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\name{jomo.MCMCchain}
\alias{jomo.MCMCchain}
\title{
JM Imputation  A tool to check convergence of the MCMC
}
\description{
This function is similar to the jomo function, 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{
jomo.MCMCchain(Y, Y2=NULL, X=NULL, X2=NULL, Z=NULL, clus=NULL,
beta.start=NULL, l2.beta.start=NULL, u.start=NULL,
l1cov.start=NULL, l2cov.start=NULL, l1cov.prior=NULL,
l2cov.prior=NULL, start.imp=NULL, l2.start.imp=NULL,
nburn=1000, a=NULL, a.prior=NULL, meth="common",output=1, out.iter=10)
}
\arguments{
\item{Y}{
A data.frame containing the outcomes of the imputation model, i.e. the partially observed level 1 variables. Columns related to continuous variables have to be numeric and columns related to binary/categorical variables have to be factors.
}
\item{Y2}{
A data.frame containing the level2 outcomes of the imputation model, i.e. the partially observed level2 variables. Columns related to continuous variables have to be numeric and columns related to binary/categorical variables have to be factors.
}
\item{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.
}
\item{X2}{
A data frame, or matrix, with level2 covariates of the joint imputation model. Rows correspond to different level1 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.
}
\item{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.
}
\item{clus}{
A data frame, or matrix, containing the cluster indicator for each observation. If missing, functions for single level imputation are automatically used.
}
\item{beta.start}{
Starting value for beta, the vector(s) of level1 fixed effects. Rows index different covariates and columns index different outcomes. For each ncategory variable we have a fixed effect parameter for each of the n1 latent normals. The default is a matrix of zeros.
}
\item{l2.beta.start}{
Starting value for beta2, the vector(s) of level2 fixed effects. Rows index different covariates and columns index different level2 outcomes. For each ncategory variable we have a fixed effect parameter for each of the n1 latent normals. The default is a matrix of zeros.
}
\item{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.
}
\item{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. Functions for imputation with random clusterspecific covariance matrices are an exception, because we need to pass the starting values for all of the matrices stacked one above the other.
}
\item{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 plus the number of level2 outcomes. The default is an identity matrix.
}
\item{l1cov.prior}{
Scale matrix for the inverseWishart prior for the covariance matrix. The default is the identity matrix.
}
\item{l2cov.prior}{
Scale matrix for the inverseWishart prior for the level 2 covariance matrix. The default is the identity matrix.
}
\item{start.imp}{
Starting value for the imputed dataset. nlevel categorical variables are substituted by n1 latent normals.
}
\item{l2.start.imp}{
Starting value for the level2 imputed variables. nlevel categorical variables are substituted by n1 latent normals.
}
\item{nburn}{
Number of iterations. Default is 1000.
}
\item{a}{
Starting value for the degrees of freedom of the inverse Wishart distribution of the clusterspecific covariance matrices. Default is 50+D, with D being the dimension of the covariance matrices. This is used only with clustered data and when option meth is set to "random".
}
\item{a.prior}{
Hyperparameter (Degrees of freedom) of the chi square prior distribution for the degrees of freedom of the inverse Wishart distribution for the clusterspecific covariance matrices. Default is D, with D being the dimension of the covariance matrices.
}
\item{meth}{
Method used to deal with level 1 covariance matrix. When set to "common", a common matrix across clusters is used (functions jomo1rancon, jomo1rancat and jomo1ranmix). When set to "fixed", fixed studyspecific matrices are considered (jomo1ranconhr, jomo1rancathr and jomo1ranmixhr with coption meth="fixed"). Finally, when set to "random", random studyspecific matrices are considered (jomo1ranconhr, jomo1rancathr and jomo1ranmixhr with option meth="random")
}
\item{output}{
When set to any value different from 1 (default), no output is shown on screen at the end of the process.
}
\item{out.iter}{
When set to K, every K iterations a dot is printed on screen. Default is 10.
}
}
\value{
A list is returned; this contains the final imputed dataset (finimp) and several 3dimensional matrices, containing all the values drawn for each parameter at each iteration: these are, potentially, fixed effect parameters beta (collectbeta), random effects (collectu), level 1 (collectomega) and level 2 covariance matrices (collectcovu) and level2 fixed effect parameters. If there are some categorical outcomes, a further output is included in the list, finimp.latnorm, containing the final state of the imputed dataset with the latent normal variables.
}
\examples{
# define all the inputs:
Y<cldata[,c("measure","age")]
clus<cldata[,c("city")]
nburn=as.integer(200);
#And finally we run the imputation function:
imp<jomo.MCMCchain(Y,clus=clus,nburn=nburn)
#We can check the convergence of the first element of beta:
plot(c(1:nburn),imp$collectbeta[1,1,1:nburn],type="l")
#Or similarly we can check the convergence of any element of the level 2 covariance matrix:
plot(c(1:nburn),imp$collectcovu[1,2,1:nburn],type="l")
}
