st: Standardized interaction terms - which p-values hold?

[Elisabeth Bublitz <elisabeth.bublitz@uni-jena.de>]

Hi Statalist,

when I compare the p-values of a baseline regression with those obtained 
from a regression with standardized coefficients and interaction terms 
the following problem comes up: The suggestions previously posted (see, 
http://www.stata.com/statalist/archive/2009-04/msg00888.html) are that 
the variables forming the interaction need to be standardized before 
they are interacted, and a second time afterwards. This changes the 
p-values and sometimes even coefficients change their signs. Intuitively 
this suggests to me that something with the previous suggestion is not 
correct.


Here is the example from the previous thread:
*-------------------Example 1--------------------------------
* This version standardizes the IA once and serves as an example of what 
is "incorrect"
sysuse auto, clear
gen ia = head*length
reg mpg head length ia, beta

* This version standardizes the IA twice and is suggested to be "correct"
egen shead = std(headroom)
egen slength = std(length)
egen smpg = std(mpg)
gen ia2 = shead*slength
egen sia2 = std(ia2)
reg smpg shead slength sia2
*-----------------------------------------------------------------


In this example the changes are visible but do not yet cross important 
levels, therefore significance levels stay the same. This is, however, 
different for the data I use. I'd be curious to learn what you think 
about this.

I found an example where the changes are more visible.

*-------------------Example 2--------------------------------
sysuse census, clear

* Standardizing coefficients
egen zdivorce = std(divorce)
egen zmarriage = std(marriage)
egen zdeath = std(death)
egen zmedage = std(medage)

* Interaction terms
gen ia= death*medage
egen zia_1= std(ia)
gen test = zdeath*zmedage
egen zia_2 = std(test)

* Regression
reg divorce marriage death medage ia, beta //(1) this follows the 
simpler procedure
reg divorce marriage death medage test, beta //(2) this standardizes the 
IA twice, note changes in significance levels and coefficient size
reg zdivorce zmarriage zdeath zmedage zia_2 // (3) for comparison 
(identical with (2)): this is the same as suggested in the previous thread
*-----------------------------------------------------------------

Unfortunately, I need to compare the size of two interactions and, thus, 
need standardized coefficients. If you have other suggestions, let me 
know. I was wondering whether it would make sense to use logarithms 
instead.

Many thanks!
Elisabeth


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