mitml (version 0.4-5)

jomoImpute: Impute single-level and multilevel missing data using jomo

Description

Performs single- and multilevel imputation for (mixed) continuous and categorical data using the jomo package Supports imputation of missing data at level 1 and 2 as well as imputation using random (residual) covariance matrices. See 'Details' for further information.

Usage

jomoImpute(data, type, formula, random.L1 = c("none", "mean", "full"),
  n.burn = 5000, n.iter = 100, m = 10, group = NULL, prior = NULL,
  seed = NULL, save.pred = FALSE, keep.chains = c("full", "diagonal"),
  silent = FALSE)

Value

An object of class mitml, containing the following components:

data

The original (incomplete) data set, sorted according to the cluster variable and (if given) the grouping variable, with several attributes describing the original order ("sort"), grouping ("group") and factor levels of categorical variables.

replacement.mat

A matrix containing the multiple replacements (i.e., imputations) for each missing value. The replacement matrix contains one row for each missing value and one one column for each imputed data set.

index.mat

A matrix containing the row and column index for each missing value. The index matrix is used to link the missing values in the data set with their corresponding rows in the replacement matrix.

call

The matched function call.

model

A list containing the names of the cluster variable, the target variables, and the predictor variables with fixed and random effects, at level 1 and level 2, respectively.

random.L1

A character string denoting the handling of the (random) covariance matrix of residuals at level 1 (see 'Details').

prior

The prior parameters used in the imputation model.

iter

A list containing the number of burn-in iterations, the number of iterations between imputations, and the number of imputed data sets.

par.burnin

A multi-dimensional array containing the parameters of the imputation model from the burn-in phase.

par.imputation

A multi-dimensional array containing the parameters of the imputation model from the imputation phase.

Arguments

data

A data frame containing the incomplete data, the auxiliary variables, the cluster indicator variable, and any other variables that should be included in the imputed datasets.

type

An integer vector specifying the role of each variable in the imputation model or a list of two vectors specifying a two-level model (see 'Details').

formula

A formula specifying the role of each variable in the imputation model or a list of two formulas specifying a two-level model. The basic model is constructed by model.matrix, which allows including derived variables in the imputation model using I() (see 'Details' and 'Examples').

random.L1

A character string denoting if the covariance matrix of residuals should vary across groups and how the values of these matrices are stored (see 'Details'). Can be "none" (common covariance matrix), "mean" (random covariance matrix, storing only mean values), or "full" (random covariance matrix, storing all values). Default is "none".

n.burn

The number of burn-in iterations before any imputations are drawn. Default is 5,000.

n.iter

The number of iterations between imputations. Default is 100.

m

The number of imputed data sets to generate. Default is 10.

group

(optional) A character string denoting the name of an additional grouping variable to be used with the formula argument. If specified, the imputation is run separately within each of these groups.

prior

(optional) A list with components Binv, Dinv, and a for specifying prior distributions for the covariance matrix of random effects and the covariance matrix of residuals (see 'Details'). Default is to use least-informative priors.

seed

(optional) An integer value initializing R's random number generator for reproducible results. Default is to use the global seed.

save.pred

(optional) Logical flag indicating if variables derived using formula should be included in the imputed data sets. Default is FALSE.

keep.chains

(optional) A character string denoting which chains of the MCMC algorithm to store. Can be "full" (stores chains for all parameters) or "diagonal" (stores chains for fixed effects and diagonal entries of the covariance matrices). Default is "full" (see 'Details').

silent

(optional) Logical flag indicating if console output should be suppressed. Default is FALSE.

Author

Simon Grund, Alexander Robitzsch, Oliver Luedtke

Details

This function serves as an interface to the jomo package and supports imputation of single-level and multilevel continuous and categorical data at both level 1 and 2 (see Carpenter & Kenward, 2013; Goldstein et al., 2009). In order for categorical variables to be detected correctly, these must be formatted as a factor variables (see 'Examples'). The imputation model can be specified using either the type or the formula argument.

The type interface is designed to provide quick-and-easy imputations using jomo. The type argument must be an integer vector denoting the role of each variable in the imputation model:

• 1: target variables containing missing data

• 2: predictors with fixed effect on all targets (completely observed)

• 3: predictors with random effect on all targets (completely observed)

• -1: grouping variable within which the imputation is run separately

• -2: cluster indicator variable

• 0: variables not featured in the model

At least one target variable and, for multilevel imputation, the cluster indicator must be specified. If the cluster indicator is omitted, single-level imputation will be performed. The intercept is automatically included as both a fixed and (for multilevel models) a random effect. If a variable of type -1 is found, then separate imputations are performed within each level of that variable.

The formula argument is intended as a more flexible and feature-rich interface to jomo. Specifying the formula argument is similar to specifying other formulae in R. Given below is a list of operators that jomoImpute currently understands:

• ~: separates the target (left-hand) and predictor (right-hand) side of the model

• +: adds target or predictor variables to the model

• *: adds an interaction term of two or more predictors

• |: denotes cluster-specific random effects and specifies the cluster indicator (e.g., 1|ID)

• I(): defines functions to be interpreted by model.matrix

If the cluster indicator is omitted, single-level imputation will be performed. For multilevel imputation, predictors are allowed to have fixed effects, random effects, or both on all target variables. The intercept is automatically included as both a fixed and (for multilevel models) a random effect. Both can be suppressed if needed (see panImpute). Note that, when specifying random effects other than the intercept, these will not be automatically added as fixed effects and must be included explicitly. Any predictors defined by I() will be used for imputation but not included in the data set unless save.pred = TRUE.

If missing data occur at both level 1 and 2, the imputation model is specified as a list of two formulas or types, respectively. The first element of this list denotes the model specification for variables at level 1. The second element denotes the model specification for variables at level 2. Missing data are imputed jointly at both levels (see 'Examples', see also Carpenter and Kenward, 2013; Goldstein et al., 2009).

