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Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

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Contributor
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Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

Hello everyone,


I need your professional opinion regarding a discriminant analysis...

Can you tell me whether it is justified to use DA for each factor separately (only main effects), or it must be conducted in one-way mode (combining factors groups to include interactions between them) and than use this grouping var. as DV in discriminant analysis, or is in that situation better to use multinomial and binary logistic regression for classification...


Thank you !!!!!!!



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Re: Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

My first inclination is to ask what is the response variable?  If this is a designed (as opposed to observational) study, you know that there are 12 separate groups.  Do you wish to use the response variable to distinguish them, or (inversely, I suppose) examine the effects of the factors on the outcome.

If this is observational, and your interest is in the former category, then I could understand a discriminant or cluster analysis.  For a designed study, I would suggest the logistic regression approach.  It all comes down to the substantive question you want to answer.

Steve Denham

Contributor
Posts: 33

Re: Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

Steve, thank you for your help....but once again I need your professional advice....


In 3-way ANOVA, i have some statistically significant interaction with no theoretical meaning..(I guess this is happening because of a crossover design and sample size)..


The question is, can I "ignore" this irrelevant interactions and look at the main effect only?


Thank you!!



Respected Advisor
Posts: 2,655

Re: Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

You can't really ignore them if they arise from the design.  They are critical in calculating predicted values/least squares means.  If they were non-significant, the point estimates wouldn't change substantively, but here they are going to shift location estimates and probably scale estimates as well.

Now if you have a strong theoretical reason that they could NOT interact (in any way imaginable), then I think you can model only those effects that actually might have an effect.

I suppose it's like using the height of the high tide as a covariate when fitting your data.  What if it was significant or had a significant interaction with other independent variables.  What do you do?

Another thought is to take the incomplete block approach, and regard the higher order interactions as being 'aliased' to the main effect, and then assuming that the effect size of the interaction is negligible compared to the main effect--and now that seems to me to be the best approach.  Look at effect sizes, rather than significances, and make a judgement as to the importance of the interaction based on relative effect size.

Steve Denham

Contributor
Posts: 33

Re: Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

Once again, thank you Steve your help....

There is one important thing that i forgot to mention in the last query about stat. significant interactions with no theoretical meaning....partial omega square for this effects is relative high (0,4 - 0,6), but p-value of Levene test for this design is highly non-significant    (1E-10)...because this and small sample size, i decide (for ANOVA) to lower my alpha level from 0,05 to 0,01 to compensate for type-1 error...


As a result of this, previously signif. interactions is now stat. non-significant....I hope that I have acted in accordance with the rules of statistics

Best wishes,

Tomislav

Contributor
Posts: 33

Re: Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

upss...p-value of Levene test is higly signif..

Respected Advisor
Posts: 2,655

Re: Performing discriminant analysis with data organized in 3 x 2 x 2 factorial design

So there is a lot of heterogeneity, and I mean, A LOT.  The p values for all tests probably are inaccurate, whether you cut off at 0.05 or 0.01 may be meaningless.

You need to come up with an analysis that reflects the heterogeneity correctly.  So, to start with, what is the dependent variable?  The distribution that it takes on will have a profound effect, both on Levene's test (which assumes normality) and the subsequent tests of factors in the model.

Steve Denham

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