"mccovey@psych" <[EMAIL PROTECTED]> wrote in message
news:<[EMAIL PROTECTED]>...
> in article [EMAIL PROTECTED], Tracey
> Continelli at [EMAIL PROTECTED] wrote on 6/13/01 4:14 PM:
>
> > "Mike Tonkovich" <[EMAIL PROTECTED]> wrote in message
> > news:<3b20f210_1@newsfeeds>...
> >> Was hoping someone might be able to confirm that my approach for comparing 2
> >> slopes was correct.
> >>
> >> I ran an analysis of covariance using PROC GLM (in SAS) with an interaction
> >> statement. My understanding was that a nonsignificant interaction term
> >> meant that the slopes were the same, and vice versa for a significant
> >> interaction term. Is this correct and is this the best way to approach this
> >> problem with SAS? Any help would certainly be apprectiated.
> >>
> >> Mike Tonkovich
> >>
> >> --
> >> Michael J. Tonkovich, Ph.D.
> >> Wildlife Research Biologist
> >> ODNR, Division of Wildlife
> >> [EMAIL PROTECTED]
> >
> > The slopes need not be "the same" if the interaction term is
> > non-significant, BUT, the difference between them will not be
> > statistically significant. If the differences between the slops *are*
> > statistically significant, this will be reflected in a statistically
> > significant product term. I have preferred using regression analyses
> > with interaction terms, which can be easily incorporated by simply
> > multiplying the variables together and then running the regression
> > equation with each independent variable plus the product term [which
> > is simply another name for the interaction term]. The results are
> > much more straightforward in my mind.
> >
> > Tracey Continelli
> > SUNY at Albany
>
>
> I agree completely but there can be problems interpreting the regression
> Output (e.g., mistakes like talking about "main effects"). For advice on
> avoiding the common interpretation pitfalls, see
>
> Aiken & West (1991). Multiple regression: Testing and interpreting
> interactions. Sage.
>
> Irwin & McClelland (2001). In Journal of Marketing Research.
>
> Gary McClelland
> Univ of Colorado
Quite so. Once you add the product term, the interpretation changes,
and the parameter estimates are now known as "simple main effects."
The interpretation is pretty straightforward however. The parameter
estimate, or slope, for your focal independent variable in the
interaction model simply represents the effect of your independent
variable upon your dependent variable when your moderator variable is
equal to zero, holding constant all other independent variables in
your model. The same may be said for the slope of your moderator
variable - it represents the effect of that variable upon your
dependent variable when your focal independent variable is equal to
zero. Because in my research [the social science variety] that
information isn't terribly useful [because most of the time you won't
realistically see the moderator variable at zero, i.e., a zero crime
rate or a zero poverty rate], what I will do is a "mean centering"
trick. I'll subtract the mean from the moderator variable, rerun the
equation with the new mean centered variable and product term, and NOW
the parameter estimates of the simple main effects are meaningful for
me. Now, when I look at the parameter estimates of the focal
independent variable, it is telling me the effect of that independent
variable upon the dependent variable when my moderator variable is at
its mean. The actual product term remains identical to the original
equation [of course], but now the simple main effects are
realistically meaningful. I'll also apply the same technique for when
the moderator variable is 2 standard deviations below the mean, 1
below the mean, all the way up to 2 standard deviations above the
mean. This gives one a nice graphic sense of the way in which the
slope between your focal independent variable and your dependent
variable changes with successive changes in your moderator variable.
Tracey Continelli
Doctoral candidate
SUNY at Albany
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