/*----------------------------------------------------------- 
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
predict ylpm, resid
gen y_dec = 0
replace y_dec = 1 if ylpm > 0.5 
tab y y_dec 

/* Heteroskedasticity */
estat hettest
imtest,white

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

/* Logistic Model */
/* Logistic Model with income */
logit y income
mfx
mfx, at(50)
mfx, at(100)

predict yhat_logit
label var yhat_logit "yhat from Logit P(x)"
gen y_logdec = 0
replace y_logdec = 1 if yhat_logit > 0.5 
tab y y_logdec

twoway (scatter (y yhat_logit) income) (line yhat income)


/* 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)