jomo1rancathr.MCMCchain {jomo}

JM Imputation of clustered data with categorical variables with cluster-specific covariance matrices - A tool to check convergence of the MCMC

Description

This function is similar to jomo1rancathr, but it returns the values of all the parameters in the model at each step of the MCMC instead of the imputations. It is useful to check the convergence of the MCMC sampler.

Usage

jomo1rancathr.MCMCchain(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, start.imp=NULL, nburn=1000, a=NULL, a.prior=NULL, meth="random", 
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 matrices, stacked one above the other. Dimension of each square matrix is equal to the number of outcomes (continuous plus latent normals) in the imputation model. The default is the identity matrix for each cluster.

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 matrices. 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.

start.imp

Starting value for the imputed dataset. n-level categorical variables are substituted by n-1 latent normals.

nburn

Number of burn in iterations. Default is 1000.

a

Starting value for the degrees of freedom of the inverse Wishart distribution of the cluster-specific covariance matrices. Default is 50+D, with D being the dimension of the covariance matrices.

a.prior

Hyperparameter (Degrees of freedom) of the chi square prior distribution for the degrees of freedom of the inverse Wishart distribution for the cluster-specific covariance matrices. Default is D, with D being the dimension of the covariance matrices.

meth

When set to "fixed", a flat prior is put on the study-specific covariance matrices and each matrix is updated separately with a different MH-step. When set to "random", we are assuming that all the covariance matrices are draws from an inverse-Wishart distribution, whose parameter values are updated with 2 steps similar to the ones presented in the case of continuous data only for function jomo1ranconhr.

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.

Value

A list with six elements is returned: the final imputed dataset (finimp) and four 3-dimensional matrices, containing all the values for beta (collectbeta), the random effects (collectu) and the level 1 (collectomega) and level 2 covariance matrices (collectcovu). Finally, the final state of the imputed dataset with the latent normals in place of the categorical variables is stored in finimp.latnorm.

Examples

#we define the inputs
#  nburn is smaller than needed. 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<-matrix(diag(1,3),30,3,2)
l2cov.start<-diag(1,3)
l1cov.prior=diag(1,3);
l2cov.prior=diag(1,3);
a=5
nburn=as.integer(100);

#Finally we run either the model with fixed or random cluster-specific covariance matrices:

imp<-jomo1rancathr.MCMCchain(Y.cat, Y.numcat, X,Z,clus,beta.start,
          u.start,l1cov.start, l2cov.start,l1cov.prior,l2cov.prior,nburn=nburn, a=a, meth="fixed")

#We can check the convergence of the first element of beta:

plot(c(1:nburn),imp$collectbeta[1,1,1:nburn],type="l")

#Or similarly we can check the convergence of any element of th elevel 2 covariance matrix:

plot(c(1:nburn),imp$collectcovu[1,2,1:nburn],type="l")