ), on logit scale to Normal scale first ? Do we
just multiply estimates (h2,rg,rp) by pi/sqrt(3) ?
2. My second question relates to convergence problem on the
binomial data (coded as 0 or 1) analysis using univariate animal model.
I first checked and removed fixed effect sub-classes that had 0 % or
100% incidence for the 0/1 trait, as likelihood in these cases is not
defined (infinity on the underlying scale and therefore it keeps diverging
?). I could have changed the model though, to avoid too many "all" or
"zero" sub-classes, but is neccessary/preferable to keep the existing
model in my analysis.
Is it neccessary to do the "above" data editing in ASREML to meet
- After removing observations that fall under "uninformative" fixed effect
sub-classes, I used logit and probit link functions. Convergence was
acheived for the logit link (in iteration 10 or so) but not for the Probit link
function (until iteration 20).
Why ? It is due to the fact that numerical integration is easeir on logitic
scale than on Normal scale or is it due to something else I didn't do
I used !GU - "unconstrained" option in both cases as default, !GP did
not work on both logit and probit link functions. I did not examine
solutions but tried with a few different starting values for variance ratio. I
am still tring to acheive convergence with probit link.
I'd appreciate your help and/or suggestions.
The normal nexty step would be to transform from the underlying scale
to the p scale using zz/pq where p is the average incidence,
q=(1-p) and zz is z-squared where z is the ordinate of the Normal curve
corresponding to the proportion. So if p=0.5, z=..399 and the factor is .64
H2 on the underlying scale is .499917/1.499917 = .3333
so h2 on the p scale is 0.21
You can get the variance of h2 from asreml (.pin file)
and scale it similarly.
Dr. Haja Kadarmideen
Animal Biology Division
Penicuik, Midlothian EH26 0PH
Telephone: +44 0131 535 3246
Fax : +44 0131 535 3121
e-mail : firstname.lastname@example.org