QR-based Multiple Imputation

This function is used to multiply impute missing values using quantile regression imputation models.

Usage

mice.impute.rq(y, ry, x, tsf = "none", symm = TRUE, dbounded = FALSE,
  lambda = NULL, x.r = NULL, par = NULL, conditional = TRUE,
  epsilon = 0.001, method.rq = "fn", ...)
mice.impute.rrq(y, ry, x, tsf = "none", symm = TRUE, dbounded = FALSE,
  lambda = NULL, epsilon = 0.001, method.rq = "fn", ...)

Arguments

y: numeric vector of length n with nmis missing values.
ry: missing data indicator. Logical vector of length n: FALSE if y is missing, TRUE if y is observed.
x: matrix n x p of completely observed covariates.
tsf: transformation to be used. Possible options are mcjI for Proposal I, bc for Box-Cox and ao for Aranda-Ordaz transformation models. No transformation is used by default.
symm: logical flag. If TRUE (default) a symmetric transformation is used.
dbounded: logical flag. If TRUE the response y is assumed to be bounded between 0 and 1.
lambda: if conditional = TRUE, a numerical value for the transformation parameter. This is provided by the user or set to zero if not specified. If conditional = FALSE, this argument is ignored.
x.r: range of the mapping for doubly bounded variables.
par: if conditional = FALSE, starting values for nlrq1 can be provided via this argument. See argument start in nlrq1 for details.
conditional: logical flag. If TRUE (default), the transformation parameter is assumed to be known and this must be provided via the argument lambda. Otherwise, it is estimated via nlrq1.
epsilon: constant used to trim the values of the sample space.
method.rq: linear programming algorithm (see rq).
...: additional arguments.

Details

This function implements the methods proposed by Geraci (2016) and Geraci and McLain (2018) to impute missing values using quantile regression models. Uniform values are sampled from [epsilon, 1 - epsilon], therefore allowing the interval to be bounded away from 0 and 1 (default is 0.001). It is possible to specify a quantile regression transformation model with parameter lambda (Geraci and Jones). The function mice.impute.rrq performs imputation based on restricted regression quantiles to avoid quantile crossing (see Geraci 2016 for details).

Value

A vector of length nmis with imputations.

References

Bottai, M., & Zhen, H. (2013). Multiple imputation based on conditional quantile estimation. Epidemiology, Biostatistics, and Public Health, 10(1), e8758.

Geraci, M. (2016). Estimation of regression quantiles in complex surveys with data missing at random: An application to birthweight determinants. Statistical Methods in Medical Research, 25(4), 1393-1421.

Geraci, M., and Jones, M. C. (2015). Improved transformation-based quantile regression. Canadian Journal of Statistics, 43(1), 118-132.

Geraci, M., and McLain, A. (2018). Multiple imputation for bounded variables. Psychometrika, 83(4), 919-940.

van Buuren, S., and Groothuis-Oudshoorn, K. (2011). mice: Multivariate imputation by chained equations in R. Journal of Statistical Software, 45(3), 1–67.

Author

Marco Geraci

Examples


if (FALSE) { # \dontrun{

# Load package 'mice'
require(mice)

# Load data nhanes
data(nhanes)
nhanes2 <- nhanes
nhanes2$hyp <- as.factor(nhanes2$hyp)

# Impute continuous variables using quantile regression
set.seed(199)
imp <- mice(nhanes2, meth = c("polyreg", "rq", "logreg", "rq"), m = 5)

# estimate linear regression and pool results
fit <- lm.mids(bmi ~ hyp + chl, data = imp)
pool(fit)

# Impute using restricted quantile regression
set.seed(199)
imp <- mice(nhanes2, meth = c("polyreg", "rrq", "logreg", "rrq"), m = 5)
fit <- lm.mids(bmi ~ hyp + chl, data = imp)
pool(fit)

# Impute using quantile regression + Box-Cox transformation with parameter
# lambda = 0 (ie, log transformation)

set.seed(199)
imp <- mice(nhanes2, meth = c("polyreg", "rq", "logreg", "rq"), m = 5, tsf = "bc", lambda = 0)
fit <- lm.mids(bmi ~ hyp + chl, data = imp)
pool(fit)


} # }