Re: interaction term in linear regression with a dummy coded predictor

On Mar 14, 6:33 am, Old Mac User <chendrixst...@xxxxxxxxx> wrote:
Ray...

You wrote "but to stop trying to interpret the so-called "main
effect" coefficients as if they were anova overall main effects,
and to start looking at the correct overall effect statistics.
For a more complete discussion,"

I don't understand this. In science and engineering it's common to
build models from data. It's also common to interpret the meaning
of those models from the values of the "slopes", i.e., the linear
regression coefficients.

What do you mean by "the correct overall effect statistics"?
If you mean the ANOVA table, that table is almost useless when
we need to values and signs of the model coefficients. OMU

Am I missing something.

In regression models with interaction terms, people misinterpret
the main effect coefficients of variables that are involved in
interactions. They interpret them as if they were analogous to
overall main effects in an anova, when they are actually analogous
to simple main effects.

The correct analog of an overall main effect is the average slope.
Centering at the mean will make the main effect coefficients equal
to the average slopes, but only if the design contains no three-way
or higher-order interactions.

Because of this limitation, I think that giving people the idea
that centering will make the main effect coefficients interpretable
as overall main effects would be a strategic mistake. A better plan
would be to teach them what those coefficients really are, and to
convince software manufacturers to provide the average slopes as
optional output from regression programs.

For more details, please see my post at
http://groups.google.ca/group/sci.stat.math/msg/00a4cb0cae567264
.

Relevant Pages

  • Re: Multiple regression in Matlab!
    ... > Regression would result in a plethora of non-estimable coefficients. ... > either -- for one thing, the components found by PCA are basically done ... 157 PCs contain all the information of the 3000 wavelengths. ... > to interpret and not the regression coefficients. ...
    (comp.soft-sys.matlab)
  • Re: Contrast Coding with Unequal Sample Sizes
    ... do Reverse Helmert coding to use in multiple regression; ... standardized beta coefficients will be interpretable. ... You should interpret the unstandardized coefficients. ...
    (sci.stat.consult)
  • interpretting F & t-vals from regression
    ... I fit a linear model in R and obtain an ANOVA table with the anova command. ... So I want to see what the coefficients are for one of my factors and whether ... How do I interpret that? ... Does the F-test just tell me that X ...
    (sci.stat.consult)
  • Re: interaction term in linear regression with a dummy coded predictor
    ... You wrote "but to stop trying to interpret the so-called "main ... effect" coefficients as if they were anova overall main effects, ... In science and engineering it's common to ... If you mean the ANOVA table, that table is almost useless when we need ...
    (sci.stat.math)