program define choi_lr_support_interval_big_or , rclass
version 14
* Calculate the upper and lower bounds for the $k_global support interval
* This program is only called when the estimated OR = infinity, in which case
* the upper bound also equals infinity.
* This is done using the nl command following an approach described in
* http://www.stata.com/support/faqs/programming/system-of-nonlinear-equations/
* The nl program fits non-linear regression functions by least squares. We get
* an exact solution to an equation by fitting a model with two parameters and
* two variables. (For some reason this approach doesn't work with only one
* record). The dependent variable must take the values 1 and 0 in records 1 & 2.
* Suppose we wish to solve f(x) = 0
* We let y = 1 = f(x) +1 in the first record and
* y = 0 = dummy in the second
* nl then findes the least squares estimates of x and dummy, which will equal
* the value of x that gives f(x) = 0, and dummy = 0, respectively.
clear // Note that this command does not erase our scalar values.
* Calculate the upper bound of the $k_global support interval
* Calculate a starting value assuming a normal approximation of the likelihood function
* We add 1 to any empty cells
local a = y1
local b = y2
local c = n1-`a'
local d = n2-`b'
* Calculate the lower bound
* Calculate the starting value. We use Woolf's approximation after adding 1
* to any empty cell.
local sigma = sqrt(1/`a' + 1/max(`b',1) +1/max(`c',1) + 1/`d')
local psi_start = log(`a') + log(`d') - log(max(`b',1)) - log(max(`c',1))
local log_lb = `psi_start' -`sigma'*sqrt(2*log($k_global))
local lb = exp(`log_lb')
local support_start = `log_lb'
quietly set obs 2
generate y = 0
quietly replace y = 1 in 1
quietly nl _choi_support_interval @ y, parameters(psi dummy ) ///
initial(psi `support_start' dummy 0 )
scalar psi = [psi]_b[_cons]
scalar dummy = [dummy]_b[_cons]
scalar LRsupport_lb = exp(psi)
choi_lr_hyperg_prob n1 n2 y1 y2 psi
local k_alpha =strofreal($k_global,"%-10.7g")
display "1/`k_alpha'LSI for the OR = [" LRsupport_lb ", infinity]"
return scalar LRsupport_lb =LRsupport_lb
return scalar LRsupport_ub =.
end // *****************************************************************