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


From   Elisabeth Bublitz <elisabeth.bublitz@uni-jena.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Standardized interaction terms - which p-values hold?
Date   Tue, 15 Jan 2013 16:01:30 +0100

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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