library(mice)
?boys
str(boys)

## impute data set (random seed only for reproducability)
imp <- mice(boys, m = 3, seed = 43)
?mice

## extract the three complete data sets
dat1 <- complete(imp, 1)
dat2 <- complete(imp, 2)
dat3 <- complete(imp, 3)
complete(imp, 4)

str(dat1)
#####
## 1) Easy using functions "with" and "pool" from package mice
## Good if you do standard analysis like lm, glm
#####
fmMI <- with(imp, lm(hc ~ age + hgt + wgt))
poolRes <- pool(fmMI)
round(summary(poolRes), 2)
## Good and simple overview: http://sites.stat.psu.edu/~jls/mifaq.html

#####
## 2) Do everything manually
## Good if you do non-standard analysis
#####
## Do analysis for each data set
fmMF1 <- lm(hc ~ age + hgt + wgt, data = dat1)
summary(fmMF1)
fmMF2 <- lm(hc ~ age + hgt + wgt, data = dat2)
summary(fmMF2)
fmMF3 <- lm(hc ~ age + hgt + wgt, data = dat3)
summary(fmMF3)

## save estimates for age
Q <- c(-0.539592, -0.503504, -0.542918)
U <- c(0.060954, 0.06156, 0.060442)^2 ## !! U is variance, not std.error

## Aggragate results
m <- 3
Qbar <- mean(Q)
Ubar <- mean(U)
B <- 1/(m-1)*sum( (Q - Qbar)^2 )
T <- Ubar + (1 + 1/m)*B
nu <- (m-1)*( 1 + Ubar/((1+1/m)*B))^2

alpha <- 0.05
c <- qt(1-alpha/2, df = nu)
## 1-alpha confidence interval for age coefficient
Qbar - c*sqrt(T)
Qbar + c*sqrt(T) ## [-0.66; -0.40]
## Compare to values from before: [-0.66; -0.40] - coincide