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# Re: st: Testing the difference between coefficients with interaction variables

 From Michael Crain <[email protected]> To [email protected] Subject Re: st: Testing the difference between coefficients with interaction variables Date Sat, 27 Aug 2011 04:14:09 -0700 (PDT)

```>> reg y x1 x2 x3 x1*x2 x1*x3

Might the test between the three groups be:

test x1 = (x1 + x1*x2) = (x1 + x1*x3)

--- On Sat, 8/27/11, Tirthankar Chakravarty <[email protected]> wrote:

> From: Tirthankar Chakravarty <[email protected]>
> Subject: Re: st: Testing the difference between coefficients with interaction variables
> To: [email protected]
> Date: Saturday, August 27, 2011, 4:00 AM
> But that is implicit in what you are
> testing (combine equation 1 and
> negative of equation 2 to get first of second set). Recall
> that Wald
> tests need the row rank of the constraint matrix to be full
> - the
> latter two constraints are redundant and would lead to a
> degenerate
> constraint matrix.
>
> T
>
> On Sat, Aug 27, 2011 at 12:43 AM, Michael Crain <[email protected]>
> wrote:
> >> /****************************/
> >> sysuse auto, clear
> >> regress price c.mpg##i.rep78
> >> testparm c.mpg#i.rep78, equal
> >> /****************************/
> >
> >
> > The output from this code seems to be testing the
> joint significance of:
> > group 2 - group 3 = 0
> > group 2 - group 4 = 0
> > group 2 - group 5 = 0
> >
> >
> > I don't see these results testing:
> > group 3 - group 4 = 0
> > group 4 - group 5 = 0
> >
> > Am I misinterpreting?
> >
> >
> > --- On Sat, 8/27/11, Tirthankar Chakravarty <[email protected]>
> wrote:
> >
> >> From: Tirthankar Chakravarty <[email protected]>
> >> Subject: Re: st: Testing the difference between
> coefficients with interaction variables
> >> To: [email protected]
> >> Date: Saturday, August 27, 2011, 3:10 AM
> >> Add the "equal" option:
> >>
> >> /****************************/
> >> sysuse auto, clear
> >> regress price c.mpg##i.rep78
> >> testparm c.mpg#i.rep78, equal
> >> /****************************/
> >>
> >> T
> >>
> >> On Sat, Aug 27, 2011 at 12:04 AM, Michael Crain
> <[email protected]>
> >> wrote:
> >> > Yes, I see this is testing for differences
> between the
> >> base group
> >> > compared to each of the other groups:
> >> >
> >> > base group - group 2 = 0
> >> > base group - group 3 = 0
> >> > etc.
> >> >
> >> > I am trying to test not only base group -
> group 2 =
> >> 0,
> >> > but also: group 2 - group 3 = 0
> >> >
> >> > Can examining coefficients between groups
> other than
> >> the base group be
> >> > done in a straightforward way?
> >> >
> >> >
> >> > --- On Sat, 8/27/11, Tirthankar Chakravarty
> <[email protected]>
> >> wrote:
> >> >
> >> >> From: Tirthankar Chakravarty <[email protected]>
> >> >> Subject: Re: st: Testing the difference
> between
> >> coefficients with interaction variables
> >> >> To: [email protected]
> >> >> Date: Saturday, August 27, 2011, 2:28 AM
> >> >> Here is an example:
> >> >>
> >> >> /****************************/
> >> >> sysuse auto, clear
> >> >> regress price c.mpg##i.rep78
> >> >> testparm c.mpg#i.rep78
> >> >> /****************************/
> >> >>
> >> >> This tests whether or not the coefficient
> on "mpg"
> >> is
> >> >> significantly
> >> >> different across categories of "rep78".
> In this
> >> case, you
> >> >> are unable
> >> >> to reject the hypothesis that they are
> >> indistinguishable
> >> >> from the
> >> >> coefficient of "mpg" for the base group.
> >> >>
> >> >> T
> >> >>
> >> >> On Fri, Aug 26, 2011 at 11:12 PM, Michael
> Crain
> >> <[email protected]>
> >> >> wrote:
> >> >> > I know testing the difference
> between
> >> coefficients of
> >> >> variables is
> >> >> > straightforward:
> >> >> >
> >> >> > reg y x1 x2 x3
> >> >> > test x1 = x2 = x3
> >> >> >
> >> >> > Is the test as straightforward for
> examining
> >> >> coefficients in models
> >> >> > with interactions variables?
> >> >> >
> >> >> > reg y x1 x2 x3 x1*x2 x1*x3
> >> >> >
> >> >> >   where:
> >> >> >
> >> >> >     x2 and x3 are dummy variables
> that
> >> identify
> >> >> groups
> >> >> >
> >> >> >     the base group is when x2=0
> and x3=0,
> >> group 2
> >> >> >     is when x2=1 and x3=0, group 3
> is when
> >> x2=0 and
> >> >> x3=1
> >> >> >
> >> >> > I am interpreting the effect of the
> base
> >> group as x1's
> >> >> coefficient. The
> >> >> > effect of group 2 is the sum of
> coefficients
> >> of the x1
> >> >> and x1*x2
> >> >> > variables. Lastly, the effect of
> group 3 is
> >> the sum of
> >> >> coefficients of
> >> >> > the x1 and x1*x3 variables.
> >> >> >
> >> >> > Now, I want to examine whether the
> effects of
> >> the
> >> >> three groups are
> >> >> > different.
> >> >> >
> >> >> > Is the test:
> >> >> >
> >> >> > test x1 = x1*x2 = x1*x3
> >> >> >
> >> >> > *
> >> >> > *   For searches and help try:
> >> >> > *   http://www.stata.com/help.cgi?search
> >> >> > *   http://www.stata.com/support/statalist/faq
> >> >> > *   http://www.ats.ucla.edu/stat/stata/
> >> >> >
> >> >>
> >> >>
> >> >>
> >> >> --
> >> >> Tirthankar Chakravarty
> >> >> [email protected]
> >> >> [email protected]
> >> >>
> >> >> *
> >> >> *   For searches and help try:
> >> >> *   http://www.stata.com/help.cgi?search
> >> >> *   http://www.stata.com/support/statalist/faq
> >> >> *   http://www.ats.ucla.edu/stat/stata/
> >> >>
> >> >
> >> >
> >> > *
> >> > *   For searches and help try:
> >> > *   http://www.stata.com/help.cgi?search
> >> > *   http://www.stata.com/support/statalist/faq
> >> > *   http://www.ats.ucla.edu/stat/stata/
> >> >
> >>
> >>
> >>
> >> --
> >> Tirthankar Chakravarty
> >> [email protected]
> >> [email protected]
> >>
> >> *
> >> *   For searches and help try:
> >> *   http://www.stata.com/help.cgi?search
> >> *   http://www.stata.com/support/statalist/faq
> >> *   http://www.ats.ucla.edu/stat/stata/
> >>
> >
> >
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/help.cgi?search
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
>
>
>
> --
> Tirthankar Chakravarty
> [email protected]
> [email protected]
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

*
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```