Re: fixed effects

# Re: fixed effects

```
>
> Dear ASREML user,
> I am estimating sheep weaning weight data. Being curious, before getting a
> final model, I tried fixed effects. Now my problem is how to fit birth
> rank(brank), rearing rank(rrank) and the combined term birth/rear
> rank(brrank). Following is the output for various order of these three
> terms, model excluding random effects.
> why df of brrank changed cross models?
> why f_inc and F_all of all three terms varied among models?
> How these tree terms should be fitted as fixed effects?

This is the classic effect of incomlete factorial classification.

Evidently you have 5 Birth classes and 3 rearing classes
giving a table with 15 cells.  However, at least 3 are
probably empty and you have not defined how brrank relates
to brank and rrank so I can't give a complete explanation.

Anyway, write down the 3 x 5 table and write down how amny in each cell.

It may look like

X  X  X  X  0
0  X  X  X  X
0  0  X  X  0

where only 10 of the cells have values giving a total of 9 DF

In every case where the 3 effects are fitted, you have a total of 9 df.

Now, if BRANK fitted first, or after RRANK, it will have 4 df
Also, if RRANK fitted first or after BRANK, it will have 2 df.

Fitted after BRANK and RRANK, BRRANK can have only 3 df because
that is all that is left.

When BRRANK is fitted first, it takes 6 df ( 4 of which were
previously allocated to BRANK) BRANK now only has 1 df.

If you identify into which of the 7 BRRABK classes the 10
cells form, you will be able to see that they have picked out
some of the BRANK classes.

Furthermore, after fitting BRANK, either RRANK or BRRANK
will explain most of whats left.  However, RRANK does it best
so you should probably fit just BRANK and RRANK.

What is sometimes done is to define BRRANK as say

1  Born Single, Raised Single
2  Born Twin  , Raised Single
3  Born Twin  , Raised Twin
4  Born Triple+ ,Raised Single
5  Born Triple+ ,Raised Twin
6  Born Triple+ ,Triple+

and this then picks up most of the variation such that,
as in your case, neither BRANK or RRANK explain any more.
Grouping is based on numbers in a cell as well as expectation
of similarirty.

Applying this to the pattern above,

X  X  X  X  0
0  X  X  X  X
0  0  X  X  0

BRRANK picks up the difference between BORN SINGLE
and BORN TWIN so For the pattern above, DF would be

(In ASREML order with bottom term fitted first)

RR    2      RR  2    BR   3  BR  2   BRR 3   BRR 3
BR    2      BRR 3    RR   2  BRR 5   RR  2   BR  4
BRR   5      BR  4    BRR  5  RR  2   BR  4   RR  2

It is aloso much easier to interpret one set of means rather than
the combined effects of 3 nonorthogonal factors across a set of
means.

>
> Thanks
> Yuandan
> Following is the digest of output
>    term                    DF       F_inc       F_all
> model wwt= mu ... brrank brank rrank
> 11 rrank                    2        2.61        2.61
> 10 brank                    1        0.08        0.38
>  9 brrank                   6       73.78        8.39
>
> 31 mu                       1    59191.67      169.91
>
>
> model wwt= mu ... brank brrank  rrank
>  11 rrank                    2        2.61        2.61
>   9 brrank                   3       34.78        0.45
>  10 brank                    4       84.60        9.76
>
>  31 mu                       1    59191.67      169.91
>
> model wwt= mu ... brank rrank brrank
>  9 brrank                   3        0.45        0.45
> 11 rrank                    2       54.09        2.61
> 10 brank                    4       84.60        9.76
> 34
> 31 mu                       1    59191.67      169.91
>
> model wwt= mu ... rrank brank brrank
>  9 brrank                   3        0.45        0.45
> 10 brank                    4       12.61        9.76
> 11 rrank                    2      198.08        2.61
>

> 31 mu                       1    59191.67      169.91
>
> model wwt= mu ... brrank
>  9 brrank                   6       73.65       73.65
>
> 31 mu                       1    59092.26      169.84
>
> model wwt= mu ... brank
> 10 brank                    4       78.58       78.58
>
> 31 mu                       1    54977.57      157.48
>
> model wwt= mu ... rrank
> 11 rrank                    2      191.79      191.79
>
> 31 mu                       1    57312.05      157.45
>
>
>
> ************************************************************************
> Yuandan Zhang
>
> Department of Animal Science
> University of New England
> Armidale, NSW 2351, Australia
>
> Phone	+61 + 2 + 6773 2756(Lab)
>
>
> Fax	+61 + 2 + 6773 3275
> E-mail yzhang@metz.une.edu.au
> homepage http://metz.une.edu.au/~yzhang/
> ************************************************************************
>

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