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Re: st: interaction between continuous variables

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: interaction between continuous variables
Date   Tue, 4 Sep 2007 18:10:04 +0100 (BST)

--- alessia matano <[email protected]> wrote:
> I am trying to perform a regression trying to put an interaction term
> between two continuous variables.
> In a first attempt I discretize one of them and then multiply the
> relative dummy with the other variable, and I obtained some
> interesting effect.
> Then I red that this is not correct to be done and it is also
> arbitrary (because I decide how descretize one variable...I was
> calcultaing some threshold using the percentiles say p(33) p(66))
> getting three values.

How to descretize a variable is just as arbitrary as assuming that the
interaction is linear, so I would not worry about that.
> Therefore I red some papers saying that you should centered the
> continuous variables (becuase of problem of multicollinearity: is
> that correct?) and then simply multiply them. In this way results
> are not so interesting anymore. The main and interacted variables
> together are never significant and it happens (and here I would
> like your help) that in one case only the interacted is significant
> while the main effect is not. Whta does it mean?

Consider the following regression:
y = b0 + b1*x1 + b2*x2 + b3*x1*x2

if x1 = 0:
y = b0 + b1*0 + b2*x2 + b3*0*x2
y = b0 + b2*x2 
effect of x2 is b2

if x1 = 1:
y = b0 + b1*1 + b2*x2 + b3*1*x2
y = b0 + b1 + (b2 + b3)*x2 
effect of x2 is b2 + b3, i.e. a unit increase in x1 resulted in b3
increase in the effect of x2 

if x1 = 2:
y = b0 + b1*2 + b2*x2 + b3*2*x2
y = b0 + 2*b1 + (b2 + 2*b3)*x2 
effect of x2 is b2 + 2*b3, i.e. a unit increase in x1 resulted in 2*b3
increase in the effect of x2 

So, the main effect of x2 (b2) is the effect of x2 when x1 = 0, and
the interaction effect (b3) tells you how much the effect of x2 changes
when x1 changes with one unit.

Centering the variable makes sense because now the main effect is
easier to interpret (Think what would happen if x1 was year of birth
when it is non-centered: than the main effect would be the effect for
someone who was bort 2007 years ago...). You don't have to center at
the mean, as long as the value zero is meaningful in your data.

Hope this helps,

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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