Re: Difference between forms of factor coding: "*" and

Further to my comments this morning,

!I treats a level coded 0 as a real level labelled '0'
but * treats a level coded 0 as a missing level.

I have fitted a series of models 01 11 21 02 12 22
to two forms of the data.

In the data Jason was using,
  rep was coded 0 for site 1,
  family was coded 0 for site 1
  clone was coded 0 for site 2

In the 'ar' tests, used a modified data file where
0 values in fields rep, clone and family were changed to *.
That is, rep and family is MISSING for site 1, clone is missing for site 2.

01 and 02 use factor definitions of the form !I !SORT
11 and 12 use factor definitions of the form !I
21 and 22 use factor definitions of the form *

01, 11, 21 fit the model as
height ~ mu site !r at(site,2).site.rep at(site,2).family at(site,2).rep.family at(site,1).clone

02, 12, 22 fit the model as
height ~ mu site !r site.rep family site.rep.family clone

artest01.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
artest11.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
artest21.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
artest02.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
artest12.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
artest22.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
mytest01.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
mytest11.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
mytest21.asr: 1 site 1 103.3 1339.04 1339.04 A <.001
mytest02.asr: 1 site 1 25.0 40.12 40.12 A <.001
mytest12.asr: 1 site 1 25.0 40.12 40.12 A <.001
mytest22.asr: 1 site 1 103.3 1339.04 1339.04 A <.001

So, all models fit the same variance parameters and generate the same LogL.
However model 2 with !I factor coding generates a vastly different F test for
the site fixed effect.

The reason is that with !I coding, replicate 0 is a real replicate so there are 32 replicates in site 2 and 1 in site 1.

This means that Site belongs to the REPS strutum and so is tested against the implicit
REPS stratum variance which apparently has 25 DF.

With * coding, or explicitly fitting at(site,2).reps means that SITE does not
belong to the REPS stratum because that is not present at site 1.

I can't precisely explain the DenDF for site (103) since there are 68 clones in
site 1, 32 reps in site 2 and 127 families in site 2 since there are
no clear strata but the combination of clone from site 1 and and rep from site 2
define 100 units which presumably effectively define the stratum for
 testing site in this case.

 I note that the estimate of the fixed site effect is NOT altered, just its
Stnd Error (and DenDF).

------------------------
Arthur Gilmour

Retired Principal Research Scientist (Biometrics)

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Received on Wed Aug 04 2009 - 23:39:50 EST