# contrasts

From: Holland, Jim <Jim.Holland_at_ARS.USDA.GOV>
Date: Wed, 20 Jan 2010 13:00:17 -0500

A question about contrasts to follow up on the discussion from last year
included at the bottom of this message:

I have an experiment with 78 lines from a selection population tested in
eight environments along with a "control" and a few other checks. I want
to use a contrast to test the difference between the mean of the 78
lines from the population and the control. I use this statement:

!CONTRAST PopvsControl Material 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -78

I checked the coefficients and they are in the correct order. According
to Arthur's response below, I think the estimate of the contrast in the
.sln file should equal:

(78*pop mean - 78*control)/(78 *(1^2) + 1*(78^2))

= (pop mean - control)/79

When the contrast is fit in the following model with all effects except
the genetic effects (named "material" here):

char ~ mu PopvsControl,

!r Loc REP.Loc BLOCK.REP.Loc PopvsControl.Loc !f mv

+ heterogeneous errors in 8 locations

I get the following F-test:

Analysis of Variance NumDF DenDF_con F_inc F_con M P_con

42 mu 1 6.9 49.38 49.35 . <.001

38 PopvsControl 1 647.2 0.07 0.07 A 0.788

and estimate (in the .sln file):

PopvsControl ... -0.1492E-01 0.5507E-01

Multiplying this effect by 79 gives = -1.178.

If I compute the difference between the predicted values of the
population and the control from a model that fits the material effect
but not the contrast, I get a difference of +4.4

I have no idea how to relate the contrast estimate to what I expected as
the difference that I am trying to estimate.

I also tried fitting the contrast simultaneously with the overall
genetic (material) effects, with this model:

char ~ mu PopvsControl Material,

!r Loc REP.Loc BLOCK.REP.Loc Material.Loc PopvsControl.Loc !f mv

+ heterogeneous errors in 8 locations

and got this output:

Analysis of Variance NumDF DenDF_con F_inc F_con M P_con

42 mu 1 23.3 45.23 37.12 . <.001

38 PopvsControl 1 556.8 0.07 0.07 a 0.790

9 Material 82 617.9 1.48 1.48 A 0.032

PopvsControl FR1064x(FR615xFR697) -0.3377 6.152

This estimate of the contrast is wildly different (by an order of
magnitude), but I still cannot relate it to the observed difference
between predicted values.

So, I have two problems. One is that I still don't understand what the
value of the contrast estimate in the .sln file "means". I also don't
understand why the value changes radically when fitting it along with
the overall genetic effects.

Any ideas? Thanks! - Jim

Here is the previous discussion:

Dear Bart,

The reported effect is the regression implicit in the contrast.

Assuming you wrote the contrast as 0 1 0 -1
the regression is Sigma XY /Sigma XX = (.385 - .975) / 2 = -.295

Now if you have unbalanced data and non-orthogonal contrasts,
the reported effect will be as in the context of the full model,
but the Wald F statistic will test the contrast as the incremental
effect as it is added in the model. So, this is another reason
the fitted contrast may not reflect the simple contrast.

But I suspect the former applies in your case.

On Wed, 2009-09-02 at 10:00 +0200, Ducro, Bart wrote:
> Dear Arthur and others,
> We have a question about the estimation of contrasts. If you look at
> the solutions of the fixed effects (in the .sln file) from a mixed
> model analysis, we get the following results:
> code estimate s.e.
> 99 0.000 0.00
> 10 0.385 0.227
> 11 0.764 0.207
> 12 0.975 0.226
>
> Based on these solutions we would expect the following contrasts
> between classes 10 and 12 of about -0.59
> If we estimate the contrast using !CONTRAST we get -0.297 (with s.e.
> of 0.089).
> Do we overlook something?
> Henk Bovenhuis and Bart Ducro
> Wageningen University
> The Netherlands

Jim Holland

USDA-ARS Plant Science Research Unit

Department of Crop Science

North Carolina State University

Phone: 919-513-4198

Fax: 919-515-7959

Received on Wed Jan 20 2010 - 13:00:17 EST

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