Imputation of quadratric terms

Description

Imputes univariate missing data of incomplete variable that appears as both main effect and quadratic effect in the complete-data model.

Usage

mice.impute.quadratic(y, ry, x, ...)

Arguments

Details

This implements polynomial combination method. First, the polynomial combination $Z = Y beta_1 + Y^2 beta_2$ is formed. $Z$ is imputed by predictive mean matching, followed by a decomposition of the imputed data $Z$ into components $Y$ and $Y^2$. See Van Buuren (2012, pp. 139-141) and Vink et al (2012) for more details. The method ensures that 1) the imputed data for $Y$ and $Y^2$ are mutually consistent, and 2) that provides unbiased estimates of the regression weights in a complete-data linear regression that use both $Y$ and $Y^2$.

Value

A vector of length nmis with imputations.

Note

There are two situations to consider. If only the linear term Y is present in the data, calculate the quadratic term YY after imputation. If both the linear term Y and the the quadratic term YY are variables in the data, then first impute Y by calling mice.impute.quadratic() on Y, and then impute YY by passive imputation as meth["YY"] <- "~I(Y^2)". See example section for details. Generally, we would like YY to be present in the data if we need to preserve quadratic relations between YY and any third variables in the multivariate incomplete data that we might wish to impute.

Author(s)

Gerko Vink (University of Utrecht), g.vink@uu.nl

References

van Buuren, S. (2012). Flexible Imputation of Missing Data. Boca Raton, FL: Chapman & Hall/CRC Press.

Vink, G., Frank, L.E., van Buuren, S. (2012). Multiple Imputation of Squares. Sociological Methods & Research, accepted for publication.

See Also

mice.impute.pmm

Examples

require(lattice)

# Create Data
B1=.5
B2=.5
X<-rnorm(1000)
XX<-X^2
e<-rnorm(1000, 0, 1)
Y <- B1*X+B2*XX+e
dat <- data.frame(x=X, xx=XX, y=Y)

# Impose 25 percent MCAR Missingness
dat[0 == rbinom(1000, 1, 1-.25), 1:2] <- NA

# Prepare data for imputation
ini <- mice(dat, maxit=0)
meth <- c("quadratic", "~I(x^2)", "")
pred <- ini$pred
pred[,"xx"] <- 0

# Impute data
imp <- mice(dat, meth=meth, pred=pred)

# Pool results
pool(with(imp, lm(y~x+xx)))

# Plot results
stripplot(imp)
plot(dat$x, dat$xx, col=mdc(1), xlab="x", ylab="xx")
points(complete(imp,1)$x[is.na(dat$x)], complete(imp,1)$xx[is.na(dat$x)], col=mdc(2))