clear all
set obs 1000
forvalues i=1/4 {
	generate x`i' = runiform(-3,3) // x's independent and balanced
	}
summarize x*
pwcorr x*, sig // no substantial correlation

egen ylo = rowtotal(x*)
//histogram ylo // normal distribution
generate ypr = invlogit(ylo)
//histogram ypr  // beta distribution
generate y = runiform() < ypr
tabulate y  // should be roughly "fair"

quietly logit y x*

predict rp, residuals // Pearson residuals
predict rd, deviance // deviance residuals
predict pxb, xb // linear predictor

scatter rd rp
scatter rp pxb
scatter rd pxb

clear
input x1 x2
-1 -1
0 0
1 1
end
fillin x1 x2
expand 20
generate ypr = invlogit(x1 + x2)
generate y = runiform() < ypr

graph bar y, over(x1) over(x2)

logit y x*, nolog
predict rp, residuals // Pearson residuals
predict rd, deviance // deviance residuals
predict pxb, xb // linear predictor
capture graph drop _all
scatter rd rp, name(PtoD)
scatter rp pxb, name(Pearson)
scatter rd pxb, name(deviance)

graph combine Pearson deviance PtoD