Re: st: Chow test to test only slope coefficient and importance of dummy variable?

[David Hoaglin <dchoaglin@gmail.com>]

Hi, Sarah.

Your tests look all right to me, except for the last one.  If the two
groups have different slopes, it may not be meaningful to test whether
they have the same intercept.  A possible exception is a model in
which the predictor variable is centered (at the same value across the
groups); one might be interested in whether the data are compatible
with lines for the two groups that pass through the same point at that
value of the predictor, but I don't have an actual example in mind.

I would describe the actual tests and not mention "Chow Test."

David Hoaglin

On Thu, Nov 14, 2013 at 2:30 PM,  <savinett@ucalgary.ca> wrote:
> Thank you very much for your informative and helpful responses Fernando
> and David, I really appreciate it.  I think I understand, I just want to
> confirm my understanding and that I am doing this properly. For my study,
> I only have 1 independent variable (I will call this mpg to be consistent
> with the FAQ example).
>
> From what I understand, even if I am only interested in the difference in
> slopes, I use a model that allows the groups to differ in both slopes and
> intercepts. So I will include group2 in the regression to allow the groups
> to have different intercepts and use the command:
> . regress price mpg mpg2 group2
>
> Then, if I wish to only test a difference in slopes, I would follow this
> up with:
> . test _b[mpg2]=0
>
> If I wanted to test both the intercept and slope I would use:
>  . test _b[mpg2]=0, notest
> . test _b[group2]=0, accum
>
> and if I were only interested in if the groups differed by intercept I
> would use:
> . test _b[group2]=0
>
> If you would please let me know if this is correct that would be awesome.
>
> Also, David, you had mentioned in your response that it is best not to
> focus on the Chow Test specifically. I am wondering for my description of
> the statistical approach is it correct to describe it as a Chow Test where
> only differences in slope were assessed? Or would it be better to instead
> describe the steps taken (and not label it with the words Chow Test)?
> Thank you very much again for your time and guidance!
>
> Sarah
>
>> Hi, Sarah.
>>
>> As that FAQ explains, we would do well not to focus so firmly on the
>> "Chow Test."  Greg Chow's 1960 result was helpful years ago, but
>> software has given us the flexibility to do that test and much more.
>> For many statisticians, hiding a straightforward test behind the name
>> "Chow Test" will produce puzzled looks.
>>
>> You can test whether only the slopes are different and allow each
>> group to have its own intercept.  In fact, that is the usual situation
>> (e.g., a one-way analysis of covariance fits a common slope and
>> separate intercepts).  As in the example in that FAQ, you can fit the
>> model that has separate intercepts and separate slopes and then test
>> whether the slopes are equal.
>>
>> That example did not use "noconstant" to remove the intercept from the
>> model.  It used that option in order to use separate coefficients
>> (including the constant) for each group.  In the command
>> . regress price mpg weight mpg2 weight2 group2
>> _const is the intercept for Group 1, and _const + _b[group2] is the
>> intercept for Group 2.  Also, the coefficient of mpg for Group 2 is
>> _b[mpg] + _b[mpg2], so the test of whether the coefficients of mpg in
>> the two groups are equal is the test of whether _b[mpg2] = 0.  (I am
>> assuming that mpg2 equals the product of mpg and the Group 2
>> indicator.)
>>
>> David Hoaglin
>>
>> Chow GC (1960).  Tests of equality between sets of coefficients in two
>> linear regressions.  Econometrica 28:591-605.
>>
>> On Wed, Nov 13, 2013 at 4:35 PM,  <savinett@ucalgary.ca> wrote:
>>> Hi,
>>>
>>> I am new to Stata and the Chow Test. I want to compare the slopes of
>>> two
>>> sets of time series data using the chow test, however I am not
>>> interested
>>> in any differences in the intercepts of these time series data.  I have
>>> read the FAQs section on this and found this one:
>>> http://www.stata.com/support/faqs/statistics/chow-tests/ to be very
>>> helpful.  I do, however, have two questions:
>>>
>>> 1.   Can I use the Chow Test to test that only the slopes are different
>>> (not both the slope and intercepts)? I still want to include the
>>> intercept
>>> in the model (i.e. not use the “noconstant”). However, for the Chow
>>> Test I
>>> would like it to reflect that if there is a significant difference
>>> between
>>> the groups that this is due to a difference in their slopes (as I
>>> expect
>>> that their intercepts will differ and am not interested this aspect).
>>>
>>> 2.  It is not clear to me why the in the example from the Chow Test FAQ
>>> (link in the first paragraph) “group2” (the dummy variable) is
>>> included in
>>> the regression:
>>> . regress price mpg weight mpg2 weight2 group2
>>>
>>> If someone could please provide me with some insight that would be
>>> amazing.
>>> Thank you very much in advance for your help with my questions!
>>>
>>> Sarah
>>
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>>
>
>
>
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