It is possible to model the covariance matrix of residuals at level 1 as random across clusters (Yucel, 2011; Carpenter & Kenward, 2013). The random.L1 argument determines this behavior and how the values of these matrices are stored. If set to "none", a common covariance matrix is assumed across groups (similar to panImpute). If set to "mean", the covariance matrices are random, but only the average covariance matrix is stored at each iteration. If set to "full", the covariance matrices are random, and all variances and covariances from all clusters are stored.

In order to run separate imputations for each level of an additional grouping variable, the group argument can be used. The name of the grouping variable must be given as a character string (i.e., in quotation marks).

The default prior distribution for the covariance matrices in jomoImpute are "least informative" inverse-Wishart priors with minimum positive degrees of freedom (largest dispersion) and the identity matrix for scale. The prior argument can be used to specify alternative prior distributions. These must be supplied as a list containing the following components:

• Binv: scale matrix for the covariance matrix of residuals at level 1

• Dinv: scale matrix for the covariance matrix of random effects and residuals at level 2

• a: starting value for the degrees of freedom of random covariance matrices of residuals (only used with random.L1 = "mean" or random.L1 = "full")

Note that jomo does not allow for the degrees of freedom for the inverse-Wishart prior to be specified by the user. These are always set to the lowest value possible (largest dispersion) or determined iteratively if the residuals at level 1 are modeled as random (see above). For single-level imputation, only Binv is relevant.

In imputation models with many parameters, the number of chains in the MCMC algorithm being stored can be reduced with the keep.chains argument (see also panImpute). This setting influences the storage mode of parameters (e.g., dimensions and indices of arrays) and should be used with caution.

References

Carpenter, J. R., & Kenward, M. G. (2013). Multiple imputation and its application. Hoboken, NJ: Wiley.

Goldstein, H., Carpenter, J., Kenward, M. G., & Levin, K. A. (2009). Multilevel models with multivariate mixed response types. Statistical Modelling, 9, 173-197.

Yucel, R. M. (2011). Random covariances and mixed-effects models for imputing multivariate multilevel continuous data. Statistical Modelling, 11, 351-370.

See Also

panImpute, mitmlComplete, summary.mitml, plot.mitml

Examples

# NOTE: The number of iterations in these examples is much lower than it
# should be. This is done in order to comply with CRAN policies, and more
# iterations are recommended for applications in practice!

data(studentratings)
data(leadership)

# ***
# for further examples, see "panImpute"
#

?panImpute

# *** ................................
# the 'type' interface
# 

# * Example 1.1 (studentratings): 'ReadDis' and 'SES', predicted by 'ReadAchiev'
# (random slope)

type <- c(-2, 0, 0, 0, 0, 1, 3, 1, 0, 0)
names(type) <- colnames(studentratings)
type

imp <- jomoImpute(studentratings, type = type, n.burn = 100, n.iter = 10, m = 5)

# * Example 1.2 (leadership): all variables (mixed continuous and categorical
# data with missing values at level 1 and level 2)

type.L1 <- c(-2, 1, 0, 1, 1)   # imputation model at level 1
type.L2 <- c(-2, 0, 1, 0, 0)   # imputation model at level 2
names(type.L1) <- names(type.L2) <- colnames(leadership)

type <- list(type.L1, type.L2)
type

imp <- jomoImpute(leadership, type = type, n.burn = 100, n.iter = 10, m = 5)

# * Example 1.3 (studentratings): 'ReadDis', 'ReadAchiev', and 'SES' predicted
# with empty model, groupwise for 'FedState' (single-level imputation)

type <- c(0, -1, 0, 0, 0, 1, 1, 1, 0, 0)
names(type) <- colnames(studentratings)
type

imp <- jomoImpute(studentratings, type = type, group = "FedState", n.burn = 100,
                  n.iter = 10, m = 5)

# *** ................................
# the 'formula' interface
# 

# * Example 2.1 (studentratings): 'ReadDis' and 'SES' predicted by 'ReadAchiev'
# (random slope)

fml <- ReadDis + SES ~ ReadAchiev + (1|ID)
imp <- jomoImpute(studentratings, formula = fml, n.burn = 100, n.iter = 10, m = 5)

# * Example 2.2 (studentratings): 'ReadDis' predicted by 'ReadAchiev' and the
# the cluster mean of 'ReadAchiev'

fml <- ReadDis ~ ReadAchiev + I(clusterMeans(ReadAchiev, ID)) + (1|ID)
imp <- jomoImpute(studentratings, formula = fml, n.burn = 100, n.iter = 10, m = 5)

# * Example 2.3 (studentratings): 'ReadDis' predicted by 'ReadAchiev', groupwise
# for 'FedState'

fml <- ReadDis ~ ReadAchiev + (1|ID)
imp <- jomoImpute(studentratings, formula = fml, group = "FedState", n.burn = 100,
                  n.iter = 10, m = 5)

# * Example 2.4 (leadership): all variables (mixed continuous and categorical
# data with missing values at level 1 and level 2)

fml <- list( JOBSAT + NEGLEAD + WLOAD ~ 1 + (1|GRPID) , COHES ~ 1 )
imp <- jomoImpute(leadership, formula = fml, n.burn = 100, n.iter = 10, m = 5)

# * Example 2.5 (studentratings): 'ReadDis', 'ReadAchiev', and 'SES' predicted
# with empty model, groupwise for 'FedState' (single-level imputation)

fml <- ReadDis + ReadAchiev + SES ~ 1
imp <- jomoImpute(studentratings, formula = fml, group = "FedState", n.burn = 100,
                  n.iter = 10, m = 5)