three way interaction vs separate analysis with 2 way interactione

[Ann-3]

Hi

maybe some of you have an opinion about a question i have. help is as usual
appreciated:)

i have two potential moderators 1 dichotomous variable and 1 continuous
variable.

is there a difference if i run a three way interaction vs splitting my
sample with help of my dichotomous variable and running 2 way interactions
with the cont. moderator?

the only advantage of the three way interaction i can come up with is to
actually have a significance test of the dichotomous variable being a
moderator, but on the other hand it gets also very complex regarding to
interpretation.

thanks for your help!

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[Maguin, Eugene]

Ann,

I guessing that you are comtemplating a regression equation like this, where
dv and iv have the usual meanings and dm and cm are 'dichotomous moderator'
and 'continuous moderator', respectively,

Dv = iv, cm, dm, iv*cm, iv*dm, iv*cm*dm.

versus

Dv = iv, cm, iv*cm for dm = 0.
Dv = iv, cm, iv*cm for dm = 1.

Notes. iv*cm is the interaction term for iv and cm. 'for dm = 0' means
regression equation is solved for the subset of cases with the first value
of dm.

These two equation sets are apples and oranges. The answer to what to do has
nothing to do with statistics. The correct answer is determined by the
question you want an answer to.

Gene Maguin



>>maybe some of you have an opinion about a question i have. help is as
usual
appreciated:)

i have two potential moderators 1 dichotomous variable and 1 continuous
variable.

is there a difference if i run a three way interaction vs splitting my
sample with help of my dichotomous variable and running 2 way interactions
with the cont. moderator?

the only advantage of the three way interaction i can come up with is to
actually have a significance test of the dichotomous variable being a
moderator, but on the other hand it gets also very complex regarding to
interpretation.

=====================
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[Bruce Weaver]

In Gene's first model, the t-test for the iv*cm*dm term can be used to test the null hypothesis that the nature of the iv*cm interaction (whatever it happens to be) does not depend on the level of dm.  I.e., it says that the iv*cm interaction is the same regardless of whether dm=0 or dm=1.  If that t-test is resoundingly non-significant, and if the sample size is adequate, and if you have no reason (e.g., theory, prior findings) to suspect that there is a 3-way interaction, then you might want to simplify the model by excluding the 3-way interaction.  

On the other hand, if the 3-way interaction is statistically significant, or if it is expected for some reason, my preference would be to use Gene's first model.  From it, you can derive all of the tests you might need.  The Aiken & West (1991) book on interaction in regression models is very good at explaining all of this.  If you are at a university or college, your library probably has a copy.

HTH.

Gene Maguin wrote

Ann,

I guessing that you are comtemplating a regression equation like this, where
dv and iv have the usual meanings and dm and cm are 'dichotomous moderator'
and 'continuous moderator', respectively,

Dv = iv, cm, dm, iv*cm, iv*dm, iv*cm*dm.

versus

Dv = iv, cm, iv*cm for dm = 0.
Dv = iv, cm, iv*cm for dm = 1.

Notes. iv*cm is the interaction term for iv and cm. 'for dm = 0' means
regression equation is solved for the subset of cases with the first value
of dm.

These two equation sets are apples and oranges. The answer to what to do has
nothing to do with statistics. The correct answer is determined by the
question you want an answer to.

Gene Maguin



>>maybe some of you have an opinion about a question i have. help is as
usual
appreciated:)

i have two potential moderators 1 dichotomous variable and 1 continuous
variable.

is there a difference if i run a three way interaction vs splitting my
sample with help of my dichotomous variable and running 2 way interactions
with the cont. moderator?

the only advantage of the three way interaction i can come up with is to
actually have a significance test of the dichotomous variable being a
moderator, but on the other hand it gets also very complex regarding to
interpretation.

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[Ann-3]

thanks to gene and bruce for your answer.

the dichot. moderator is gender, so i just splited the sample and calculated
the 2 way interactions for men and women seperately.

my assumption was that if i for example get a sign. interaction for men but
not for women, that i can claim that there is a gender difference.

but as i understand you two, you both would recommend a three way
interaction model.

gene you wrote the following 'These two equation sets are apples and
oranges. The answer to what to do has nothing to do with statistics. The
correct answer is determined by the question you want an answer to. '

can you give an example when you would go for split sample with 2 way
interactions. thanks for your helpful input!

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[Maguin, Eugene]

Ann,

>>the dichot. moderator is gender, so i just split the sample and calculated
the 2 way interactions for men and women seperately.

>>my assumption was that if i for example get a sign. interaction for men
but
not for women, that i can claim that there is a gender difference.

Gene: You can claim it but as a reviewer I don't think I'd accept it. For
instance, suppose the two-way interaction coefficient was -.03 (se=.06) for
men and +.03 (se=.07) for women. Neither is significant and the signs are
different. I wouldn't believe that women and differ.


>>but as i understand you two, you both would recommend a three way
interaction model.

>>gene you wrote the following 'These two equation sets are apples and
oranges. The answer to what to do has nothing to do with statistics. The
correct answer is determined by the question you want an answer to. '

>>can you give an example when you would go for split sample with 2 way
interactions. thanks for your helpful input!

