Re: MANCOVA: describing effect directions

On 06 Sep 2008 10:52:29 GMT, Niklaus Kuehnis
<kuehnik_0505@xxxxxxxxxxxxxx> wrote:

Ray Koopman <koopman@xxxxxx> wrote:
On Sep 4, 12:51 pm, Niklaus Kuehnis <kuehnik_0...@xxxxxxxxxxxxxx>
wrote:


c) How to plot an interaction between a binary IV and a covariate?
Run two bivariate regressions for each group and plot two linear
regressions?

Yes.

Thanks for you reply!

Interestingly, many textbooks say there is no such thing as an ANCOVA
with factor*covariate interaction. It seems to be an assumption of
classical ANCOVA that the slopes of different groups are equal. Thus,
an ANCOVA plot with regression lines with different slopes wouldn't
make sense.

I have read Cohen's "Applied Multiple Regression/Correlation Analysis
for the Behavioral Sciences" (1983). If I understand him correctly,
he agrees there is no factor*covariate interaction in "ANCOVA" but if
you interpret your analysis as a multiple regression with a binary
predictor it does make sense to look at the difference of slopes.

Maybe I shouldn't call it an ANCOVA if I am testing the interaction?

It does make sense to "look at the interaction" in terms of
testing the assumptions of ANCOVA. But it is a test of the
appropriateness or testability of the model and not a part
of a model. If it is significant, then you don't have a
legitimate, simple ANCOVA.

That raises the question of what is *reportable* if you find
the interaction to be nominally significant.

In the easiest case,
(a) the covariate is similar for all levels of the factor, and
(b) the "significance" of the interaction is *much* inferior
to the significance of the other tests that are interesting.
Then, you dismiss the interaction as trivial.

Otherwise, you have some work to do, to properly disentangle
what is going on and to describe it economically.

Your problem started with a MANOVA, where there are multiple
outcome variables. One big reason that I don't like MANOVA is
that it does a very fuzzy job of showing what you have, even if
it does manage to test a proper set of hypotheses, and comes
up with something that is "significant".

- Whatever tests you have are tests between covariates, etc.,
controlling for each other (just as in ordinary regression), and some
*combinations* of the outcome variables. The full model is
canonical correlation, and you are looking at canonical roots,
of which there will be several if there are not restrictions that
specify a single d.f. contrast.

Once you have a MANOVA outcome that is interesting, you
probably need to follow up with smaller analyses, using fewer
variables and using specific contrasts of variables.



--
Rich Ulrich
.

Relevant Pages

  • Re: MANCOVA: describing effect directions
    ... one binary categorical IV and several metric covariates. ... regression: if your data are naturalistic observations then you need ... How to plot an effect of a metric covariate on a single metric DV? ...
    (sci.stat.math)
  • Re: Residual Plot Question
    ... > independence of the errors on the observed Xs in a multiple regression. ... residual against x plot has patterns may not violate the ... > To check the stochastic independence of the residuals, ...
    (sci.stat.math)
  • Logistic regression with few successes
    ... I have an issue with regression on count data. ... I'm looking at collocations in linguistic data, that is, co-occurrences ... of the same linguistic structures at a certain distance (1<d<30 ... When I plot the model, I see things that don't look good at all: ...
    (sci.stat.math)
  • Re: inclusion criteria for regression covariates
    ... > the list of potential variables to include in the multiple regression. ... > the treatment variable and the covariate. ... in a model does NOT in any way depend on its slope being similar to ...
    (sci.stat.consult)
  • Re: Linearity- Multiple Regrression
    ... By "the assumption behind regression", ... at in the scatter plots of your Y vs any of the Xs that is relevant to ... You can't look at any plot about the ... When you try to visualize the functional relationship between Y and X1, ...
    (sci.stat.math)