RE: st: comparing coefficients across models

[Cameron McIntosh <cnm100@hotmail.com>]

I would also suggest being wary of non-homogeneity of within-group error variance across the levels of the categorical moderator.  That can be dealt with fairly easily, however.

Su, H., & Liang, H. (2010). An Empirical Likelihood-Based Method for Comparison of Treatment Effects—Test of Equality of Coefficients in Linear Models. Computational Statistics and Data Analysis, 54(4), 1079–1088.

Smithson, M. (2012). A simple statistic for comparing moderation of slopes and correlations. Frontiers in Psychology, 3(231).
http://www.frontiersin.org/Quantitative_Psychology_and_Measurement/10.3389/fpsyg.2012.00231/full

Weerahandi, S. (1987). Testing Regression Equality with Unequal Variances. Econometrica, 55(5), 1211-1215.

http://www.weerahandi.org/

Cam

> Date: Sat, Aug 012 3::5::8 -700<
> From: ggs_da@yahoo.com
> Subject: Fw: st: comparing coefficients across models
> To: statalist@hsphsun..harvard.edu
> 
> 
> David,
> 
> 
> Thank you so much for helping me think this through. I very much appreciate it. 
> 
> Here are the sample sizes for group_dummy (//))
> 
> group dummy
>             |      Freq.     Percent        Cum.
> ------------+-----------------------------------
>           |      ,,98        1..5        1..5<
>           |      ,,97        8..5       00..0<
> ------------+-----------------------------------
>       Total |      ,,95       00..0<
> 
> Your assumptions are correct. Business group dummy is different from group_dummy. Also, the group_dummy in the interaction model is when group== and when group ==.. Also, I am only interested in whether the slope against x differs when group_dummy=//.. I am not intersted in the intercept for the group dummy. From what I understand, I can get at the slope for x by running the regression for the two groups separately, and then comparing the coefficients for x.. Is this correct? Or are you saying something different?
> 
> As you suggested I also looked at the graphs for the relationship between the two variables that are highly correlated (degree centrality and betweenness centrality) for ()) the whole sample, ()) for group_dummy== and ()) for group_dummy==.. The three graphs look extremely similar with a negative, slightly curving slope (I can't seem to figure out how to attach a file, and not get my mail bounced from statalist). Also, I apologize, but I made a mistake in my earlier email, the high correlation is between x degree centrality and x betweenness centrality, and not between x and x.. 
> 
> Thanks once again for your help
> Dalhia
> 
> ----- Original Message -----
> From: David Hoaglin <dchoaglin@gmail.com>
> To: statalist@hsphsun..harvard.edu
> Cc: 
> Sent: Friday, August ,, 012 ::8 PM
> Subject: Re: st: comparing coefficients across models
> 
> Dalhia,
> 
> Thanks for the correction.
> 
> I may not understand the relation between the variable group, which
> took the values and in your initial example, and group_dummy in
> the interaction model.  I assume that group_dummy is when group = <
> and when group = ..
> 
> I'm also assuming that group_dummy is different from x..
> 
> From the substantial negative correlation between x and x,, I infer
> that the mean of x differs substantially between the two business
> groups distinguished by x..
> 
> I wonder whether the relation between group_dummy and x is part of
> the problem.  Also, what are the relative sample sizes for the two
> values of group_dummy?
> 
> Without x**group_dummy in the model, you would be fitting a slope
> against x,, an offset for x,, and a slope against x..  When you
> include x**group_dummy, you are fitting an additional slope against x<
> for the two groups defined by group_dummy (i.e., if b is the
> coefficient of x and b is the coefficient of x**group_dummy, the
> slope against x is b when group_dummy = and b + b when
> group_dummy = )).
> 
> You aren't including group_dummy itself as a predictor, so I assume
> that you don't want different intercepts for those two groups.
> 
> You have few enough variables that you should be able to diagnose the
> problem by looking at how x and x are each related to x and
> plotting x against x (overall, within the two groups defined by x,,
> and within the two groups defined by group_dummy).  Also, as I
> suggested above, look at a crosstab of x and group_dummy.
> 
> David Hoaglin
> 
> On Fri, Aug ,, 012 at ::6 AM, Dalhia <ggs_da@yahoo.com> wrote:
> > David,
> > Sorry about the confusion. Typo.
> >
> > Here is what I should have said:
> >
> > This is how I ran the interaction model:
> > xtreg y x x x x**group_dummy, fe robust
> >
> >
> > where y is log of Tobin's q (a measure of firm performance)
> > x is degree centrality (a network measure - continuous)
> > x is business group dummy (codes whether or not a firm belongs to a cluster of firms)
> > x is betweenness centrality (a network measure - continuous)
> > group_dummy is whether or not the firm belongs to a particular component in the network.
> >
> > x and x are the most  highly correlated (-..3)).
> >
> > Thanks.
> > Dalhia
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