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

From   Elisabeth Bublitz <>
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, 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!

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