Re: Statistical methods to investigate interactions between factors and continuous covariates

[Kersting, Nicole]

Hi all,
 
I ran an ANCOVA model which yielded a significant interaction between a
fixed factor and a continuous covariate.  I am interested in
investigating the interaction further but I ran into the following
problem:  I created a median split in the continuous covariate, which in
combination with the factor gave me four means for pairwise comparisons.
While I realize all the issues attached to median splits, I have the
additional problem that the pairwise comparisons weren;t significant,
indicating that the interactions is not represented well by the median
split.
 
So I am wondering if there are any other statistical methods to
investigate an interaction between a continuous covariate and a factor
or if I am doomed to fish around for the appropriate split because for
reporting purposes I will need the pairwise comparisons.  What do people
do in general in those cases.  Given that we didn't expect the
interaction (not part of the design) it's hard to come up with a
theoretical rationale on how to split the data for pairwise comparisons
and graphs.
 
Many thanks in advance,
Nicki

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[statisticsdoc]

Stephen Brand
www.statisticsdoc.com

Hi Nicole,

One of the core assumptions of ANCOVA is that the relationship between the
covariate and the dependent variable is the same for both groups.  When you
have a significant group by covariate interaction, then this assumption is
not met.  The significant interaction term implies that the relationship
between the covariate and the dependent variable differs between groups.  As
a result, I would not use ANCOVA to analyse these data.  I would use a
regression framework instead, with the following predictors: 1.) the
continuous variable; 2.) dummy codes for the categorical variable (or effect
codes, if these are appropriate); 3.) the cross-product, or interaction,
between the continuous variable and each of the dummy codes.  You can use
the regression weights to compute values of the dependent variable for each
group at one standard deviation above and below the mean on the continuous
variable.  These points will allow you to plot the slope and intercept of
the continuous variable for each group.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Kersting, Nicole
Sent: Thursday, December 14, 2006 1:48 PM
To: [hidden email]
Subject: Re: Statistical methods to investigate interactions between
factors and continuous covariates


Hi all,

I ran an ANCOVA model which yielded a significant interaction between a
fixed factor and a continuous covariate.  I am interested in
investigating the interaction further but I ran into the following
problem:  I created a median split in the continuous covariate, which in
combination with the factor gave me four means for pairwise comparisons.
While I realize all the issues attached to median splits, I have the
additional problem that the pairwise comparisons weren;t significant,
indicating that the interactions is not represented well by the median
split.

So I am wondering if there are any other statistical methods to
investigate an interaction between a continuous covariate and a factor
or if I am doomed to fish around for the appropriate split because for
reporting purposes I will need the pairwise comparisons.  What do people
do in general in those cases.  Given that we didn't expect the
interaction (not part of the design) it's hard to come up with a
theoretical rationale on how to split the data for pairwise comparisons
and graphs.

Many thanks in advance,
Nicki

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[Pirritano, Matthew]

Nicki,

I've often wondered about this myself. How to interpret the interaction
between a factor and a continuous covariate? Recently I've been exposed
to Cluster Analysis. If you have a number of variables that are related
in some theoretical way to your covariate you could run a Cluster
Analysis to create profiles of individuals based on the covariate and
the other variables that it is theoretically associated with and then
see if those profiles differ as a function of your factor. Basically
what you will have done is divided up your sample into much more
meaningful groupings than a median split would do. You'd have to
interpret what each cluster represents as you would do in a factor
analysis. You would then look at the interaction between cluster
membership and the factor. If you get an interaction it is then more
interpretable because you have all of the other variables (the
theoretically associated variables that you used to help create your
clusters) that characterize each cluster. Furthermore, now that your
sample is divided up into the theoretically meaningful clusters (of
which you can have more than 2) it seems to me that you're preserving
more info about your data than with a median split.

Of course, it would rely on your having other variables that logically
relate to you covariate.

I'd be curious to know what others think about this. It seems to me like
it gets rid of some of the messiness of interpreting an interaction
between a factor and a continuous covariate.

I've not done much of this, but this has been my impression.

Thanks,
Matt

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Kersting, Nicole
Sent: Thursday, December 14, 2006 10:48 AM
To: [hidden email]
Subject: Re: Statistical methods to investigate interactions between
factors and continuous covariates

Hi all,

I ran an ANCOVA model which yielded a significant interaction between a
fixed factor and a continuous covariate.  I am interested in
investigating the interaction further but I ran into the following
problem:  I created a median split in the continuous covariate, which in
combination with the factor gave me four means for pairwise comparisons.
While I realize all the issues attached to median splits, I have the
additional problem that the pairwise comparisons weren;t significant,
indicating that the interactions is not represented well by the median
split.

