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*To*: Haja Kadarmideen <h.kadarmideen@ed.sac.ac.uk>*Subject*: Re: And now what?*From*: Arthur Gilmour <gilmoua@ornsun.agric.nsw.gov.au>*Date*: Tue, 1 Dec 1998 21:24:26 +1100 (EST)*cc*: asreml@ram.chiswick.anprod.csiro.au*In-Reply-To*: <3F132CF7A43@ed.sac.ac.uk>*Sender*: owner-asreml@chiswick.anprod.csiro.au

Dear Haja and colleaques. My comments are below. I'm replying from Perth (WA) via a modem so please forgive any typos. On Mon, 30 Nov 1998, Haja Kadarmideen wrote: > 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? > This formula is indeed for converting a heritability from underlying Normal to observed scale. There is an equivalent for the logit scale which from memory is just pq being (pqpq/pq). > > Please correct me if I am wrong or if I missed something in the earlier > discussions. > > > 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 ? > The underling variance of a standard normal (implied by PROBIT) is 1. The underlying variance for a standard logistic distribition is 3.3= p1^2 /3 hence the factor. In the lamb example in the manual (with !disp option) the variance components are PROBIT LOGIT SIRE .032 .011 Error 2.035 2.057 Therefor PROBIT heritability is 4 0.032 / (.032+2.035x1) = 0.128/2.067 = .062 LOGIT heritability is 4 0.11 / (.011 + 2.057x3.3) = 0.44 / 6.7991 = .0647 > > 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) ? > I would not convert correlatations at all as the scale factors should cancel. I apologise if I have lean anyone astray by not noting the issue of how to calculate heritability for logit data. I probzbly did it wrong on the earlier example. [In the above example, the 4 is there becasue it is a sire model] > > 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. > Good. This is a major problem with these analyses. > > Is it neccessary to do the "above" data editing in ASREML to meet > convergence ? Generally YES. ASREML tries to limit how close it proceeds to INFINITY but it is better to avaid the problem rather than to hope an algorithm can safely handle it. > > > - 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 > properly ? > I would need to examine the example to answer this. Probits are harder to calculate. It could be problems with the random effects going to infinity as well. > > 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. > !GU just allows the component to go negative. !GP forces it to remain positive. I do not understand your comment assuming the component is positive. Arthur > > I'd appreciate your help and/or suggestions. > > > Many Thanks > > Haja > > > > 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. > > > > Arthur > > > <nofill> > -------------------------------------------------- > Dr. Haja Kadarmideen > Animal Biology Division > SAC > Bush Estates > Penicuik, Midlothian EH26 0PH > Scotland, UK > > Telephone: +44 0131 535 3246 > Fax : +44 0131 535 3121 > > e-mail : h.kadarmideen@ed.sac.ac.uk > -------------------------------------------------- > <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Arthur Gilmour PhD email: Arthur.Gilmour@agric.nsw.gov.au Senior Research Scientist (Biometrics) fax: <61> 2 6391 3899 NSW Agriculture <61> 2 6391 3922 Orange Agricultural Institute telephone work: <61> 2 6391 3815 Forest Rd, ORANGE, 2800, AUSTRALIA home: <61> 2 6362 0046 ASREML is still free by anonymous ftp from pub/aar on ftp.res.bbsrc.ac.uk or point your web browser at ftp://ftp.res.bbsrc.ac.uk/pub/aar/ To join the asreml discussion list, send the message subscribe to asreml-request@chiswick.anprod.CSIRO.au The address for messages to the list is asreml@chiswick.anprod.CSIRO.au <> <> <> <> <> <> <> "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord." Romans 6:23 <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

**References**:**Re: And now what?***From:*"Haja Kadarmideen" <h.kadarmideen@ed.sac.ac.uk>

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