*
* Example from section 15.7, page 600
* Grouped logit and probit
*
all 10
open data table15-4.prn
*
* We use "own" rather than "n" for the number owning a home because RATS doesn't
* take case into account in processing variable names, that is, "n" and "N" can't
* be used if you want different series.
*
data(format=prn,org=columns) / x N own
*
* Generate phat, the logit function and the variance series for the
* heteroscedasticity correction.
*
set phat   = own/N
set logit = log(phat/(1-phat))
set v     = 1.0/(phat*(1-phat)*n)
*
* Estimate the grouped logit model. Note that the coefficients are slightly
* different because the variables are computed to full precision here, while in
* table 15.5, the x=20 phat is truncated to 2 decimal places.
*
linreg(spread=v) logit
# constant x
*
* PRJ(DISTRIB=LOGIT) computes statistics based upon the fitted values using the
* logistic distribution. PHAT will be the predicted probabilities and DP will be
* the density function. If we multiply DP by %BETA(2), we'll get the sensitivity
* of the probability to changes in the "X" variable.
*
prj(distrib=logit,cdf=phat,density=dp)
set dp = dp*%beta(2)
scatter(hlabel="X, Income, thousands of dollars",vlabel="Change in probability")
# x dp
*
* Grouped probit. We recompute the data phat's because we used the same name for
* the predicted probabilities. Again, the output will be slightly different
* because of rounding.
*
set phat  = own/N
set index = %invnormal(phat)
*
linreg index
# constant x
*
*  Compute, print and graph the predicting probabilities
*
prj(cdf=phat) ihat
print / x ihat phat
scatter
# x phat
*
*  For completeness, do the regression with 5 added to the index
*
set probit = 5+index
linreg probit
# constant x