// Case A
clear
set seed 1
set obs 300
generate e = 0 + (200 - 0) * runiform() // To generate random variates over the
generate x = 0 + (600 - 0) * runiform() // interval [a,b), a+(b-a)*runiform()
generate y = e // Relationship between X and Y random
generate id = 1
replace y = (e + 200) if x > 200 & x <= 400
replace id = 2 if x > 200 & x <= 400
replace y = (e + 400) if x > 400
replace id = 3 if x > 400
bys id: egen ym = mean(y) // Generate cluster means for Y and X
bys id: egen xm = mean(x)
twoway (scatter y x if id == 1, msymbol(oh)) ///
(scatter y x if id == 2, msymbol(dh)) ///
(scatter y x if id == 3, msymbol(sh)) ///
(scatter ym xm, msymbol(S)) ///
(lfit ym xm, lpattern(solid)) ///
(lfit y x if id == 1, lpattern(dash)) ///
(lfit y x if id == 2, lpattern(dash)) ///
(lfit y x if id == 3, lpattern(dash)) ///
, /*legend(order(1 "A" 2 "B" 3 "C") title(Region))*/ legend(off) ///
xtitle("Component 1") ytitle("Component 2") ///
title("Case A:" "Regional correlation," "individual orthogonality") ///
xlabel(none) ylabel(none) name(casea, replace)
// Case B
clear
set seed 1
set obs 4 // Generate four clusters
generate id = _n
generate u_i = 300 if id == 1 // Generate cluster-specific intercepts
replace u_i = 0 if id == 2
replace u_i = 0 if id == 3
replace u_i = -300 if id == 4
expand 100 // Generate units in clusters
bysort id: generate x = -100 + (600 + 100) * runiform()
generate e_ij = rnormal(0,70) // Generate level-1 error term
generate y = x + u_i + e_ij
drop if y < 0 | x < 0
drop if id == 2 & x >= 300
drop if id == 3 & x < 300
bys id: egen ym = mean(y)
bys id: egen xm = mean(x)
twoway (scatter ym xm, msymbol(S)) ///
(scatter y x if id == 1, msymbol(oh)) ///
(scatter y x if id == 2, msymbol(dh)) ///
(scatter y x if id == 3, msymbol(sh)) ///
(scatter y x if id == 4, msymbol(th)) ///
(lfit y x if id == 1, lpattern(dash)) ///
(lfit y x if id == 2, lpattern(dash)) ///
(lfit y x if id == 3, lpattern(dash)) ///
(lfit y x if id == 4, lpattern(dash)) ///
(lfit ym xm, lpattern(solid)) ///
, legend(order(2 "A" 3 "B" 4 "C" 5 "D" 1 "Means") size(small) title(Region:, size(small)) row(1)) ///
xtitle("Component 1") ytitle("Component 2") ///
title("Case B:" "Regional orthogonality," "individual correlation") ///
xlabel(none) ylabel(none) name(caseb, replace)
// Case C
clear
set seed 1
set obs 3
generate id = _n
generate u_i = 300 if id == 1
replace u_i = 0 if id == 2
replace u_i = -300 if id == 3
expand 150
bysort id: generate x = -100 + (600 + 100) * runiform()
generate e_ij = rnormal(0,70) // Generate level-1 error term
generate y = x + u_i + e_ij
drop if y < 0 | x < 0
bys id: egen ym = mean(y)
bys id: egen xm = mean(x)
twoway (scatter y x if id == 1, msymbol(oh)) ///
(scatter y x if id == 2, msymbol(dh)) ///
(scatter y x if id == 3, msymbol(sh)) ///
(scatter ym xm, msymbol(S)) ///
(lfit y x if id == 1, lpattern(dash)) ///
(lfit y x if id == 2, lpattern(dash)) ///
(lfit y x if id == 3, lpattern(dash)) ///
(lfit ym xm, lpattern(solid)) ///
, /*legend(order(1 "A" 2 "B" 3 "C") title(Region))*/ legend(off) ///
xtitle("Component 1") ytitle("Component 2") ///
title("Case C:" "Negative regional correlation," "positive individual correlation") ///
xlabel(none) ylabel(none) ///
name(casec, replace)
grc1leg casea caseb casec, legendfrom(caseb) span pos(6) row(1) name(combined, replace)
