/*******************

power.do
Example file demonstrating increase in power from
multiple imputation

Written by Russell Dimond, Summer 2012 for the
Social Science Computing Cooperative at UW-Madison

********************/
clear all
set more off

// generate random data
// x1-x10 drawn independently from standard normal distribution
// y is sum of x's, plus normal error term
set obs 1000
set seed 17
forval i=1/10 {
	gen x`i'=invnorm(runiform())
}
egen y=rowtotal(x*)
replace y=y+8*invnorm(runiform())

// drop values at random
forval i=1/10 {
	replace x`i'=. if runiform()<.1
}

// complete cases analysis
reg y x*

// run the imputation models to see how they perform
// note the low R-squared values
unab vars: *
foreach x of varlist x* {
	local xvars: list vars - x
	reg `x' `xvars'
}

// impute
mi set wide
mi register imputed x*
mi register regular y
mi impute chained (regress) x*=y, add(10)

// results after multiple imputation
mi estimate: reg y x*