Re: st: Statistical Significance of the difference between two estimates from two separate regressions

[William Buchanan <william@williambuchanan.net>]

Hi Andri,

The Chow test (Antonakis's first example) is possible, but why not fit a single model to test your moderation hypothesis?  Another advantage that you gain with greater ease testing the moderation effect in a single model are access to some extremely helpful tools to do some visualization of the modeled relationships (look at the help files for -margins- and -marginsplot-).  See Michael Mitchell's book on visualizing regression results for additional information.

HTH,
Billy

Sent from my iPhone

> On Mar 14, 2014, at 7:16, "Kyrizi, Andri" <ak196@leicester.ac.uk> wrote:
> 
> Dear Mr Hoaglin,
> 
> Thank you for your helpful comments. 
> Yes the two regressions have exactly the same sets of predictors and my education variable is continuous.
> 
> So your suggestion would be to use a single regression? Or since my education variable is continuous I can do the first test that Professor Antonakis suggested?
> (my main 'concern' is to test whether the return to schooling for males is statistically different to that of females)
> 
> All the best,
> Andri
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of David Hoaglin [dchoaglin@gmail.com]
> Sent: 14 March 2014 11:47
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Statistical Significance of the difference between two estimates from two separate regressions
> 
> Dear Andri,
> 
> Do the two regressions have exactly the same sets of predictors?  If
> not, the definition of the coefficient for education is not the same.
> 
> The suggestion from John Antonakis to use a single regression for
> males and females, with an additional predictor for the difference in
> the effect of education, has the benefit of using a pooled estimate of
> the residual variance.  (If education is a categorical predictor, the
> combined regression will have an additional predictor for each
> non-reference category.)
> 
> The combined regression will also make it easier to investigate the
> possibility of interactions between male/female and other variables.
> You should consider whether the coefficients for the other variables
> differ between the male regression and the female regression.
> 
> It is also possible, but perhaps less likely, that the residual
> variances differ between the male regression and the female
> regression.
> 
> David Hoaglin
> 
>> On Fri, Mar 14, 2014 at 6:03 AM, Kyrizi, Andri <ak196@leicester.ac.uk> wrote:
>> Dear Statalisters,
>> 
>> I am running two (pooled ols) wage regressions: one for males and one for females.
>> 
>> I would like to test whether there is a difference between the estimates of the two groups and if the difference is statistically significant.
>> 
>> Most importantly I am interested to see if the coefficient I receive for education is statistically different between the two groups.
>> 
>> Could anyone help me with this? Is there a test to do this?
>> 
>> Thank you,
>> Andri
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