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Joseph Coveney

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/* Examples of the Hauck-Donner Phenomenon
   and the ability of the Huber-White-sandwich
   variance estimator to help Wald tests to overcome it.

   First example, from
   http://www.math.yorku.ca/Who/Faculty/Monette/pub/s-98/0028.html
*/
clear
set more off
set obs 200
generate byte y = _n>_N/2
generate byte x = -15
replace x = -1 in 99
replace x = -1 in 101
replace x = 1 in 100
replace x = 1 in 102
replace x = 15 in 103/l
glm y x, family(binomial) link(logit)
/*  The recommended approach to overcome the 
    sensitivity of the Wald test to this phenomenon
    is to use a likelihood-ratio test or a Fisher-Rao
    efficient score test (but see Douglas McManus's posting at
    http://www.math.yorku.ca/Who/Faculty/Monette/S-news/0049.html)
    . . . */
estimates store A
glm y, family(binomial) link(logit) nolog
lrtest A ., stats
*  Well enough; however, with -robust- . . .
glm y x, family(binomial) link(logit) robust nolog
/*  Second example, from
    http://maths.newcastle.edu.au/~rking/R/help/02b/3791.html
*/
clear
input byte pid byte x byte y byte z 
 1 8 7 1 
 2 8 3 1 
 3 0 5 0 
 4 0 9 0 
 5 8 1 1
end
glm z y x, family(binomial) link(logit)
estimates store A
glm z y, family(binomial) link(logit) nolog
lrtest A ., stats
* Again, . . .
glm z y x, family(binomial) link(logit) robust nolog
exit

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