clear
* creat the dataset for six cities 
* cd C:\TA-LDA 

insheet using lab5.meta-6cities.csv
gen var=se^2

*graph(f)=fixed
meta logrr se, graph(f) cline xline(0) id(city) xlab 

*graph(r)=random effects estimate
meta logrr se, graph(r) cline xline(0) id(city) xlab 

*graph(e)=empirical bayes
meta logrr se, graph(e) cline xline(0) id(city) xlab 



* The plot which put EB estimates and original estimates together
gen n=_n
gen gmean=0.66
graph twoway scatter ebest logrr  gmean n, connect( . . l)

* caculate the empirical bayes estimates
*LA lambda, Empirical Bayes, and weights (the w_j from the notes -- used to calculate overall log RR)
display 0.134/(0.134+0.0169)
display (0.25*0.134+0.66*0.0169)/(0.134+0.0169)
display 1/(0.134+0.0169)/(2/(0.134+0.0169)+1/(0.134+0.0625)+1/(0.134+0.3025)+1/(0.134+0.16)+1/(0.134+0.2025))
*NY
display 0.134/(0.134+0.0625)
display (1.4*0.134+0.66*0.0625)/(0.134+0.0625)
display 1/(0.134+0.0625)/(2/(0.134+0.0169)+1/(0.134+0.0625)+1/(0.134+0.3025)+1/(0.134+0.16)+1/(0.134+0.2025))

*Chicago (lambda and weights are same as those for LA)
display (0.6*0.134+0.66*0.0169)/(0.134+0.0169)
*Dallas
display 0.134/(0.134+0.3025)
display (0.25*0.134+0.66*0.3025)/(0.134+0.3025)
display 1/(0.134+0.3025)/(2/(0.134+0.0169)+1/(0.134+0.0625)+1/(0.134+0.3025)+1/(0.134+0.16)+1/(0.134+0.2025))


*Houston
display 0.134/(0.134+0.16)
display (0.45*0.134+0.66*0.16)/(0.134+0.16)
display 1/(0.134+0.16)/(2/(0.134+0.0169)+1/(0.134+0.0625)+1/(0.134+0.3025)+1/(0.134+0.16)+1/(0.134+0.2025))
display 1/(0.134+0.16)/(2/(0.134+0.0169)+1/(0.134+0.0625)+1/(0.134+0.3025)+1/(0.134+0.16)+1/(0.134+0.2025))

*SD 
display 0.134/(0.134+0.2025)
display (1*0.134+0.66*0.2025)/(0.134+0.2025)
display 1/(0.134+0.2025)/(2/(0.134+0.0169)+1/(0.134+0.0625)+1/(0.134+0.3025)+1/(0.134+0.16)+1/(0.134+0.2025))


* other commands we can use to get similar results 
metan logrr se,random
metareg logrr, wsvar(var)