[R] How do I test against a simple null that two regressions coefficients are equal?

[chen jia]

Thanks, Chuck. I am reading the references, which are helpful.

Just to understand what I have done wrong here,

I proposed an alternative testing strategy:
I run regressions y = a3 + b1 * x + b2 * z + e3 and test alternative
hypothesis b1 !=  b2 against the null hypothesis b1 = b2 in this
equation.

Is it this the same test as

y = a1 + b1*x + e1
y = a2 + b2*x + e2
test alternative hypothesis b1 != b2 against null hypothesis b1 = b2.

Best,
Jia

On Wed, Jul 7, 2010 at 11:12 PM, Charles C. Berry <cberry at tajo.ucsd.edu> wrote:
> On Wed, 7 Jul 2010, chen jia wrote:
>
>> Hi there,
>>
>> I run two regressions:
>>
>> y = a1 + b1 * x + e1
>> y = a2 + b2 * z + e2
>>
>> I want to test against the null hypothesis: b1 = b2.  How do I design the
>> test?
>>
>
> You are testing a non-nested hypothesis, which requires special handling.
>
> The classical test is due to Hotelling, but see the references (and R code
> snippets) in this posting:
>
>        http://markmail.org/message/egnowmdzpzjtahy7
>
> (it is the merest coincidence that the above thread was initiated by Mark
> Leeds and that the URL is 'markmail' :-) )
>
> HTH,
>
> Chuck
>
>
>> I think I can add two equations together and divide both sides by 2:
>> y = 0.5*(a1+a2) + 0.5*b1 * x + 0.5*b2 * z + e3, where e3 = 0.5*(e1 + e2).
>> or just y = a3 + 0.5*b1 * x + 0.5*b2 * z + e3
>>
>> If I run this new regression, I can test against the null b1 = b2 in
>> this regression.  Is it an equivalent test as the original one? If
>> yes, how do I do that in R?
>>
>> Alternatively, I think I can just test against the null:
>> correlation(y, x) = correlation(y, z), where correlation(. , .) is the
>> correlation between two random variables. Is this equivalent too? If
>> yes, how do I do it in R?
>>
>> Thanks.
>>
>> Best,
>> Jia
>>
>> --
>>                        Ohio State University - Finance
>>                                  248 Fisher Hall
>>                                   2100 Neil Ave.
>>                             Columbus, Ohio  43210
>>                            Telephone: 614-292-2830
>>                      http://www.fisher.osu.edu/~chen_1002/
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> Charles C. Berry                            (858) 534-2098
>                                            Dept of Family/Preventive
> Medicine
> E mailto:cberry at tajo.ucsd.edu               UC San Diego
> http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901
>
>
>



-- 
                         Ohio State University - Finance
                                   248 Fisher Hall
                                    2100 Neil Ave.
                              Columbus, Ohio  43210
                             Telephone: 614-292-2830
                       http://www.fisher.osu.edu/~chen_1002/