Estimating slopes and intercept using empirical Bayes estimation

[Chi-Chi Ojinnaka]

Good evening,

I am using a multilevel to predict the effect of parent's income on children's reading scores accounting for variations across schools. The children are nested within schools.

I am using the following syntax: xtmixed reading income || sch:, var

I also want to obtain the estimates of the slope and intercept for each school using empirical bayes method.

Please, how can I obtain the empirical bayes estimates using Stata?

Thank you very much.

[Aspen Chen]

The best linear unbiased predictions (BLUPs) can be placed in variable eb after -xtmixed- with

predict eb, reffects

You asked for the slop and intercept for each school, but what you have is just a random intercept model; the effect of income is modeled to be constant across the schools. You would need something like

xtmixed reading income || sch:income, var

to allow the slopes to vary.

[Chi-Chi Ojinnaka]

Thanks so much. I have another question.

The final mode I have is


xtmixed reading income || sch:income, var
predict yhat, fitted
predict ebslope ebint , reffects
gen bayeint = _b[_cons] + ebint
gen bayeslope = _b[ses] + ebslope ///http://data.princeton.edu/pop510/lang2.html///


Please, how can I obtain the standard errors and 95% confidence intervals. I apologize in advance if this is a fundamental question.

Thank you.

[Aspen Chen]

For standard errors, use

predict slope_se inter_se, reses

to store the standard errors separately

The confidence interval would depend on the value of the predictor(s). For your example, if the intention is to compare/rank the school effects on the reading outcome, a common "naive" approach is to just set the income at zero. Then you can retrieve the lower and upper bounds with

gen lower=ebint-1.96*inter_se
gen upper=ebint+1.96*inter_se

Or simply a "caterpillar plot" of the effects at the intercept can be drawn with

serrbar ebint inter_se id, yline(0) scale(1.96)

[Chi-Chi Ojinnaka]

Thanks very much