Bayes estimates for proportions and their CI

 

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EXAMPLE:
If in the sample of 400 respondents we have:
(1)  60 votes for "red"
(2) 120 votes for "blue"
(3)  20 votes for "green"
(4) 200 votes for "grey"
(5)   0 votes for "black"
i.e. nobody voted for blacks but we know for sure that such a party
exists, then Bayes estimates for proportions with 99% confidence interval
can be calculated as:

bayes 60 120 20 200 0 / 99%.

In the case of 95% confidence interval the last argument can be omitted.

bayes 60 120 20 200 0.

********************************
* Macros: Bayes.sps            *
* Author: Evgeny Ivashkevich   *
* E-mail: ivashkev@yandex.ru)  *
* Date  : 2005/07/19           *
********************************

preserve.
set printback=off.
define bayes  (!positional !charend ('/')
              /!positional !charend ('%') !default(95)).

!let !n = 0.
!let !r = 0.
!do !k !in (!1).
!let !n = !length(!concat(!blanks(!n),!blanks(!k))).
!let !r = !length(!concat(!blanks(!r),!blanks(1))).
!doend.

input program.
numeric id (f2) pr se lb ub (f7.5).
vector cov(!r e10.3) #p(!r).
string info(A10).
variable labels  info ' '
 id '#'
 pr 'Proportion'
 se 'Standard Error'
 lb 'Lower Bound'
 ub 'Upper Bound'.

compute #i = 0.
!do !k !in (!1).
  compute #i = #i+1.
  compute #p(#i) = (!k+1)/(!n+!r).
!doend.

loop #i=1 to !r.
  compute id = #i.
  compute pr = #p(#i).
  compute se = sqrt(#p(#i)*(1-#p(#i))/(!n+!r+1)).
  compute lb = max(#p(#i)+probit((100-!2)/200)*se,0).
  compute ub = min(#p(#i)+probit((100+!2)/200)*se,1).
  loop #j=1 to !r.
    if (#j =#i) cov(#j) =  #p(#i)*(1-#p(#i))/(!n+!r+1).
    if (#j<>#i) cov(#j) = -#p(#i)*#p(#j)/(!n+!r+1).
  end loop.
  if ($casenum=1) info = concat('P =',string(!2,f4),'%').
  if ($casenum=2) info = concat('N =',string(!n,f5)).
  if ($casenum>2) info = ' '.
end case.
end loop.
end file.
end input program.
execute.

report format = list automatic align(center)
 /variables = id pr se lb ub info
 /title 'BAYES ESTIMATES FOR PROPORTIONS AND CONFIDENCE INTERVALS'.
!enddefine.
restore.

bayes 60 120 20 200 0 / 99%.
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