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


From   Joerg Luedicke <joerg.luedicke@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Standardized interaction terms - which p-values hold?
Date   Tue, 15 Jan 2013 11:22:23 -0500

Sorry, was too hasty. For some reason I did not see the second part of
the original post. I was just referring to the two examples shown
under "Example 1".

Joerg

On Tue, Jan 15, 2013 at 11:13 AM, Joerg Luedicke
<joerg.luedicke@gmail.com> wrote:
> In your two examples, you are comparing apples and oranges. If you
> center your variables in example 1 such that their mean is zero, you
> should get the same results as in example 2. However, I would not
> standardize the interaction term itself because it does not seem to be
> very meaningful. If the two predictors are standardized, then their
> interaction shows the effect of one predictor on the effect of the
> other in standard deviation unit. If the interaction term itself is
> standardized (or if you calculate a standardized coefficient) you
> can't interpret it that way.
>
> Joerg
>
> On Tue, Jan 15, 2013 at 10:01 AM, Elisabeth Bublitz
> <elisabeth.bublitz@uni-jena.de> wrote:
>> 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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