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st: predict with adjusted constant in e(b) returns probabilities outof range after logit


From   Daniel Mueller <dm_lists@gmx.net>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   st: predict with adjusted constant in e(b) returns probabilities outof range after logit
Date   Wed, 15 Nov 2006 08:01:04 +0100

Greetings!

After disproportionate sampling in a -logit- model I adjust the constant
term in e(b), leaving all other elements of e(b) unchanged. The adjustment procedure is based on Maddala (2001, p. 352). There, he states that coefficients are unaffected by disproportionate sampling in logit while the constant term needs to be decreased by log(p_1)-log(p_0) where p_1 and p_0 are the proportion of observations selected from each groups of y=1 and y=0.

I use the procedure pasted below to adjust the constant in e(b). But it returns predicted probabilities that are out of the range of 0 to 1 (between -11 and +3, see bottom of page). What have I overlooked? Why, in any case, is -predict- after logit returning predicted values that are out of range? How can I fix that?

Thank you in advance for any insights!

Daniel

// do-file with -coefadj-
prog def coefadj, eclass
version 9
syntax , coef(int) val(real)
mat b = e(b)
mat V = e(V)
mat b[1,`coef'] = `val'
eret post b V
end
// (prog based on a post from Kit Baum)

sysuse auto, clear
loc samobs = 20

// generate proportions
qui cou if foreign == 0
loc for0 = (`samobs'/`r(N)') * 100
qui cou if foreign == 1
loc for1 = (`samobs'/`r(N)') * 100
loc constadj = log(`for1') - log(`for0')
loc depvar "mpg price weight"
qui logit foreign `depvar', nolo
qui predict pfor_base

// unadjusted e(b)
mat li e(b)
loc newcons = _b[_cons] - `constadj'
loc coefno0 : word count `depvar'
loc coefno = `coefno0' + 1
coefadj, coef(`coefno') val(`newcons')

// predictions with constant-adjusted e(b)
mat li e(b)
qui predict pfor_adj
su pfor*


--- relevant output
. // unadjusted e(b)
. mat li e(b)

e(b)[1,4]
mpg price weight _cons
y1 -.12109183 .00092639 -.00684974 14.422375

. // e(b) with adjusted constant
. mat li e(b)

e(b)[1,4]
mpg price weight _cons
y1 -.12109183 .00092639 -.00684974 13.56217

. // adjusted predictions - incorrect..
. qui predict pfor_adj

. su pfor*

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
pfor_base | 74 .2972973 .3698118 .0000411 .9838551
pfor_adj | 74 -3.987828 4.049815 -10.96 3.249673


Maddala, G.S. (2001) Introduction to Econometrics, Chichester: John Wiley & Sons.

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