Re: And now what?

# Re: And now what?

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Dear Haja and colleaques.
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
> 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>
> --------------------------------------------------
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>
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> --------------------------------------------------
>

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
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

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