So I am wondering if there are any other statistical methods to
investigate an interaction between a continuous covariate and a factor
or if I am doomed to fish around for the appropriate split because for
reporting purposes I will need the pairwise comparisons.  What do people
do in general in those cases.  Given that we didn't expect the
interaction (not part of the design) it's hard to come up with a
theoretical rationale on how to split the data for pairwise comparisons
and graphs.

Many thanks in advance,
Nicki

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[JOHN ANTONAKIS]

Hi:

I second Stephen's suggestion.  The following reference will
be useful:

Aiken, L.S., & West, S.G. 1991. Multiple regression: Testing
and interpreting interactions. London: Sage.

You should steer clear of median splits. It is a big "no no"
nowadays.  Not only do you throw away information but in
most cases you lose power. Using regressiona and plotting
the interaction is the best thing to do.

HTH,
John Antonakis

----- Original Message -----
Expéditeur: Statisticsdoc <[hidden email]>
à: [hidden email]
Sujet: Re: Statistical methods to investigate interactions
between factors and continuous covariates
Date: Thu, 14 Dec 2006 14:15:34 -0500

> Stephen Brand
> www.statisticsdoc.com
>
> Hi Nicole,
>
> One of the core assumptions of ANCOVA is that the
> relationship between the covariate and the dependent
> variable is the same for both groups.  When you have a
> significant group by covariate interaction, then this
> assumption is not met.  The significant interaction term
> implies that the relationship between the covariate and
> the dependent variable differs between groups.  As a
> result, I would not use ANCOVA to analyse these data.  I
> would use a regression framework instead, with the
> following predictors: 1.) the continuous variable; 2.)
> dummy codes for the categorical variable (or effect codes,
> if these are appropriate); 3.) the cross-product, or
> interaction, between the continuous variable and each of
> the dummy codes.  You can use the regression weights to
> compute values of the dependent variable for each group at
> one standard deviation above and below the mean on the
> continuous variable.  These points will allow you to plot
> the slope and intercept of the continuous variable for
> each group.
>
> HTH,
>
> Stephen Brand
>
> For personalized and professional consultation in
> statistics and research design, visit
> www.statisticsdoc.com
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion
> [mailto:[hidden email]]On Behalf Of Kersting,
> Nicole Sent: Thursday, December 14, 2006 1:48 PM
> To: [hidden email]
> Subject: Re: Statistical methods to investigate
> interactions between factors and continuous covariates
>
>
> Hi all,
>
> I ran an ANCOVA model which yielded a significant
> interaction between a fixed factor and a continuous
> covariate.  I am interested in investigating the
> interaction further but I ran into the following problem:
> I created a median split in the continuous covariate,
> which in combination with the factor gave me four means
> for pairwise comparisons. While I realize all the issues
> attached to median splits, I have the additional problem
> that the pairwise comparisons weren;t significant,
> indicating that the interactions is not represented well
> by the median split.
>
> So I am wondering if there are any other statistical
> methods to investigate an interaction between a continuous
> covariate and a factor or if I am doomed to fish around
> for the appropriate split because for reporting purposes I
> will need the pairwise comparisons.  What do people do in
> general in those cases.  Given that we didn't expect the
> interaction (not part of the design) it's hard to come up
> with a theoretical rationale on how to split the data for
> pairwise comparisons and graphs.
>
> Many thanks in advance,
> Nicki
>
> **********************************************************
> ************* This email may contain confidential
> material. If you were not an intended recipient,
> please notify the sender and delete all copies.
> We may monitor email to and from our network.
>
> **********************************************************
> *************

___________________________________

Prof. John Antonakis
Faculty of Management and Economics
University of Lausanne
Internef #527
CH-1015 Lausanne-Dorigny
Switzerland

Tel: ++41 (0)21 692-3438
Fax: ++41 (0)21 692-3305

http://www.hec.unil.ch/jantonakis
___________________________________

[Art Kendall]

I concur with the recommendations.
Wrt  avoiding median splits.
In public policy for the past couple of decades we like to use
adjectives with pejorative connotations before median split such as
deceptive median split
nefarious median split
insidious median split
invidious median split
misleading median split
etc.

Art Kendall
Social Research Consultants

John Antonakis wrote:

