jomo.polr.MCMCchain {jomo}

polr Compatible JM Imputation - A tool to check convergence of the MCMC

Description

This function is similar to the jomo.polr 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.polr.MCMCchain(formula, data, beta.start=NULL, l1cov.start=NULL, 
  l1cov.prior=NULL, betaY.start=NULL, nburn=1000, 
  start.imp=NULL, start.imp.sub=NULL, output=1, out.iter=10) 
  

Arguments

formula

an object of class formula: a symbolic description of the model to be fitted. It is possible to include in this formula interactions (through symbols '*' and '

data

A data.frame containing all the variables to include in the imputation model. Columns related to continuous variables have to be numeric and columns related to binary/categorical variables have to be factors.

start.imp

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

start.imp.sub

Starting value for the imputations of the outcome. When using binomial family, this is the value of the latent normal.

beta.start

Starting value for beta, the vector(s) of fixed effects for the joint model for the covariates. For each n-category variable we have a fixed effect parameter for each of the n-1 latent normals. The default is a matrix of zeros.

l1cov.start

Starting value of the level-1 covariance matrix of the joint model for the covariates. Dimension of this square matrix is equal to the number of covariates (continuous plus latent normals) in the imputation model. The default is the identity matrix.

l1cov.prior

Scale matrix for the inverse-Wishart prior for the covariance matrix. The default is the identity matrix.

betaY.start

Starting value for betaY, the vector of fixed effects for the substantive analysis model. The default is the complete records estimate.

nburn

Number of burn in iterations. Default is 1000.

output

When set to 0, no output is shown on screen at the end of the process. When set to 1, only the parameter estimates related to the substantive model are shown (default). When set to 2, all parameter estimates (posterior means) are displayed.

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 3-dimensional matrices, containing all the values drawn for each parameter at each iteration: these are fixed effect parameters of the covariates beta (collectbeta), level 1 covariance matrices (collectomega), fixed effect estimates of the substantive model and associated residual variances. 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

  # make sure social is a factor:
  
  sldata<-within(sldata, social<-factor(social))
  
  # we define the data frame with all the variables 
  
  data<-sldata[,c("measure","age", "social")]
  
  # And the formula of the substantive lm model 
  # social as an outcome only because it is the only ordinal variable in the dataset...
  
  formula<-as.formula(social~age+measure)
  
  #And finally we run the imputation function:
  
  imp<-jomo.polr.MCMCchain(formula,data, nburn=100)
  
  # Note we are using only 100 iterations to avoid time consuming examples,
  # which go against CRAN policies. In real applications we would use
  # much larger burn-ins (around 1000, to say the least).
  
  # We can check, for example, the convergence of the first element of beta:
  
  plot(c(1:100),imp$collectbeta[1,1,1:100],type="l")