```
# Check that aregImpute can almost exactly estimate missing values when
# there is a perfect nonlinear relationship between two variables
# Fit restricted cubic splines with 4 knots for x1 and x2, linear for x3
set.seed(3)
x1 <- rnorm(200)
x2 <- x1^2
x3 <- runif(200)
m <- 30
x2[1:m] <- NA
a <- aregImpute(~x1+x2+I(x3), n.impute=5, nk=4, match='closest')
a
matplot(x1[1:m]^2, a$imputed$x2)
abline(a=0, b=1, lty=2)
x1[1:m]^2
a$imputed$x2
# Multiple imputation and estimation of variances and covariances of
# regression coefficient estimates accounting for imputation
# Example 1: large sample size, much missing data, no overlap in
# NAs across variables
x1 <- factor(sample(c('a','b','c'),1000,TRUE))
x2 <- (x1=='b') + 3*(x1=='c') + rnorm(1000,0,2)
x3 <- rnorm(1000)
y <- x2 + 1*(x1=='c') + .2*x3 + rnorm(1000,0,2)
orig.x1 <- x1[1:250]
orig.x2 <- x2[251:350]
x1[1:250] <- NA
x2[251:350] <- NA
d <- data.frame(x1,x2,x3,y, stringsAsFactors=TRUE)
# Find value of nk that yields best validating imputation models
# tlinear=FALSE means to not force the target variable to be linear
f <- aregImpute(~y + x1 + x2 + x3, nk=c(0,3:5), tlinear=FALSE,
data=d, B=10) # normally B=75
f
# Try forcing target variable (x1, then x2) to be linear while allowing
# predictors to be nonlinear (could also say tlinear=TRUE)
f <- aregImpute(~y + x1 + x2 + x3, nk=c(0,3:5), data=d, B=10)
f
if (FALSE) {
# Use 100 imputations to better check against individual true values
f <- aregImpute(~y + x1 + x2 + x3, n.impute=100, data=d)
f
par(mfrow=c(2,1))
plot(f)
modecat <- function(u) {
tab <- table(u)
as.numeric(names(tab)[tab==max(tab)][1])
}
table(orig.x1,apply(f$imputed$x1, 1, modecat))
par(mfrow=c(1,1))
plot(orig.x2, apply(f$imputed$x2, 1, mean))
fmi <- fit.mult.impute(y ~ x1 + x2 + x3, lm, f,
data=d)
sqrt(diag(vcov(fmi)))
fcc <- lm(y ~ x1 + x2 + x3)
summary(fcc) # SEs are larger than from mult. imputation
}
if (FALSE) {
# Example 2: Very discriminating imputation models,
# x1 and x2 have some NAs on the same rows, smaller n
set.seed(5)
x1 <- factor(sample(c('a','b','c'),100,TRUE))
x2 <- (x1=='b') + 3*(x1=='c') + rnorm(100,0,.4)
x3 <- rnorm(100)
y <- x2 + 1*(x1=='c') + .2*x3 + rnorm(100,0,.4)
orig.x1 <- x1[1:20]
orig.x2 <- x2[18:23]
x1[1:20] <- NA
x2[18:23] <- NA
#x2[21:25] <- NA
d <- data.frame(x1,x2,x3,y, stringsAsFactors=TRUE)
n <- naclus(d)
plot(n); naplot(n) # Show patterns of NAs
# 100 imputations to study them; normally use 5 or 10
f <- aregImpute(~y + x1 + x2 + x3, n.impute=100, nk=0, data=d)
par(mfrow=c(2,3))
plot(f, diagnostics=TRUE, maxn=2)
# Note: diagnostics=TRUE makes graphs similar to those made by:
# r <- range(f$imputed$x2, orig.x2)
# for(i in 1:6) { # use 1:2 to mimic maxn=2
# plot(1:100, f$imputed$x2[i,], ylim=r,
# ylab=paste("Imputations for Obs.",i))
# abline(h=orig.x2[i],lty=2)
# }
table(orig.x1,apply(f$imputed$x1, 1, modecat))
par(mfrow=c(1,1))
plot(orig.x2, apply(f$imputed$x2, 1, mean))
fmi <- fit.mult.impute(y ~ x1 + x2, lm, f,
data=d)
sqrt(diag(vcov(fmi)))
fcc <- lm(y ~ x1 + x2)
summary(fcc) # SEs are larger than from mult. imputation
}
if (FALSE) {
# Study relationship between smoothing parameter for weighting function
# (multiplier of mean absolute distance of transformed predicted
# values, used in tricube weighting function) and standard deviation
# of multiple imputations. SDs are computed from average variances
# across subjects. match="closest" same as match="weighted" with
# small value of fweighted.
# This example also shows problems with predicted mean
# matching almost always giving the same imputed values when there is
# only one predictor (regression coefficients change over multiple
# imputations but predicted values are virtually 1-1 functions of each
# other)
set.seed(23)
x <- runif(200)
y <- x + runif(200, -.05, .05)
r <- resid(lsfit(x,y))
rmse <- sqrt(sum(r^2)/(200-2)) # sqrt of residual MSE
y[1:20] <- NA
d <- data.frame(x,y)
f <- aregImpute(~ x + y, n.impute=10, match='closest', data=d)
# As an aside here is how to create a completed dataset for imputation
# number 3 as fit.mult.impute would do automatically. In this degenerate
# case changing 3 to 1-2,4-10 will not alter the results.
imputed <- impute.transcan(f, imputation=3, data=d, list.out=TRUE,
pr=FALSE, check=FALSE)
sd <- sqrt(mean(apply(f$imputed$y, 1, var)))
ss <- c(0, .01, .02, seq(.05, 1, length=20))
sds <- ss; sds[1] <- sd
for(i in 2:length(ss)) {
f <- aregImpute(~ x + y, n.impute=10, fweighted=ss[i])
sds[i] <- sqrt(mean(apply(f$imputed$y, 1, var)))
}
plot(ss, sds, xlab='Smoothing Parameter', ylab='SD of Imputed Values',
type='b')
abline(v=.2, lty=2) # default value of fweighted
abline(h=rmse, lty=2) # root MSE of residuals from linear regression
}
if (FALSE) {
# Do a similar experiment for the Titanic dataset
getHdata(titanic3)
h <- lm(age ~ sex + pclass + survived, data=titanic3)
rmse <- summary(h)$sigma
set.seed(21)
f <- aregImpute(~ age + sex + pclass + survived, n.impute=10,
data=titanic3, match='closest')
sd <- sqrt(mean(apply(f$imputed$age, 1, var)))
ss <- c(0, .01, .02, seq(.05, 1, length=20))
sds <- ss; sds[1] <- sd
for(i in 2:length(ss)) {
f <- aregImpute(~ age + sex + pclass + survived, data=titanic3,
n.impute=10, fweighted=ss[i])
sds[i] <- sqrt(mean(apply(f$imputed$age, 1, var)))
}
plot(ss, sds, xlab='Smoothing Parameter', ylab='SD of Imputed Values',
type='b')
abline(v=.2, lty=2) # default value of fweighted
abline(h=rmse, lty=2) # root MSE of residuals from linear regression
}
d <- data.frame(x1=rnorm(50), x2=c(rep(NA, 10), runif(40)),
x3=c(runif(4), rep(NA, 11), runif(35)))
reformM(~ x1 + x2 + x3, data=d)
reformM(~ x1 + x2 + x3, data=d, nperm=2)
# Give result or one of the results as the first argument to aregImpute
```

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