interpreting MR interactions with transformed variables

[Sonia Patil]

Using multiple regression analyses, I'm testing the interaction effects of
classroom climate and student aggression on behavioral outcomes. I applied
transformations to the predictor (reflect and square root), moderator
(square root) and dependent (log) variables because the distributions were
signfiicantly nonnormal.

I realize that I need to be mindful when interpreting the results given that
I've transformed the variables. However, I can't find a good reading on what
exactly I should be doing, and I'm getting even more confused because I need
to calculate slopes for my interaction effects. As I understand I it is the
direction of the association b/n two variables that I need to consider. So
if I have a positive beta between X and Y, I should change the beta sign to
negative. Is this correct? And, how do I account for the fact that I
transformed my predictor, moderator and outcome variables?

I hope this makes sense. I'd appreciate any feedback or thoughts.

Thanks,
S.Patil

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[statisticsdoc]

Sonia,

Before you interpret this regression, are you quite sure that you want to
use so many transformations?  If you are concerned that your variables have
a skewed distribution, bear in mind that with a large sample size,
regression is reasonably robust against skewness.  If you have outliers in
the data, or if the plot of the residuals is problematic, there are other
solutions that will yield a more readily interpretable model (e.g.,
investigating and possibly removing the outliers, adding quadratic terms to
the regression model, etc.)

If you have decided to use a model with the transformed variables, the
following should help with the interpretation of the parameters.  Start by
plotting the predicted values of the transformed dependent variable using
the transformed values of the predictor variables.  Use the standardized
beta weights to compute the predicted value of log(Y) for each of the
following combinations  of the predictors:

transformed(X1)             transformed(X2)
1 SD above mean             1 SD above mean
1 SD above mean             1 SD below mean
1 SD below mean             1 SD above mean
1 SD below mean             1 SD below mean

using the standard deviations of the transformed variables.  In this model,
the direction of one of the predictors (is it climate or aggression?) has
been reversed in sign from the direction of the original raw scores.  So,
for conceptual understanding, if higher raw scores on this predictor
variable indicated more aggression or better climate, higher transformed
scores indicate less aggression or poorer climate.

If you want to consider the prediction model in terms of the original
variables, that is somewhat more involved, since the raw scores underwent a
non-linear transformation.  You could plot the predicted transformed scores
at each combination of -2, -1, 0, 1, and 2 standard deviations above and
below the mean for the transformed predictors, and then convert the
transformed scores back into raw form by undoing the transformations.
However, this would not be necessary for interpreting the direction of the
effects or the interaction - just bear in mind that one of the predictors is
reverse keyed.

One question about the transformations.  I see that the outcome variable
underwent a log transformation - is it a ratio-level  variable (i.e., it has
a real zero point)?

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
Sonia Patil
Sent: Sunday, January 28, 2007 5:44 PM
To: [hidden email]
Subject: interpreting MR interactions with transformed variables


Using multiple regression analyses, I'm testing the interaction effects of
classroom climate and student aggression on behavioral outcomes. I applied
transformations to the predictor (reflect and square root), moderator
(square root) and dependent (log) variables because the distributions were
signfiicantly nonnormal.

I realize that I need to be mindful when interpreting the results given that
I've transformed the variables. However, I can't find a good reading on what
exactly I should be doing, and I'm getting even more confused because I need
to calculate slopes for my interaction effects. As I understand I it is the
direction of the association b/n two variables that I need to consider. So
if I have a positive beta between X and Y, I should change the beta sign to
negative. Is this correct? And, how do I account for the fact that I
transformed my predictor, moderator and outcome variables?

I hope this makes sense. I'd appreciate any feedback or thoughts.

Thanks,
S.Patil

_________________________________________________________________
Turn searches into helpful donations. Make your search count.
http://click4thecause.live.com/search/charity/default.aspx?source=hmemtaglin
e_donation&FORM=WLMTAG

[Brian J. Hall]

Dear list,

I am conducting a multiple regression analysis, entering IVs in several
blocks/steps. The final step in my model includes a squared term to test for
a curvilinier relationship between one of my predictors and the DV. I have a
significant curvilinear relationship indicated by the significance of the
squared term in the model. I would like to plot this curve, to demonstrate
the shape of the parabala. I know how to do this with just one IV using SPSS
curve estimation, but does anyone know how I can plot this relatiosnhip
using SPSS linear, with multiple IVs?

Thanks in advance,

Brian

[statisticsdoc]

Brian,

You might want to consider entering the model parameters in an Excel
spreadsheet, and computing predicted values.

For example, if your model includes X1, X2, X3 and X3^2, then compute the
predicted values when X1 and X2 are at their respective means, and X3 takes
on a range of values (as would X3^2).  You can start with values of X3 that
are -2 -1 0 1 and 2 standard deviations from the mean, although you can use
finer grained steps in X3 if you wish.

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
Brian J. Hall
Sent: Monday, January 29, 2007 9:12 AM
To: [hidden email]
Subject: Re: interpreting MR interactions with transformed variables


Dear list,

I am conducting a multiple regression analysis, entering IVs in several
blocks/steps. The final step in my model includes a squared term to test for
a curvilinier relationship between one of my predictors and the DV. I have a
significant curvilinear relationship indicated by the significance of the
squared term in the model. I would like to plot this curve, to demonstrate
the shape of the parabala. I know how to do this with just one IV using SPSS
curve estimation, but does anyone know how I can plot this relatiosnhip
using SPSS linear, with multiple IVs?

Thanks in advance,

Brian