mice.impute.SuperLearner {superMICE}

SuperLearner method for mice package.

Description

Method for the mice package that uses SuperLearner as the predctive algorithm. Model fitting is done using the SuperLearner package.

Usage

mice.impute.SuperLearner(
  y,
  ry,
  x,
  wy = NULL,
  SL.library,
  kernel = c("gaussian", "uniform", "triangular"),
  bw = c(0.1, 0.2, 0.25, 0.3, 0.5, 1, 2.5, 5, 10, 20),
  bw.update = TRUE,
  ...
)

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.

SL.library

For SuperLearner: Either a character vector of prediction algorithms or list containing character vectors as specified by the SuperLearner package. See details below.

kernel

One of "gaussian", "uniform", "triangular". Kernel function used to compute weights.

bw

NULL or numeric value for bandwidth of kernel function (as standard deviations of the kernel).

bw.update

logical indicating whether bandwidths should be computed every iteration or only on the first iteration. Default is TRUE, but FALSE may speed up the run time at the cost of accuracy.

...

Further arguments passed to SuperLearner.

Details

mice.impute.SuperLearner() is a method for use with the mice() function that implements the ensemble predictive model, SuperLearner (van der Laan, 2011), into the mice (van Buuren, 2011) multiple imputation procedure. This function is never called directly, instead a user that wishes to use SuperLearner in MICE simply needs to set the argument method = "SuperLearner" in the call to mice(). Arguments for the SuperLearner() function are passed from mice as extra arguments in the mice() call.

All MICE methods randomly generate imputed values for a number of data sets. The approach of SuperMICE is to estimate parameters for a normal distribution centered at the point estimate for an imputed value predicted by a SuperLearner model. The point estimates are obtained by fitting a selection of different predictive models on complete cases and determining an optimal weighted average of candidate models to predict the missing cases. SuperMICE uses the implementation of SuperLearner found in the SuperLearner package. The models to be used with SuperLearner() are supplied by the user as a character vector. For a full list of available methods see listWrappers().

SuperLearner models do not produce standard errors for estimates, so instead we use a kernel based estimate of local variance around each point estimate as the variance parameter in the normal distribution used to randomly sample values. The kernel can be set by the user with the kernel argument as either a gaussian kernel, uniform kernel, or triangular kernel. The user must also supply a list of candidate bandwidths in the bw argument as a numeric vector. For more information on the variance and bandwidth selection see Laqueur, et. al (2021). In every iteration the mice procedure, the optimal bandwidth is reselected. This may be changed to select the bandwidth only on the first iteration to speed up the total run time of the imputation by changing bw.update to FALSE; however this may bias your results. Note that this only applies to continuous response variables. In the binary case the variance is a function of the SuperLearner estimate.

Value

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

References

Laqueur, H. S., Shev, A. B., Kagawa, R. M. C. (2021). SuperMICE: An Ensemble Machine Learning Approach to Multiple Imputation by Chained Equations. American Journal of Epidemiology, kwab271, doi:10.1093/aje/kwab271.

Van Buuren, S., Groothuis-Oudshoorn, K. (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. doi:10.18637/jss.v045.i03.

van der Laan, M. J., Polley, E. C. and Hubbard, A. E. (2008) Super Learner, Statistical Applications of Genetics and Molecular Biology, 6, article 25.

See Also

mice(), SuperLearner()

Examples

  #Multiple imputation with missingness on a continuous variable.

  #Randomly generated data with missingness in x2. The probability of x2
  #  being missing increases with with value of x1.
  n <- 20
  pmissing <- 0.10
  x1 <- runif(n, min = -3, max = 3)
  x2 <- x1^2 + rnorm(n, mean = 0, sd = 1)
  error <- rnorm(n, mean = 0, sd = 1)
  y <- x1 + x2 + error
  f <- ecdf(x1)
  x2 <- ifelse(runif(x2) < (f(x1) * 2 * pmissing), NA, x2)
  dat <- data.frame(y, x1, x2)

  #Create vector of SuperLearner method names
  #  Note: see SuperLearner::listWrappers() for a full list of methods
  #    available.
  SL.lib <- c("SL.mean", "SL.glm")

  #Run mice().
  #  Note 1: m >= 30 and maxit >= 10 are recommended outside of this
  #    toy example
  #  Note 2: a denser bandwidth grid is recommended, see default for bw
  #    argument for example.
  imp.SL <- mice::mice(dat, m = 2, maxit = 2,
                       method = "SuperLearner",
                       print = TRUE, SL.library = SL.lib,
                       kernel = "gaussian",
                       bw = c(0.25, 1, 5))