Gene: Not offhand. But, I'd bet that if you stated your hypothesis or
question, it would imply a three way interaction.

Gene Maguin

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[Burleson,Joseph A.]

One can get a significant interaction in which for each gender there are opposite-sign 2-way interactions, but neither is significantly different from zero.

The 3-way interaction is still significant.

The "simple 2-way" effects are then tested, each for their own significance; they may or may not be, each in their own right, significantly different from zero. But the original 3-way interaction was explicitly NOT testing whether either (or both) was significantly different from zero. IT was testing whether the 2-way interaction was parallel for the two genders.

So: report the 3-way from the total n analysis. Then "decompose" the interaction, if desired and report the significance of each from zero.

Joe Burleson

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Gene Maguin
Sent: Tuesday, July 20, 2010 1:36 PM
To: [hidden email]
Subject: Re: three way interaction vs separate analysis with 2 way interactione

Ann,

>>the dichot. moderator is gender, so i just split the sample and calculated
the 2 way interactions for men and women seperately.

>>my assumption was that if i for example get a sign. interaction for men
but
not for women, that i can claim that there is a gender difference.

Gene: You can claim it but as a reviewer I don't think I'd accept it. For
instance, suppose the two-way interaction coefficient was -.03 (se=.06) for
men and +.03 (se=.07) for women. Neither is significant and the signs are
different. I wouldn't believe that women and differ.


>>but as i understand you two, you both would recommend a three way
interaction model.

>>gene you wrote the following 'These two equation sets are apples and
oranges. The answer to what to do has nothing to do with statistics. The
correct answer is determined by the question you want an answer to. '

>>can you give an example when you would go for split sample with 2 way
interactions. thanks for your helpful input!

Gene: Not offhand. But, I'd bet that if you stated your hypothesis or
question, it would imply a three way interaction.

Gene Maguin

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[Ryan]

Ann,

I have some concerns about an equation presented in a previous post.
In particular, I do not agree with fitting a model that includes a
3-way interaction term that excludes any of the  lower level 2-way
interactions. I typically include all lower level interactions when
testing an upper level interaction.

To avoid confusion it's useful to write out the equation, particularly
when dealing with higher-level interaction terms. If you have two
dichotomous variables and one continuous variable, then let A2 and B2
be indicators of the dichtomous variables and X be the continuous
variable. Lowercase letters are coefficients. (I've adapted this
notation from a previous post presented to me a while back). I made
the first levels of the dichomtous variables the referent levels (a1
and b1).

y = m
    + a2*A2
    + b2*B2
    + c*X
    + ab22*A2*B2
    + ac2*A2*X
    + bc2*B2*X
    + abc22*A2*B2*X

I would start by testing the 3-way interaction by fitting the full
model presented above. As Bruce suggested, if this is not significant
and previous research or theory does NOT suggest a 3-way interaction,
then you can consider dropping the 3-way interaction. How would we
test this three-way interaction using  the REGRESSION procedure in
SPSS?

I'll start by generating some data and then fit the model. I'm
generating data that will result in a significant 3-way interaction
effect. If you want to make the 3-way interaction non-significant,
then change the beta coefficient from 7 to 0. (Consider mean-centering
continuous variable(s) before entering them into regression models
that have interaction terms)

Ryan

--

set seed 98765432.
new file.

inp pro.

loop ID= 1 to 100000.

comp beta0 = 0.
comp beta1 = 1.
comp beta2 = 2.
comp beta3 = 3.
comp beta4 = 4.
comp beta5 = 5.
comp beta6 = 6.
comp beta7 = 7.

     comp A2 = rv.bernoulli(0.5).
     comp B2 = rv.bernoulli(0.5).
     comp X = normal(2).
     comp e = normal(2).

     comp y = beta0
              + beta1*A2
              + beta2*B2
              + beta3*X
              + beta4*A2*B2
              + beta5*A2*X
              + beta6*B2*X
              + beta7*A2*B2*X
              + e.

     end case.
   end loop.
end file.
end inp pro.
exe.

delete variables beta0 beta1 beta2 beta3 beta4 beta5 beta6 beta7 e.

    comp A2B2 = A2 * B2.
    comp A2X = A2 * X.
    comp B2X = B2 * X.
    comp A2B2X = A2 * B2 * X.
    exe.

REGRESSION
  /STATISTICS COEFF OUTS R ANOVA
  /DEPENDENT y
  /METHOD=ENTER A2 B2 X A2B2 A2X B2X A2B2X.

On Tue, Jul 20, 2010 at 3:01 AM, ann <[hidden email]> wrote:

> thanks to gene and bruce for your answer.
>
> the dichot. moderator is gender, so i just splited the sample and calculated
> the 2 way interactions for men and women seperately.
>
> my assumption was that if i for example get a sign. interaction for men but
> not for women, that i can claim that there is a gender difference.
>
> but as i understand you two, you both would recommend a three way
> interaction model.
>
> gene you wrote the following 'These two equation sets are apples and
> oranges. The answer to what to do has nothing to do with statistics. The
> correct answer is determined by the question you want an answer to. '
>
> can you give an example when you would go for split sample with 2 way
> interactions. thanks for your helpful input!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>

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