Imputation of quadratic terms
Imputes incomplete variable that appears as both main effect and quadratic effect in the complete-data model.
mice.impute.quadratic(y, ry, x, wy = NULL, ...)
y |
Vector to be imputed |
ry |
Logical vector of length |
x |
Numeric design matrix with |
wy |
Logical vector of length |
... |
Other named arguments. |
This function implements the "polynomial combination" method. First, the polynomial combination Z = Y β_1 + Y^2 β_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.
Vector with imputed data, same type as y, and of length
sum(wy)
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.
Gerko Vink (University of Utrecht), g.vink@uu.nl
mice.impute.pmm
Van Buuren, S. (2018).
Flexible Imputation of Missing Data. Second Edition.
Chapman & Hall/CRC. Boca Raton, FL.
Vink, G., van Buuren, S. (2013). Multiple Imputation of Squared Terms. Sociological Methods & Research, 42:598-607.
Other univariate imputation functions:
mice.impute.cart(),
mice.impute.lda(),
mice.impute.logreg.boot(),
mice.impute.logreg(),
mice.impute.mean(),
mice.impute.midastouch(),
mice.impute.mnar.logreg(),
mice.impute.norm.boot(),
mice.impute.norm.nob(),
mice.impute.norm.predict(),
mice.impute.norm(),
mice.impute.pmm(),
mice.impute.polr(),
mice.impute.polyreg(),
mice.impute.rf(),
mice.impute.ri()
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$xx, col = mdc(1), xlab = "x", ylab = "xx")
cmp <- complete(imp)
points(cmp$x[is.na(dat$x)], cmp$xx[is.na(dat$x)], col = mdc(2))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.