Imputation by a two-level logistic model using glmer

Imputes univariate systematically and sporadically missing data using a two-level logistic model using lme4::glmer()

Usage

mice.impute.2l.bin(
  y,
  ry,
  x,
  type,
  wy = NULL,
  intercept = TRUE,
  random.effects = c("laplace", "eb", "marginal"),
  ...
)

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: Vector of length ncol(x) identifying random and class variables. Random variables are identified by a '2'. The class variable (only one is allowed) is coded as '-2'. Fixed effects are indicated by a '1'.
wy: Logical vector of length length(y). A TRUE value indicates locations in y for which imputations are created.
intercept: Logical determining whether the intercept is automatically added.
random.effects: Character string specifying how the random effect is drawn for sporadic clusters. One of "laplace" (default), "eb", or "marginal". See Details.
...: Arguments passed down to glmer

Value

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

Details

Data are missing systematically if they have not been measured, e.g., in the case where we combine data from different sources. Data are missing sporadically if they have been partially observed.

The random.effects argument controls how the cluster-specific random effect \(b_i^*\) is drawn for clusters that have missing values:

"laplace": (default) For clusters with observed data, draws \(b_i^*\) from \(N(m_i, V_i)\) where \(m_i\) is the posterior mode (BLUP) and \(V_i\) is the Laplace-approximated posterior variance returned by lme4::ranef(fit, condVar = TRUE). For clusters with no observed data, draws from the marginal prior \(N(0, \psi^*)\). This is the method recommended by Audigier et al. (2018).
"eb": Empirical Bayes: for clusters with observed data, uses the BLUP as the mean but draws with the full marginal variance \(\psi^*\), ignoring posterior uncertainty in \(b_i\).
"marginal": Draws all \(b_i^*\) from the marginal prior \(N(0, \psi^*)\) regardless of whether the cluster has observed data. This was the original behaviour and is correct only for systematic missingness.

References

Audigier, V., White, I. R., Jolani, S., Debray, T. P. A., Quartagno, M., Carpenter, J., van Buuren, S., & Resche-Rigon, M. (2018). Multiple imputation for multilevel data with continuous and binary variables. Statistical Science, 33(2), 160-183. doi:10.1214/18-STS646

Jolani S., Debray T.P.A., Koffijberg H., van Buuren S., Moons K.G.M. (2015). Imputation of systematically missing predictors in an individual participant data meta-analysis: a generalized approach using MICE. Statistics in Medicine, 34:1841-1863.

Author

Shahab Jolani, 2015; adapted to mice, SvB, 2018; random.effects argument, SvB, 2026

Examples

library(tidyr)
library(dplyr)
#> 
#> Attaching package: ‘dplyr’
#> The following objects are masked from ‘package:stats’:
#> 
#>     filter, lag
#> The following objects are masked from ‘package:base’:
#> 
#>     intersect, setdiff, setequal, union
data("toenail2")
data <- tidyr::complete(toenail2, patientID, visit) %>%
  tidyr::fill(treatment) %>%
  dplyr::select(-time) %>%
  dplyr::mutate(patientID = as.integer(patientID))
if (FALSE) { # \dontrun{
pred <- mice(data, print = FALSE, maxit = 0, seed = 1)$pred
pred["outcome", "patientID"] <- -2
imp <- mice(data, method = "2l.bin", pred = pred, maxit = 1, m = 1, seed = 1)
imp_laplace <- mice(data, method = "2l.bin", pred = pred, maxit = 1, m = 1,
                    seed = 1, random.effects = "laplace")
imp_eb <- mice(data, method = "2l.bin", pred = pred, maxit = 1, m = 1,
               seed = 1, random.effects = "eb")
imp_marginal <- mice(data, method = "2l.bin", pred = pred, maxit = 1, m = 1,
                     seed = 1, random.effects = "marginal")
} # }

Imputation by a two-level logistic model using `glmer`