Running a 3 -Way ANOVA reduced Model

[Donna Alden-Bugden]

I am wondering about running a reduced/custom model
 
I have dependent variable quality of life in last month
independent variables: political affiliation, exercise, eat 3 meals a day
 
in a previous test, political affiliation is found to not be significant so
our instructor has asked us to run a reduced/custom model on the interaction
of eat*exercise including the main effects....however she said to include
all the dependent and independent variables (including political
affiliation). The video we were given says to include all independent
variables and the only interaction you are interested...and it shows all 3
variables being copied but only one interaction term
 
so why would you run a custom model on all 3 variables when you only want to
look at the interaction and the main effects of 2 factors.
 
under analyze I go to GLM>Univariate   depend variable: qualcur;
independent variables: exerciser, eat, polaff
model custom: include all 3 variables and interaction of eat*exerciser
 
I plot only eat*exerciser
post hoc: eat only as the other variables have only 2 groups each
options: includes factors and factor interactions: eat, exerciser, polaff
and eat*exerciser
 
not the output comes out...and polaff is used in the formulas to determine F
scores, degrees of freedom, etc but it just really seems odd that if I don't
care about polaff as I found it to be insignificant, why am I including it
at all in the variables...why can't I just leave it out altogether and in
essence do a 2 way anova on the variables eat and exerciser?
 
Donna
 
 
 
****************************************************************************
****
Donna L. Alden-Bugden, BScN, RN(EP), MN (ANP), DNP-Student
NPCanada.ca - Promoting Nurse Practitioners in Canada
Family Nurse Practitioner - Winnipeg, Manitoba
Doctoral Student - Cleveland, Ohio
[hidden email]
Alternate E-mail:
[hidden email]
http://www.NPCanada.ca <http://www.npcanada.ca/>  
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***
 

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[Samir Omerovic]

Hi to all,

I was wondering is there a way to run a fixed effects model in SPSS. I
recently got some data that supposedly should be analyzed with fixed
effects model so I am looking for a way to do it. Could anyone recommend
some good book that deals with this model also?

Regards

Samir


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Samir Omerovic

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[Richard Ristow]

At 04:27 AM 3/11/2008, [Samir Omeroviæ] wrote:

>I was wondering is there a way to run a fixed effects model in SPSS.

 From the menus, try Analyze>Compare
Means>One-Way ANOVA... if you have a single categorical independent variable.

Otherwise, look at Analyze>General Linear Model>Univariate...

Or, in syntax, look at command ANOVA.


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[xiexy]

I have encounted a similar question with your post in 3 years ago. And i am wondering about running a custom model also. Do you have a clear answer to date?
Second, If i have three fixed factors (a,b and c), can i run reduced model including the main effect (a, b and c) and my interested interaction term (a*b, a*b*c)，and excluding other possible interaction terms, based on my theoretical hypotheses. BTW, the result of custom model is different to the result of the full model obviously.  

Best wishes,




As mentioned:

I am wondering about running a reduced/custom model
 
I have dependent variable quality of life in last month
independent variables: political affiliation, exercise, eat 3 meals a day
 
in a previous test, political affiliation is found to not be significant so
our instructor has asked us to run a reduced/custom model on the interaction
of eat*exercise including the main effects....however she said to include
all the dependent and independent variables (including political
affiliation). The video we were given says to include all independent
variables and the only interaction you are interested...and it shows all 3
variables being copied but only one interaction term
 
so why would you run a custom model on all 3 variables when you only want to
look at the interaction and the main effects of 2 factors.
 
under analyze I go to GLM>Univariate   depend variable: qualcur;
independent variables: exerciser, eat, polaff
model custom: include all 3 variables and interaction of eat*exerciser
 
I plot only eat*exerciser
post hoc: eat only as the other variables have only 2 groups each
options: includes factors and factor interactions: eat, exerciser, polaff
and eat*exerciser
 
not the output comes out...and polaff is used in the formulas to determine F
scores, degrees of freedom, etc but it just really seems odd that if I don't
care about polaff as I found it to be insignificant, why am I including it
at all in the variables...why can't I just leave it out altogether and in
essence do a 2 way anova on the variables eat and exerciser?
 
Donna

[Bruce Weaver]

The following is an excerpt from the Aiken & West (1991) book on interactions in multiple regression models.  It is relevant insofar as your ANOVA model is equivalent to a regression model using k-1 indicator variables for each factor (where k = the number of levels for the factor).

--- Start of excerpt ---

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. [End note 1]

End note 1. Social science research areas differ in their position about the permissibility of omitting lower order terms in regression equations.  The only case in which a justification for this practice may be offered is when strong theory dictates a lower order effect must equal zero (see Fisher, 1988; Kmenta, 1986).

--- End of excerpt ---

For a three-way interaction (A*B*C), the lower order terms are the 3 main effects (A, B, C), and all two-way interactions (A*B, A*C, B*C).

References

Aiken, L.S. & West, S.G. (1991). Multiple regression: Testing and interpreting interactions.  Newbury Park, CA: Sage.

Fisher, G.A. (1988). Problems in the use and interpretation of product variables. In J. Scott Long (Ed.), Common problems/proper solutions: Avoiding error on quantitative research (pp. 84-107). Newbury Park, CA: Sage.

Kmenta, J. (1986). Elements of econometrics (2nd Ed.). New York: Macmillan.

HTH.

xiexy wrote

I have encounted a similar question with your post in 3 years ago. And i am wondering about running a custom model also. Do you have a clear answer to date?
Second, If i have three fixed factors (a,b and c), can i run reduced model including the main effect (a, b and c) and my interested interaction term (a*b, a*b*c)，and excluding other possible interaction terms, based on my theoretical hypotheses. BTW, the result of custom model is different to the result of the full model obviously.  

