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

[Daniel Mueller <dm_lists@gmx.net>]

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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