st: Re: Re: Anova

[David Airey <david.airey@vanderbilt.edu>]

> .
>
> I have an experiment where a component is stressed (nominally to  
> the same
>
> Sorry for not being explicit in my description. The component is  
> strecthed
> until it reaches a specified stress, the first value, and then held  
> for a 4
> hours and the stress at this time measured. Due to experimental  
> constarints
> it is not always possible to obtainn this first stress "exactly". The
> outcome is the difference between these two stresses. My concern  
> was that
> the value of the first stress may have an effect on the difference  
> ae a
> covariate or confounding effect, and I wanted to estimate or  
> eliminate this.
> Paul
>
> level) and the stress measured a constant time afterwards for 5  
> different
> materials. I wanted to investigate the effect of material on the  
> difference
> in stress giving me the simple model:
> anova diff system
> The problem is that the initial nominal stress is not constant and  
> may have
> en effect on diff.
> How can do I formulate this model? I tried anova diff f1, continuous 
> (f1)
> but f1 now enters the model as a both a main factor and a component of
> diff.
Sounds like you've got a factor for material with five levels, and  
measurements of stress on each material at two time points. Material  
you are treating as a fixed effect since you are specifically  
interested in each kind of material. Time as a factor with two levels  
you have decided to do away with and treat as a derived difference  
measure.

You are concerned about some experimental error in determining the  
first time point, which is supposed to represent a baseline. One way  
of dealing with this is to hope that error is not systematic, and  
examine many examples of each material. If you do this, then you will  
need a factor for specimen, nested in kind of material.

modeling difference:

anova difference material / specimen|material /

Even when you do this, if you model the difference between times of  
measurement, you can still use the first measurement as a covariate  
(I think).

modeling difference with covariate:

anova difference baseline material / specimen|material /, cont(baseline)

If you choose not to model the derived difference variable and  
modeled both time points directly, the design is a split plot (I think).

modeling times directly:

anova stress material/specimen|material time material*time/, repeated 
(time)

Post-hoc comparisons and contrasts using anova in Stata are a little  
under developed, however. For example, it is not possible to specify  
an alternate error term when using the matrix syntax of the test  
command. Online FAQ show convolutions to test such, using the cell  
means anova, but for most users, a cell means anova approach with  
complicated mixed model designs, as described in the online FAQ, is  
inaccessible. There are two commands written by others that can help  
a semi-manual computation of comparisons and contrasts with alternate  
error terms (do findit anovacontrast or findit sme). Obviously, I  
would prefer Stata incorporate improved versions of these commands. I  
cannot recommend Stata to colleagues who wish to analyze their data  
by ANOVA, because they invariable need to get beyond the omnibus  
tests and to determine simple main effects, comparisons at certain  
levels of a factor, etc., using pooled error terms or error terms  
specific to each comparison or contrast.

As a comparison, JMP makes it very easy to examine posthoc contrasts  
and comparisons for designed experiments with random effects. Even  
then, however, JMP seems to restrict the user to pooled error terms.

You can also make good use of Stata's mixed model command xtmixed for  
this situation. Each of the models above could be done with xtmixed.

-Dave


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