>Hi:
>
>I second Stephen's suggestion.  The following reference will
>be useful:
>
>Aiken, L.S., & West, S.G. 1991. Multiple regression: Testing
>and interpreting interactions. London: Sage.
>
>You should steer clear of median splits. It is a big "no no"
>nowadays.  Not only do you throw away information but in
>most cases you lose power. Using regressiona and plotting
>the interaction is the best thing to do.
>
>HTH,
>John Antonakis
>
>----- Original Message -----
>Expéditeur: Statisticsdoc <[hidden email]>
>à: [hidden email]
>Sujet: Re: Statistical methods to investigate interactions
>between factors and continuous covariates
>Date: Thu, 14 Dec 2006 14:15:34 -0500
>
>
>
>>Stephen Brand
>>www.statisticsdoc.com
>>
>>Hi Nicole,
>>
>>One of the core assumptions of ANCOVA is that the
>>relationship between the covariate and the dependent
>>variable is the same for both groups.  When you have a
>>significant group by covariate interaction, then this
>>assumption is not met.  The significant interaction term
>>implies that the relationship between the covariate and
>>the dependent variable differs between groups.  As a
>>result, I would not use ANCOVA to analyse these data.  I
>>would use a regression framework instead, with the
>>following predictors: 1.) the continuous variable; 2.)
>>dummy codes for the categorical variable (or effect codes,
>>if these are appropriate); 3.) the cross-product, or
>>interaction, between the continuous variable and each of
>>the dummy codes.  You can use the regression weights to
>>compute values of the dependent variable for each group at
>>one standard deviation above and below the mean on the
>>continuous variable.  These points will allow you to plot
>>the slope and intercept of the continuous variable for
>>each group.
>>
>>HTH,
>>
>>Stephen Brand
>>
>>For personalized and professional consultation in
>>statistics and research design, visit
>>www.statisticsdoc.com
>>
>>
>>-----Original Message-----
>>From: SPSSX(r) Discussion
>>[mailto:[hidden email]]On Behalf Of Kersting,
>>Nicole Sent: Thursday, December 14, 2006 1:48 PM
>>To: [hidden email]
>>Subject: Re: Statistical methods to investigate
>>interactions between factors and continuous covariates
>>
>>
>>Hi all,
>>
>>I ran an ANCOVA model which yielded a significant
>>interaction between a fixed factor and a continuous
>>covariate.  I am interested in investigating the
>>interaction further but I ran into the following problem:
>>I created a median split in the continuous covariate,
>>which in combination with the factor gave me four means
>>for pairwise comparisons. While I realize all the issues
>>attached to median splits, I have the additional problem
>>that the pairwise comparisons weren;t significant,
>>indicating that the interactions is not represented well
>>by the median split.
>>
>>So I am wondering if there are any other statistical
>>methods to investigate an interaction between a continuous
>>covariate and a factor or if I am doomed to fish around
>>for the appropriate split because for reporting purposes I
>>will need the pairwise comparisons.  What do people do in
>>general in those cases.  Given that we didn't expect the
>>interaction (not part of the design) it's hard to come up
>>with a theoretical rationale on how to split the data for
>>pairwise comparisons and graphs.
>>
>>Many thanks in advance,
>>Nicki
>>
>>**********************************************************
>>************* This email may contain confidential
>>material. If you were not an intended recipient,
>>please notify the sender and delete all copies.
>>We may monitor email to and from our network.
>>
>>**********************************************************
>>*************
>>
>>
>
>___________________________________
>
>Prof. John Antonakis
>Faculty of Management and Economics
>University of Lausanne
>Internef #527
>CH-1015 Lausanne-Dorigny
>Switzerland
>
>Tel: ++41 (0)21 692-3438
>Fax: ++41 (0)21 692-3305
>
>http://www.hec.unil.ch/jantonakis
>___________________________________
>
>
>
>

[Zdaniuk, Bozena]

I don't know if that's of any use but if you run your ANCOVA using GLM
procedure in SPSS, you can request /PRINT=PARAMETER which basically
prints slopes for regressions where covariate predicts DV separately at
each level of fixed factor var. This allows you to look at the slopes
and see in what way they differ.
Bozena

Bozena Zdaniuk, Ph.D.

University of Pittsburgh

UCSUR, 6th Fl.

121 University Place

Pittsburgh, PA 15260

Ph.: 412-624-5736

Fax: [phone]

email: [hidden email]

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Kersting, Nicole
Sent: Thursday, December 14, 2006 1:48 PM
To: [hidden email]
Subject: Re: Statistical methods to investigate interactions between
factors and continuous covariates

Hi all,

I ran an ANCOVA model which yielded a significant interaction between a
fixed factor and a continuous covariate.  I am interested in
investigating the interaction further but I ran into the following
problem:  I created a median split in the continuous covariate, which in
combination with the factor gave me four means for pairwise comparisons.
While I realize all the issues attached to median splits, I have the
additional problem that the pairwise comparisons weren;t significant,
indicating that the interactions is not represented well by the median
split.

So I am wondering if there are any other statistical methods to
investigate an interaction between a continuous covariate and a factor
or if I am doomed to fish around for the appropriate split because for
reporting purposes I will need the pairwise comparisons.  What do people
do in general in those cases.  Given that we didn't expect the
interaction (not part of the design) it's hard to come up with a
theoretical rationale on how to split the data for pairwise comparisons
and graphs.

Many thanks in advance,
Nicki

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