Regression question

[Salbod]

Happy Saturday Everyone,



West and Aiken (1991) state, "The usual requirement for developing a
regression equation that includes a three-way interaction is that all first
order and second order terms must be included in the equation."



Here is my plan for a hierarchical regression analyses of attachment
(avoidance and anxiety scores) on Martial Status and Parent Bonding
Inventory (PBI).



Step 1:

Divorced (=1) (X1)



Step 2:

MomCare (X2)

MomOver (X3)

DadCare(X4)

DadOver(X5)



Step 3: (Second Order Interactions)

X2*X3 (Meaningful)

X4*X5 (Meaningful)



(X1*X2

X1*X3

X1*X4

X1*X5

X2*X4

X2*X5

X3*X4

X3*X5)



Step 4: (Third Order Interactions)

X1*X2*X3

X1*X4*X5



Question1: Step 3 contains a block of second order interactions not relevant
to the study; they are eating up precious dfs (-8). Is there any way to
remove them from the analysis?  Or as West and Aiken say, they are essential
for Step 4?



My  Answer: Whether I like it or not, they are essential for Step 4.



Question2:  Many moons ago, I read an article on the advantages of using
regression analysis rather than median splits when using the Bem Sex Role
Inventory. Does anyone have that reference or a more recent reference
demonstrating the advantages of the regression analysis over median splits?



Thank you in advance for any help or suggestions you can give me regarding
the above questions.





Stephen Salbod, Pace University, Psychology Department, NYC

[lts1]

Hi Stephen,

> Question2:  Many moons ago, I read an article on the advantages of using
> regression analysis rather than median splits when using the Bem Sex Role
> Inventory. Does anyone have that reference or a more recent reference
> demonstrating the advantages of the regression analysis over median splits?
>

MacCallum and colleagues do not recommend median splits.  They say the practice is "rarely defensible and often will yield misleading results."

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19-40.


    Best,
        Lisa

Lisa T. Stickney
Ph.D. Candidate
The Fox School of Business
     and Management
Temple University
[hidden email]

[F. Gabarrot]

Hello,

You may always avoid to use median-split, for the BSRI or for any other variable.
If your model contains only one continuous variable, the median-split procedure induce a substantial loss of statistical power (around 30-40%). If your model contains more than one variable, and if these variables have a non-zero correlation (or if group size are inequals), median-split procedure not only induces a loss a power, but it also may lead to spuriously significant results (notably for the non splitted variable). You may wish to read Maxwell and Delaney (1993) for further demonstration.

Maxwell, S. E., & Delaney, H. D. (1993). Bivariate median splits and spurious statistical significance. Psychological Bulletin, 113, 181-190.

Lisa Stickney wrote

Hi Stephen,

> Question2:  Many moons ago, I read an article on the advantages of using
> regression analysis rather than median splits when using the Bem Sex Role
> Inventory. Does anyone have that reference or a more recent reference
> demonstrating the advantages of the regression analysis over median splits?
>

MacCallum and colleagues do not recommend median splits.  They say the practice is "rarely defensible and often will yield misleading results."

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7, 19-40.


    Best,
        Lisa

Lisa T. Stickney
Ph.D. Candidate
The Fox School of Business
     and Management
Temple University
[e-mail]

[Burleson,Joseph A.]

I concur wholeheartedly with the other two comments on the advisability
of never using median splits. One might be forced, in some
circumstances, to use them for illustration purposes for the
uninitiated, or in an applied setting, but the underlying analyses
should involve the continuum. Other caveats apply if the continuous
covariates are not symmetrical and cannot be transformed.

Insofar as your regression model, yes, you may leave out any lower-order
interactions that are not antecedent ("parent") predictors to the
higher-order ("child") predictors that are interesting.

E.g., if you are only interested in two 3-ways: X1*X2*X3, and X1*X4*X5,
then the following 2-ways can be left out of the equation. They may,
however, be included, for their own sake/interest, but not as a prelude
to the above 3-ways:

X2*X4
X2*X5
X3*X4
X3*X5

As such, the following do need to be left in.

X1*X2
X1*X3
X1*X4
X1*X5

X2*X3

X4*X5

Joe Burleson

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Stephen Salbod
Sent: Saturday, May 05, 2007 12:12 PM
To: [hidden email]
Subject: Regression question

Happy Saturday Everyone,



West and Aiken (1991) state, "The usual requirement for developing a
regression equation that includes a three-way interaction is that all
first
order and second order terms must be included in the equation."



Here is my plan for a hierarchical regression analyses of attachment
(avoidance and anxiety scores) on Martial Status and Parent Bonding
Inventory (PBI).



Step 1:

Divorced (=1) (X1)



Step 2:

MomCare (X2)

MomOver (X3)

DadCare(X4)

DadOver(X5)



Step 3: (Second Order Interactions)

X2*X3 (Meaningful)

X4*X5 (Meaningful)



(X1*X2

X1*X3

X1*X4

X1*X5

X2*X4

X2*X5

X3*X4

X3*X5)



Step 4: (Third Order Interactions)

X1*X2*X3

X1*X4*X5



Question1: Step 3 contains a block of second order interactions not
relevant
to the study; they are eating up precious dfs (-8). Is there any way to
remove them from the analysis?  Or as West and Aiken say, they are
essential
for Step 4?



My  Answer: Whether I like it or not, they are essential for Step 4.



Question2:  Many moons ago, I read an article on the advantages of using
regression analysis rather than median splits when using the Bem Sex
Role
Inventory. Does anyone have that reference or a more recent reference
demonstrating the advantages of the regression analysis over median
splits?



Thank you in advance for any help or suggestions you can give me
regarding
the above questions.





Stephen Salbod, Pace University, Psychology Department, NYC