SPSSX Discussion

Regression 2-way Interactions?

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Salbod

Regression 2-way Interactions?

Good Afternoon Friends,

I have a question regarding two-way interactions in regression analysis. I have three variables (gender, A, B, the latter two are continuous variables). I am interested only in two 2-way interactions (gender*A, gender*B) out of three. I plan to enter at Step 1: gender; Step 2: A, B; Step 3: gender*A, gender*B. To test these 2-way interactions (R square change), do I need to include the A*B interaction too?

Any suggestion or references will be greatly appreciated.

Stephen Salbod, Pace University, NYC

Swank, Paul R

Re: Regression 2-way Interactions?

No, you do not have to specify A*B if you have no reason to. However, sometimes interactions occur when we don’t expect them.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Salbod, Mr. Stephen
Sent: Friday, February 25, 2011 10:25 AM
To: [hidden email]
Subject: Regression 2-way Interactions?

Good Afternoon Friends,

Any suggestion or references will be greatly appreciated.

Stephen Salbod, Pace University, NYC

Ryan

Re: Regression 2-way Interactions?

In reply to this post by Salbod

Stephen,

The answer to your question has already been provided. You do not have
to include the A*B interaction term to obtain the usual interpretation
of the A*gender or B*gender. The a*b interaction term is not a lower
order term for the interactions of interest.

The model that includes all possible fixed effects can be written as follows:

y = b0
+ b1*A
+ b2*B
+ b3*gender
+ b4*A*B
+ b5*A*gender
+ b6*B*gender
+ b7*A*B*gender

The coefficients (b0, b1, b2, ... , b7) associated with any excluded
terms are set to zero. Whether that is a reasonable assumption should
be examined.

Ryan

On Fri, Feb 25, 2011 at 11:24 AM, Salbod, Mr. Stephen <[hidden email]> wrote:

> Good Afternoon Friends,
>
> I have a question regarding two-way interactions in regression analysis. I
> have three variables (gender, A, B, the latter two are continuous
> variables). I am interested only in two 2-way interactions (gender*A,
> gender*B) out of three. I plan to enter at Step 1: gender; Step 2: A, B;
> Step 3: gender*A, gender*B. To test these 2-way interactions (R square
> change), do I need to include the A*B interaction too?
>
> Any suggestion or references will be greatly appreciated.
>
> Stephen Salbod, Pace University, NYC

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Rich Ulrich

Re: Regression 2-way Interactions?

In reply to this post by Salbod

As others have said - No, you do not need to include the interaction.

If you are creating your own dummy variables for the interactions,
be sure to compute them as the product of the *centered* variables.

- When you use a regression-like program that lets you enter
interactions as A*B (for instance), it is always safer to use
centered versions of A and B, too, because the programs do not
always do the centering... For some hypotheses, it does not matter,
but you minimize your risk if you do it the safe way.

--
Rich Ulrich

-------------------------------- original message
Date: Fri, 25 Feb 2011 16:24:37 +0000
From: [hidden email]
Subject: Regression 2-way Interactions?
To: [hidden email]

Good Afternoon Friends,
I have a question regarding two-way interactions in regression analysis. I have three
variables (gender, A, B, the latter two are continuous variables). I am interested only
in two 2-way interactions (gender*A, gender*B) out of three. I plan to enter at
Step 1: gender; Step 2: A, B; Step 3: gender*A, gender*B. To test these 2-way interactions
(R square change), do I need to include the A*B interaction too?

Any suggestion or references will be greatly appreciated.
Stephen Salbod, Pace University, NYC

=====================
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

Salbod

Re: Regression 2-way Interactions?

In reply to this post by Swank, Paul R

Thanks RB, Rich and Paul for getting back to me.

That is exactly what is happening here. At the beginning, I separately looked at Y = b0+ b1gender + b2A + b3gender*A and Y = b0 + b1gender + b2B + b3gender*B. All variables had been centered. The test of the increment in R squared at Step 3 (interaction) was significant only for A but not for B. However, when I incorporate interactions into a single model, Step 3 reveals both interactions to be significant. I assumed that suppression is present; that, I might need to include all interactions involving the two predictors.

I feel I should report the complete model (7 effects) and footnote the separate regressions.

Any comments will be greatly appreciated. --Steve

From: Swank, Paul R [mailto:[hidden email]]
Sent: Friday, February 25, 2011 11:53 AM
To: Salbod, Mr. Stephen; [hidden email]
Subject: RE: Regression 2-way Interactions?

No, you do not have to specify A*B if you have no reason to. However, sometimes interactions occur when we don’t expect them.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

Good Afternoon Friends,

Any suggestion or references will be greatly appreciated.

Stephen Salbod, Pace University, NYC

Swank, Paul R

Re: Regression 2-way Interactions?

It would not have to be suppression. It might be the increase in power by adding additional predictors to the model that account for substantial variance. Look at the parameter estimates. If the parameter for the gender*b interaction gets larger but it standard error does not change, then it could be suppression. If the parameter is the same size but the standard error is smaller, then it’s more likely the increase in power. But I would report it.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Salbod, Mr. Stephen
Sent: Friday, February 25, 2011 3:00 PM
To: [hidden email]
Subject: Re: Regression 2-way Interactions?

