mice (version 3.17.0)

mice.impute.quadratic: Imputation of quadratic terms

Description

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

Usage

mice.impute.quadratic(y, ry, x, wy = NULL, quad.outcome = NULL, ...)

Value

Vector with imputed data, same type as y, and of length sum(wy)

Arguments

y

Vector to be imputed

ry

Logical vector of length length(y) indicating the the subset y[ry] of elements in y to which the imputation model is fitted. The ry generally distinguishes the observed (TRUE) and missing values (FALSE) in y.

x

Numeric design matrix with length(y) rows with predictors for y. Matrix x may have no missing values.

wy

Logical vector of length length(y). A TRUE value indicates locations in y for which imputations are created.

quad.outcome

The name of the outcome in the quadratic analysis as a character string. For example, if the substantive model of interest is y ~ x + xx, then "y" would be the quad.outcome

...

Other named arguments.

Author

Mingyang Cai and Gerko Vink

Details

This function implements the "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 \(Y^2\).

See Also

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.lasso.logreg(), mice.impute.lasso.norm(), mice.impute.lasso.select.logreg(), mice.impute.lasso.select.norm(), mice.impute.lda(), mice.impute.logreg(), mice.impute.logreg.boot(), mice.impute.mean(), mice.impute.midastouch(), mice.impute.mnar.logreg(), mice.impute.mpmm(), mice.impute.norm(), mice.impute.norm.boot(), mice.impute.norm.nob(), mice.impute.norm.predict(), mice.impute.pmm(), mice.impute.polr(), mice.impute.polyreg(), mice.impute.rf(), mice.impute.ri()

Examples

# 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, quad.outcome = "y")

# 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))