Best wishes,




As mentioned:

I am wondering about running a reduced/custom model
 
I have dependent variable quality of life in last month
independent variables: political affiliation, exercise, eat 3 meals a day
 
in a previous test, political affiliation is found to not be significant so
our instructor has asked us to run a reduced/custom model on the interaction
of eat*exercise including the main effects....however she said to include
all the dependent and independent variables (including political
affiliation). The video we were given says to include all independent
variables and the only interaction you are interested...and it shows all 3
variables being copied but only one interaction term
 
so why would you run a custom model on all 3 variables when you only want to
look at the interaction and the main effects of 2 factors.
 
under analyze I go to GLM>Univariate   depend variable: qualcur;
independent variables: exerciser, eat, polaff
model custom: include all 3 variables and interaction of eat*exerciser
 
I plot only eat*exerciser
post hoc: eat only as the other variables have only 2 groups each
options: includes factors and factor interactions: eat, exerciser, polaff
and eat*exerciser
 
not the output comes out...and polaff is used in the formulas to determine F
scores, degrees of freedom, etc but it just really seems odd that if I don't
care about polaff as I found it to be insignificant, why am I including it
at all in the variables...why can't I just leave it out altogether and in
essence do a 2 way anova on the variables eat and exerciser?
 
Donna

[xiexy]

Thanks for Bruce's reply. Especially, you gave a comprehensive and professional interpretation.
However, i confusioned for a long time about this issue. Contradictionary argument as below:

--- Start of excerpt ---
In Univariate of GLM,......The default is for SPSS to create interactions among all fixed factors. So if you have 5 fixed factors and don't want to test 5-way interactions that you'll never be able to interpret, you'll need to create a custom model by clicking Model and removing some of the interactions

Article Source: http://EzineArticles.com/1902896
--- End of excerpt ---

[Bruce Weaver]

What Aiken & West are saying is that if you DO include the 5-way interaction, you should also include all lower order terms involving those 5 factors.  But there is nothing wrong with excluding some interaction terms.  E.g., suppose the highest order interaction I included (for a model with 5 fixed factors) is the A*B*C interaction.  I.e., I have in my model:

   A B C D E ABC

According to A&W are saying, my model should also include all two-way interactions involving A, B, and C.  But it would not have to necessarily include the other possible two-way interactions (AD, AE, BD, BE, CD, CE).  

   A B C D E AB AC BC ABC

HTH.

Cheers,
Bruce

xiexy wrote

Thanks for Bruce's reply. Especially, you gave a comprehensive and professional interpretation.
However, i confusioned for a long time about this issue. Contradictionary argument as below:

--- Start of excerpt ---
In Univariate of GLM,......The default is for SPSS to create interactions among all fixed factors. So if you have 5 fixed factors and don't want to test 5-way interactions that you'll never be able to interpret, you'll need to create a custom model by clicking Model and removing some of the interactions

Article Source: http://EzineArticles.com/1902896
--- End of excerpt ---

[xiexy]

Thanks for your helpful reply!!!

However, i think full model is more data-driven than custom model, some interaction term means nothing from theoretical side...

[Swank, Paul R]

But if they exist, whether of interest or not, ignoring them will bias the other parameters in the model.

Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of xiexy
Sent: Friday, April 22, 2011 3:02 AM
To: [hidden email]
Subject: Re: Running a 3 -Way ANOVA reduced Model

Thanks for your helpful reply!!!

However, i think full model is more data-driven than custom model, some
interaction term means nothing from theoretical side...


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[xiexy]

Thank Paul and all. However, i think there is much difference between regression and Univariate, the latter means experimental manipulation generally from a research design perspective. Obviously, we can manipulate and make nearly zero correlation among treatments (predictors) in experiment; but, So-called "zero-correlation" is seems unlikely in field setting from a research design perspective. Thus, In order to get an rigor statistic, it is reasonable that all possible combines(A*B, A*C, B*C, A*B*C) among A×B×C regression should be included. However, does it have the same requirement in UNIVARIATE (experiment) even on  suspicion of data-driven?

[Swank, Paul R]

Actually, there is no difference between regression and ANOVA. There are differences in design. ANOVA can be used with observed categorical variables as well as manipulated ones and regression can be used to analyze experimental designs. I mean, that's what general linear models are, regression. The correlation among the predictors has nothing to do with whether of not you include interactions. The research question of hypothesis determines this. You do need to be careful about multicollinearity in designs with interactions with observed variables, but this is not usually a severe problem. You can have questions about interactions in regression models and experiments where you expect additive effects. Typically, however, interactions are more likely to be hypothesized with factorial experiments. And in cases of, say, ANCOVA designs, the interaction is tested often as it is the test of an assumption for ANCOVA. I disagree that all possible interactions must be included, simply because they can. One needs to have some reason for including high level interactions.

Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of xiexy
Sent: Tuesday, April 26, 2011 1:13 AM
To: [hidden email]
Subject: Re: Running a 3 -Way ANOVA reduced Model

Thank Paul and all. However, i think there is much difference between
regression and Univariate, the latter means experimental manipulation
generally from a research design perspective. Obviously, we can manipulate
and make nearly zero correlation among treatments (predictors) in
experiment; but, So-called "zero-correlation" is seems unlikely in field
setting from a research design perspective. Thus, In order to get an rigor
statistic, it is reasonable that all possible combines(A*B, A*C, B*C, A*B*C)
among A×B×C regression should be included. However, does it have the same
requirement in UNIVARIATE (experiment) even on  suspicion of data-driven?

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