/*----------------------------------------------------------- 
Binary Dependent Variable Example 
Public Transportation by income level
y            =1 if take public transportation =0 otherwise
income       Income (in $1,000)
gender       =1 if male = 0 if female
distance     Commute Distance in miles
------------------------------------------------------------*/
clear all 
use https://bigblue.depaul.edu/jlee141/econdata/eco304/binary_transp.dta

/* Linear Probability Model */
regr y income
eststo lpm
predict y_lpm
gen y_dec = 0
replace y_dec = 1 if y_lpm > 0.5 
tab y y_dec 

/* Prediction for out of boundary check */
label var y_lpm "yhat from LPM"  
twoway (scatter (y y_lpm) income)

/* Probit Model */
probit y income
eststo probit
predict y_probit 
twoway (scatter (y y_probit) income)

/* Logistic Model */
/* Logistic Model with income */
logit y income
eststo logit
predict y_logit
label var y_logit "yhat from Logit P(x)"
gen y_logdec = 0
replace y_logdec = 1 if y_logit > 0.5 
tab y y_logdec
twoway (scatter (y y_logit) income) (line y_lpm income)

/* Comparison of Three Models */
esttab lpm probit logit, r2 ar2 pr2 sca( ll_0 chi2 p) 

/* Prediction and Marginal Effects at given X */
qui: regr y income
mfx
mfx, at(50)
mfx, at(100)

qui: probit y income
mfx
mfx, at(50)
mfx, at(100)

qui: logit y income
mfx
mfx, at(50)
mfx, at(100)



/* Multivariate Logistic Model with income gender distance */
logit y income gender distance 
mfx
mfx, at(50 0 5)
mfx, at(100 1 5)
predict yhat_logit2
label var yhat_logit2 "yhat from Logit P(x)"
gen y_logdec2 = 0
replace y_logdec2 = 1 if yhat_logit2 > 0.5
tab y y_logdec2
twoway (scatter (y yhat_logit) income) (scatter yhat_logit2 income)