jomo1rancat: JM Imputation of clustered data with categorical variables

In jomo: Multilevel Joint Modelling Multiple Imputation

JM Imputation of clustered data with categorical variables

Description

Impute a clustered dataset with categorical variables as outcome. A joint multivariate model for partially observed data is assumed and imputations are generated through the use of a Gibbs sampler where the covariance matrix is updated with a Metropolis-Hastings step. Fully observed categorical covariates may be considered as covariates as well, but they have to be included as dummy variables.

Usage

jomo1rancat( Y.cat, Y.numcat, X=NULL, Z=NULL, clus, beta.start=NULL, 
u.start=NULL, l1cov.start=NULL, l2cov.start=NULL, l1cov.prior=NULL, 
l2cov.prior=NULL, nburn=1000, nbetween=1000, nimp=5, output=1, out.iter=10)

Arguments

Y.cat	A data frame, or matrix, with categorical (or binary) responses of the joint imputation model. Rows correspond to different observations, while columns are different variables. Missing values are coded as NA.
Y.numcat	A vector with the number of categories in each categorical (or binary) variable.
X	A data frame, or matrix, with covariates of the joint imputation model. Rows correspond to different observations, while columns are different variables. Missing values are not allowed in these variables. In case we want an intercept, a column of 1 is needed. The default is a column of 1.
Z	A data frame, or matrix, for covariates associated to random effects in the joint imputation model. Rows correspond to different observations, while columns are different variables. Missing values are not allowed in these variables. In case we want an intercept, a column of 1 is needed. The default is a column of 1.
clus	A data frame, or matrix, containing the cluster indicator for each observation.
beta.start	Starting value for beta, the vector(s) of fixed effects. Rows index different covariates and columns index different outcomes. For each n-category variable we define n-1 latent normals. The default is a matrix of zeros.
u.start	A matrix where different rows are the starting values within each cluster for the random effects estimates u. The default is a matrix of zeros.
l1cov.start	Starting value for the covariance matrix. Dimension of this square matrix is equal to the number of outcomes (continuous plus latent normals) in the imputation model. The default is the identity matrix.
l2cov.start	Starting value for the level 2 covariance matrix. Dimension of this square matrix is equal to the number of outcomes (continuous plus latent normals) in the imputation model times the number of random effects. The default is an identity matrix.
l1cov.prior	Scale matrix for the inverse-Wishart prior for the covariance matrix. The default is the identity matrix.
l2cov.prior	Scale matrix for the inverse-Wishart prior for the level 2 covariance matrix. The default is the identity matrix.
nburn	Number of burn in iterations. Default is 1000.
nbetween	Number of iterations between two successive imputations. Default is 1000.
nimp	Number of Imputations. Default is 5.
output	When set to any value different from 1 (default), no output is shown on screen at the end of the process.
out.iter	When set to K, every K iterations a dot is printed on screen. Default is 10.

Details

The Gibbs sampler algorithm used is described in detail in Chapter 9 of Carpenter and Kenward (2013). Regarding the choice of the priors, a flat prior is considered for beta and for the covariance matrix. A Metropolis Hastings step is implemented to update the covariance matrix, as described in the book. Binary or continuous covariates in the imputation model may be considered without any problem, but when considering a categorical covariate it has to be included with dummy variables (binary indicators) only.

Value

On screen, the posterior mean of the fixed effects estimates and of the covariance matrix are shown. The only argument returned is the imputed dataset in long format. Column "Imputation" indexes the imputations. Imputation number 0 are the original data.

References

Carpenter J.R., Kenward M.G., (2013), Multiple Imputation and its Application. Chapter 9, Wiley, ISBN: 978-0-470-74052-1.

Examples

#we define all the inputs:
# nimp, nburn and nbetween are smaller than they should. This is
#just because of CRAN policies on the examples.

Y.cat=cldata[,c("social"), drop=FALSE]
Y.numcat=matrix(4,1,1)
X=data.frame(rep(1,1000),cldata[,c("sex")])
colnames(X)<-c("const", "sex")
Z<-data.frame(rep(1,1000))
clus<-cldata[,c("city")]
beta.start<-matrix(0,2,3)
u.start<-matrix(0,10,3)
l1cov.start<-diag(1,3)
l2cov.start<-diag(1,3)
l1cov.prior=diag(1,3);
l2cov.prior=diag(1,3);
nburn=as.integer(100);
nbetween=as.integer(100);
nimp=as.integer(4);

#And finally we run the imputation function:

imp<-jomo1rancat(Y.cat, Y.numcat, X,Z,clus,beta.start,u.start,l1cov.start, 
               l2cov.start,l1cov.prior,l2cov.prior,nburn,nbetween,nimp)

 cat("Original value was missing (",imp[3,1],"), imputed value:", imp[1003,1])
 
  # Check help page for function jomo to see how to fit the model and 
  # combine estimates with Rubin's rules
             

jomo documentation built on April 15, 2023, 5:07 p.m.