in article [EMAIL PROTECTED], Tracey
Continelli at [EMAIL PROTECTED] wrote on 6/20/01 7:06 AM:
> "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
I hope everyone in the social sciences using product terms or "moderator
regression" reads Tracey's thoughtful comments above. Failing to realize
the coefficient for one of the components of a product is the effect of that
variable when the other variable of the product is zero is one of my
candidates for most common statistical error in the social sciences. Mean
centering is indeed quite useful, even if one does not have products in the
model. Also note that mean centering will always reduce the correlation
between the product and its components and if the component distributions
are symmetric it will reduce it to zero. There always exists a change of
origin for the components that will make the correlation zero; hence, the
colinearity warnings when testing products are not meaningful.
Gary McClelland
Univ of Colorado
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