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


From   Jeffrey Wooldridge <jmwooldridge60@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Standardized interaction terms - which p-values hold?
Date   Tue, 15 Jan 2013 11:24:23 -0500

For what it's worth, I agree with Joerg. I don't see that
standardizing the interaction makes sense; nor does it solve a
substantive problem. Centering the variables before interacting them
often does, but that's because it forces the coefficients on the level
variables to be interpreted as marginal effects at the means of the
covariates. This often does make more sense than the partial effects
at zero. For example, what sense would it make to estimate the effects
of headroom on mpg for a car with length = 0?

In your example, I assume the variables are rates at something like
the county level. But it still would make no sense to evaluate the
partial effect of death -- whether it is standardized or not -- at
medage = 0.

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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