/*** DAY 4 CODE ***/

use http://www.stata-press.com/data/mlmus2/gcse, clear

regress gcse lrt if school==1
predict p_gcse, xb 
twoway (scatter gcse lrt) (line p_gcse lrt, sort) if school==1, xtitle(LRT) ytitle(GCSE)

egen num = count(gcse), by(school)
statsby inter=_b[_cons] slope=_b[lrt], by(school) saving(ols): regress gcse lrt if num>4 
sort school
merge school using ols
drop _merge

twoway scatter slope inter, xtitle(Intercept) ytitle(Slope)

egen pickone = tag(school)
summarize inter slope if pickone==1
correlate inter slope if pickone==1, covariance

generate pred = inter + slope*lrt

sort school lrt
twoway (line pred lrt, connect(ascending)), xtitle(LRT) ytitle(Fitted regression lines)


** 4.5.1 Using xtmixed 
xtmixed gcse lrt || school:, mle
estimates store ri

xtmixed gcse lrt || school: lrt,  cov(unstructured) mle
estat recovariance
estimates store rc


*** 4.6 Testing the slope variance

lrtest ri rc