Thanks RB, Rich and Paul for getting back to me.

I feel I should report the complete model (7 effects) and footnote the separate regressions.

Any comments will be greatly appreciated. --Steve

From: Swank, Paul R [mailto:[hidden email]]
Sent: Friday, February 25, 2011 11:53 AM
To: Salbod, Mr. Stephen; [hidden email]
Subject: RE: Regression 2-way Interactions?

No, you do not have to specify A*B if you have no reason to. However, sometimes interactions occur when we don’t expect them.

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

Good Afternoon Friends,

Any suggestion or references will be greatly appreciated.

Stephen Salbod, Pace University, NYC

Ryan

Re: Regression 2-way Interactions?

In reply to this post by Salbod

I generate data BELOW for the scenario where one observes
non-significant A*gender and B*gender interaction terms when the A*B
interaction term is excluded from the model. However, when A*B is
included in the model, A*gender and B*gender effects become
signfiicant at alpha=.05. The interaction, A*B, is explaining a
significant amount of variance which is increasing statistical power
for the other two-way interaction terms. (Note that I specify b7 =
0.00 in the simulation).

Ryan
--

***Generate data.

*Set seed for random number generator.
set seed 98765432.

new file.
inp pro.

*Start loop.
loop ID= 1 to 200.

*Fix parameters.
comp b0 = 1.62.
comp b1 = 0.90.
comp b2 = 0.51.
comp b3 = 1.20.
comp b4 = 0.53.
comp b5 = 0.30.
comp b6 = 0.42.
comp b7 = 0.00.

*Compute random variables.
comp A = rv.normal(0,1).
comp B = rv.normal(0,1).
comp gender = rv.bernoulli(0.5).
comp error = rv.normal(0,1).

*Construct linear function.
comp y = b0
+ b1*A
+ b2*B
+ b3*gender
+ b4*A*B
+ b5*A*gender
+ b6*B*gender
+ b7*A*B*gender
+ error.

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

*Delete no longer needed variables.
delete variables b0 b1 b2 b3 b4 b5 b6 b7 error.

*Compute interaction terms.
comp A_B = A*B.
comp A_gender = A*gender.
comp B_gender = B*gender.
comp A_B_gender = A*B*gender.
execute.

*Fit full model.
regression
/statistics coeff outs r anova
/dependent y
/method = enter A B gender A_B A_gender B_gender A_B_gender.

*Fit model without 3-way interaction.
regression
/statistics coeff outs r anova
/dependent y
/method = enter A B gender A_B A_gender B_gender.

*Fit model without 3-way interaction or A*B interaction.
regression
/statistics coeff outs r anova
/dependent y
/method = enter A B gender A_gender B_gender.

On Fri, Feb 25, 2011 at 3:59 PM, Salbod, Mr. Stephen <[hidden email]> wrote:

> Thanks RB, Rich and Paul for getting back to me.
>
>
>
> That is exactly what is happening here. At the beginning, I separately
> looked at Y = b0+ b1gender + b2A + b3gender*A and Y = b0 + b1gender + b2B +
> b3gender*B. All variables had been centered. The test of the increment in R
> squared at Step 3 (interaction) was significant only for A but not for B.
> However, when I incorporate interactions into a single model, Step 3 reveals
> both interactions to be significant. I assumed that suppression is present;
> that, I might need to include all interactions involving the two
> predictors.
>
>
>
> I feel I should report the complete model (7 effects) and footnote the
> separate regressions.
>
>
>
> Any comments will be greatly appreciated. --Steve
>
>
>
>
>
> From: Swank, Paul R [mailto:[hidden email]]
> Sent: Friday, February 25, 2011 11:53 AM
> To: Salbod, Mr. Stephen; [hidden email]
> Subject: RE: Regression 2-way Interactions?
>
>
>
> No, you do not have to specify A*B if you have no reason to. However,
> sometimes interactions occur when we don’t expect them.
>
>
>
> Dr. Paul R. Swank,
>
> Professor and Director of Research
>
> Children's Learning Institute
>
> University of Texas Health Science Center-Houston
>
>
>
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Salbod, Mr. Stephen
> Sent: Friday, February 25, 2011 10:25 AM
> To: [hidden email]
> Subject: Regression 2-way Interactions?
>
>
>
> Good Afternoon Friends,
>
> I have a question regarding two-way interactions in regression analysis. I
> have three variables (gender, A, B, the latter two are continuous
> variables). I am interested only in two 2-way interactions (gender*A,
> gender*B) out of three. I plan to enter at Step 1: gender; Step 2: A, B;
> Step 3: gender*A, gender*B. To test these 2-way interactions (R square
> change), do I need to include the A*B interaction too?
>
> Any suggestion or references will be greatly appreciated.
>
> Stephen Salbod, Pace University, NYC