# Imputation of a Continuous or a Binary Variable From a Two-Level Regression Model using `lme4` or `blme` The function `mice.impute.2l.continuous` imputes values of continuous variables with a linear mixed effects model using `lme4::lmer` or `blme::blmer`. The `lme4::lmer` or `blme::blmer` function is also used for predictive mean matching where the match is based on predicted values which contain the fixed and (sampled) random effects. Binary variables can be imputed from a two-level logistic regression model fitted with the `lme4::glmer` or `blme::bglmer` function. See Snijders and Bosker (2012) and Zinn (2013) for details. ```r mice.impute.2l.continuous(y, ry, x, type, intercept=TRUE, groupcenter.slope=FALSE, draw.fixed=TRUE, random.effects.shrinkage=1E-6, glmer.warnings=TRUE, blme_use=FALSE, blme_args=NULL, ... ) mice.impute.2l.pmm(y, ry, x, type, intercept=TRUE, groupcenter.slope=FALSE, draw.fixed=TRUE, random.effects.shrinkage=1E-6, glmer.warnings=TRUE, donors=5, match_sampled_pars=TRUE, blme_use=FALSE, blme_args=NULL, ... ) mice.impute.2l.binary(y, ry, x, type, intercept=TRUE, groupcenter.slope=FALSE, draw.fixed=TRUE, random.effects.shrinkage=1E-6, glmer.warnings=TRUE, blme_use=FALSE, blme_args=NULL, ... ) ``` ## Arguments - `y`: Incomplete data vector of length `n` - `ry`: Vector of missing data pattern (`FALSE` -- missing, `TRUE` -- observed) - `x`: Matrix (`n` x `p`) of complete predictors. - `type`: Type of predictor variable. The cluster identifier has type `-2`, fixed effects predictors without a random slope type `1` and predictors with fixed effects and random effects have type `2`. If the cluster mean should be included for a covariate, `3` should be chosen. The specification `4` includes the cluster mean, the fixed effect and the random effect. - `intercept`: Optional logical indicating whether the intercept should be included. - `groupcenter.slope`: Optional logical indicating whether covariates should be centered around group means - `draw.fixed`: Optional logical indicating whether fixed effects parameter should be randomly drawn - `random.effects.shrinkage`: Shrinkage parameter for stabilizing the covariance matrix of random effects - `glmer.warnings`: Optional logical indicating whether warnings from `glmer` should be displayed - `blme_use`: Logical indicating whether the `blme` package should be used. - `blme_args`: (Prior) Arguments for `blme`, see `blme::blmer` and `blme::bmerDist-class`. - `donors`: Number of donors used for predictive mean matching - `match_sampled_pars`: Logical indicating whether values of nearest neighbors should also be sampled in pmm imputation. - ``...``: Further arguments to be passed ## Returns A vector of length `nmis=sum(!ry)` with imputed values. ## References Snijders, T. A. B., & Bosker, R. J. (2012). **Multilevel analysis: An introduction to basic and advanced multilevel modeling**. Thousand Oaks, CA: Sage. Zinn, S. (2013). **An imputation model for multilevel binary data**. NEPS Working Paper No 31. ## See Also See `mice.impute.ml.lmer` for imputation for datasets with more than two levels (e.g., three-level datasets or cross-classified datasets). Variables at a higher level (e.g. at level 2) can be imputed using `2lonly` functions, for example the `mice::mice.impute.2lonly.norm` function in the `mice` package or the general `mice.impute.2lonly.function` function in the `miceadds` package which using an already defined imputation method at level 1. If a level-2 variable for 3-level data should be imputed, then `mice.impute.ml.lmer` can also be used to impute this variable with a two-level imputation model in which level 1 corresponds to the original level-2 units and level 2 corresponds to the original level-3 units. See `mice::mice.impute.2l.norm` and `mice::mice.impute.2l.pan` for imputation functions in the `mice` package under fully conditional specification for normally distributed variables. The function `mice::mice.impute.2l.norm` allows for residual variances which are allowed to vary across groups while `mice::mice.impute.2l.pan` assumes homogeneous residual variances. The `micemd` package provides further imputation methods for the `mice` package for imputing multilevel data with fully conditional specification. The function `micemd::mice.impute.2l.jomo` has similar functionality like `mice::mice.impute.2l.pan` and imputes normally distributed two-level data with a Bayesian MCMC approach, but relies on the `jomo` package instead of the `pan` package. The functions `mice::mice.impute.2l.lmer` and `micemd::mice.impute.2l.glm.norm` have similar functionality like `mice.impute.2l.continuous` and imputes normally distributed two-level data. The function `{micemd::mice.impute.2l.glm.bin}` has similar functionality like `mice.impute.2l.binary` and imputes binary two-level data. The `hmi` package imputes single-level and multilevel data and is also based on fully conditional specification. The package relies on the MCMC estimation implemented in the `MCMCglmm` package. The imputation procedure can be run with the `hmi::hmi` function. See the `pan` (`pan::pan`) and the `jomo` (`jomo::jomo`) package for joint multilevel imputation. See `mitml::panImpute` and `mitml::jomoImpute` for wrapper functions to these packages in the `mitml` package. Imputation by chained equations can also be conducted in blocks of multivariate conditional distributions since `mice` 3.0.0 (see the `blocks` argument in `mice::mice`). The `mitml::panImpute` and `mitml::jomoImpute` functions can be used with `mice::mice` by specifying imputation methods `"panImpute"` (see `mice::mice.impute.panImpute`)) and `"jomoImpute"` (see `mice::mice.impute.jomoImpute`)). ## Examples ```r ## Not run: ############################################################################# # EXAMPLE 1: Imputation of a binary variable ############################################################################# #--- simulate missing values set.seed(976) G <- 30 # number of groups n <- 8 # number of persons per group iccx <- .2 # intra-class correlation X iccy <- .3 # latent intra-class correlation binary outcome bx <- .4 # regression coefficient threshy <- stats::qnorm(.70) # threshold for y x <- rep( rnorm( G, sd=sqrt( iccx) ), each=n ) + rnorm(G*n, sd=sqrt( 1 - iccx) ) y <- bx * x + rep( rnorm( G, sd=sqrt( iccy) ), each=n ) + rnorm(G*n, sd=sqrt( 1 - iccy) ) y <- 1 * ( y > threshy ) dat <- data.frame( group=100+rep(1:G, each=n), x=x, y=y ) #* create some missings dat1 <- dat dat1[ seq( 1, G*n, 3 ),"y" ] <- NA dat1[ dat1$group==2, "y" ] <- NA #--- prepare imputation in mice vars <- colnames(dat1) V <- length(vars) #* predictor matrix predmat <- matrix( 0, nrow=V, ncol=V) rownames(predmat) <- colnames(predmat) <- vars predmat["y", ] <- c(-2,2,0) #* imputation methods impmeth <- rep("",V) names(impmeth) <- vars impmeth["y"] <- "2l.binary" #** imputation with logistic regression ('2l.binary') imp1 <- mice::mice( data=as.matrix(dat1), method=impmeth, predictorMatrix=predmat, maxit=1, m=5 ) #** imputation with predictive mean matching ('2l.pmm') impmeth["y"] <- "2l.pmm" imp2 <- mice::mice( data=as.matrix(dat1), method=impmeth, predictorMatrix=predmat, maxit=1, m=5 ) #** imputation with logistic regression using blme package blme_args <- list( "cov.prior"="invwishart") imp3 <- mice::mice( data=as.matrix(dat1), method=impmeth, predictorMatrix=predmat, maxit=1, m=5, blme_use=TRUE, blme_args=blme_args ) ## End(Not run) ```

mice_imputation_2l_lmer function