Measurement error.

Dear Jim,

re:
I am wondering what your thoughts on the units term (measurement error)
for a multi-environment crop trial are. Specifically, it seems to me that
the measurement error variance can differ across environments (we have
different people taking measurements in different places in many cases).
So, it makes sense to model separate units variances across locations.
But, my model is already huge and execution times with a single units
variance plus heterogeneous AR1 x AR1 error structures is already pushing
the limits of estimability. So, I have not yet tried a heterogeneous
units model, but I am wondering if, in the case that it is too complex,
does it make more sense to include a common homogenous units variance in
the model or instead drop it and allow the measurement variance to be
incorporated back into the heterogeneous AR1 x AR1 error structures? If
the units variance really is heterogeneous, would dropping the units
variance be better than trying to model a common variance?

My thoughts are as follows.
1) The situation will vary between crops, and trial characteristics
2) It is usual to analyse each trial separately first, and this is the
time to consider whether 'units' is required as well as ARxAR residuals.
In smaller trials it is often difficult to estimate both.
3) Just thinking in one dimension, the AR parameter is the ratio of lag 1
variance to lag 0 variance.
When UNITS is added, the AR parameter is then controlled by the ratio of
lag 2 variance to lag 1 variance..
and the UNITS variance is the 'excess' over what is predicted for lag 0.
Consequently, adding UNITS is
just adjusting the covariance model to better reflect higher lags.

4) In forestry applications where an 'tree' model is used, it is important
to have the units term because
otherwise the 'genetic' variance is inflated.

5) Concerning the specific question of the utility of a common measurment
(units) variance; I would judge it was reasonable
provided each trial had its own variance at the AR level, and prior
analysis indicates the measurement variances are
in the same ballpark. It would be counter productive if there was say a
100 fold difference in trial variances.

PS:
It seems the archives address given below is only internal to NSW DPI. I
am trying to discover if there is an external
address to the archives.

May Jesus Christ be gracious to you,

Arthur Gilmour, His servant .

Mixed model regression mapping for QTL detection in experimental crosses.
Computational Statistics and Data Analysis 51:3749-3764 now available at
http://dx.doi.org/10.1016/j.csda.2006.12.031

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Principal Research Scientist (Biometrics)
NSW Department of Primary Industries
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Received on Tue Aug 31 2007 - 11:39:15 EST