File: jomo1ran.MCMCchain.Rd

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\name{jomo1ran.MCMCchain}
\alias{jomo1ran.MCMCchain}

\title{
JM Imputation of clustered data - A tool to check convergence of the MCMC
}
\description{
This function is similar to jomo1ran, 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{
jomo1ran.MCMCchain(Y, 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="common", output=1, 
out.iter=10) 

}
%- maybe also 'usage' for other objects documented here.
\arguments{
 \item{Y}{
    A data.frame containing the outcomes of the imputation model. 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{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. 
}
  \item{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.
}
  \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.
}
  \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. The default is an identity matrix.
}
  \item{l1cov.prior}{
Scale matrix for the inverse-Wishart prior for the covariance matrix. The default is the identity matrix.
}
  \item{l2cov.prior}{
Scale matrix for the inverse-Wishart prior for the level 2 covariance matrix. The default is the identity matrix.
}
 \item{start.imp}{
Starting value for the imputed dataset. n-level categorical variables are substituted by n-1 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 cluster-specific covariance matrices. Default is 50+D, with D being the dimension of the covariance matrices. This is used only 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 cluster-specific covariance matrices. Default is the starting value for a.
}
\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 study-specific matrices are considered (jomo1ranconhr, jomo1rancathr and jomo1ranmixhr with coption meth="fixed"). Finally, when set to "random", random study-specific 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 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, for cases where categorical variabels are present, the final state of the imputed dataset with the latent normals in place of the categorical variables is stored in finimp.latnorm.
}

\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<-jomo1ran.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")
}