Imputation at level 2 by Bayesian linear regression

Imputes univariate missing data at level 2 using Bayesian linear regression analysis. Variables are level 1 are aggregated at level 2. The group identifier at level 2 must be indicated by type = -2 in the predictorMatrix.

Usage

mice.impute.2lonly.norm(y, ry, x, type, wy = NULL, ...)

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.
type: Group identifier must be specified by '-2'. Predictors must be specified by '1'.
wy: Logical vector of length length(y). A TRUE value indicates locations in y for which imputations are created.
...: Other named arguments.

Value

A vector of length nmis with imputations.

Details

This function allows in combination with mice.impute.2l.pan switching regression imputation between level 1 and level 2 as described in Yucel (2008) or Gelman and Hill (2007, p. 541).

The function checks for partial missing level-2 data. Level-2 data are assumed to be constant within the same cluster. If one or more entries are missing, then the procedure aborts with an error message that identifies the cluster with incomplete level-2 data. In such cases, one may first fill in the cluster mean (or mode) by the 2lonly.mean method to remove inconsistencies.

Note

For a more general approach, see miceadds::mice.impute.2lonly.function().

References

Gelman, A. and Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge, Cambridge University Press.

Yucel, RM (2008). Multiple imputation inference for multivariate multilevel continuous data with ignorable non-response. Philosophical Transactions of the Royal Society A, 366, 2389-2404.

Van Buuren, S. (2018). Flexible Imputation of Missing Data. Second Edition. Chapman & Hall/CRC. Boca Raton, FL.

Author

Alexander Robitzsch (IPN - Leibniz Institute for Science and Mathematics Education, Kiel, Germany), robitzsch@ipn.uni-kiel.de

Examples

# simulate some data
# x,y ... level 1 variables
# v,w ... level 2 variables

G <- 250 # number of groups
n <- 20 # number of persons
beta <- .3 # regression coefficient
rho <- .30 # residual intraclass correlation
rho.miss <- .10 # correlation with missing response
missrate <- .50 # missing proportion
y1 <- rep(rnorm(G, sd = sqrt(rho)), each = n) + rnorm(G * n, sd = sqrt(1 - rho))
w <- rep(round(rnorm(G), 2), each = n)
v <- rep(round(runif(G, 0, 3)), each = n)
x <- rnorm(G * n)
y <- y1 + beta * x + .2 * w + .1 * v
dfr0 <- dfr <- data.frame("group" = rep(1:G, each = n), "x" = x, "y" = y, "w" = w, "v" = v)
dfr[rho.miss * x + rnorm(G * n, sd = sqrt(1 - rho.miss)) < qnorm(missrate), "y"] <- NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "w"] <- NA
dfr[rep(rnorm(G), each = n) < qnorm(missrate), "v"] <- NA

# empty mice imputation
imp0 <- mice(as.matrix(dfr), maxit = 0)
predM <- imp0$predictorMatrix
impM <- imp0$method

# multilevel imputation
predM1 <- predM
predM1[c("w", "y", "v"), "group"] <- -2
predM1["y", "x"] <- 1 # fixed x effects imputation
impM1 <- impM
impM1[c("y", "w", "v")] <- c("2l.pan", "2lonly.norm", "2lonly.pmm")

# y ... imputation using pan
# w ... imputation at level 2 using norm
# v ... imputation at level 2 using pmm

imp1 <- mice(as.matrix(dfr),
  m = 1, predictorMatrix = predM1,
  method = impM1, maxit = 1, paniter = 500
)
#> 
#>  iter imp variable
#>   1   1  y  w  v

# Demonstration that 2lonly.norm aborts for partial missing data.
# Better use 2lonly.mean for repair.
data <- data.frame(
  patid = rep(1:4, each = 5),
  sex = rep(c(1, 2, 1, 2), each = 5),
  crp = c(
    68, 78, 93, NA, 143,
    5, 7, 9, 13, NA,
    97, NA, 56, 52, 34,
    22, 30, NA, NA, 45
  )
)
pred <- make.predictorMatrix(data)
pred[, "patid"] <- -2
# only missing value (out of five) for patid == 1
data[3, "sex"] <- NA
if (FALSE) { # \dontrun{
# The following fails because 2lonly.norm found partially missing
# level-2 data
# imp <- mice(data, method = c("", "2lonly.norm", "2l.pan"),
#             predictorMatrix = pred, maxit = 1, m = 2)
# > iter imp variable
# > 1   1  sex  crpError in .imputation.level2(y = y, ... :
# >   Method 2lonly.norm found the following clusters with partially missing
# >    level-2 data: 1
# > Method 2lonly.mean can fix such inconsistencies.
} # }

# In contrast, if all sex values are missing for patid == 1, it runs fine,
# except on r-patched-solaris-x86. I used dontrun to evade CRAN errors.
if (FALSE) { # \dontrun{
data[1:5, "sex"] <- NA
imp <- mice(data,
  method = c("", "2lonly.norm", "2l.pan"),
  predictorMatrix = pred, maxit = 1, m = 2
)
} # }