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Imputes univariate systematically and sporadically missing data using a two-level normal model using lme4::lmer().


mice.impute.2l.lmer(y, ry, x, type, wy = NULL, intercept = TRUE, ...)



Vector to be imputed


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.


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


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'.


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


Logical determining whether the intercept is automatically added.


Arguments passed down to lmer


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


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.

While the method is fully Bayesian, it may fix parameters of the variance-covariance matrix or the random effects to their estimated value in cases where creating draws from the posterior is not possible. The procedure throws a warning when this happens.

If lme4::lmer() fails, the procedure prints the warning "lmer does not run. Simplify imputation model" and returns the current imputation. If that happens we see flat lines in the trace line plots. Thus, the appearance of flat trace lines should be taken as an additional alert to a problem with imputation model fitting.


Jolani S. (2017) Hierarchical imputation of systematically and sporadically missing data: An approximate Bayesian approach using chained equations. Forthcoming.

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.

Van Buuren, S. (2011) Multiple imputation of multilevel data. In Hox, J.J. and and Roberts, J.K. (Eds.), The Handbook of Advanced Multilevel Analysis, Chapter 10, pp. 173--196. Milton Park, UK: Routledge.

See also


Shahab Jolani, 2017