# sbgcop.mcmc: Semiparametric Bayesian Gaussian copula estimation and... In sbgcop: Semiparametric Bayesian Gaussian copula estimation and imputation

## Description

`sbgcop.mcmc` is used to semiparametrically estimate the parameters of a Gaussian copula. It can be used for posterior inference on the copula parameters, and for imputation of missing values in a matrix of ordinal and/or continuous values.

## Usage

 ```1 2 3 4 5 6``` ```sbgcop.mcmc(Y, S0 = diag(dim(Y)[2]), n0 = dim(Y)[2] + 2, nsamp = 100, odens = max(1, round(nsamp/1000)), impute=any(is.na(Y)), plugin.threshold=100, plugin.marginal=(apply(Y,2,function(x){ length(unique(x))})>plugin.threshold), seed = 1, verb = TRUE) ```

## Arguments

 `Y` an n x p matrix. Missing values are allowed. `S0` a p x p positive definite matrix `n0` a positive integer `nsamp` number of iterations of the Markov chain. `odens` output density: number of iterations between saved samples. `impute` save posterior predictive values of missing data(TRUE/FALSE)? `plugin.threshold` if the number of unique values of a variable exceeds this integer, then plug-in the empirical distribution as the marginal. `plugin.marginal` a logical of length p. Gives finer control over which margins to use the empirical distribution for. `seed` an integer for the random seed `verb` print progress of MCMC(TRUE/FALSE)?

## Details

This function produces MCMC samples from the posterior distribution of a correlation matrix, using a scaled inverse-Wishart prior distribution and an extended rank likelihood. It also provides imputation for missing values in a multivariate dataset.

## Value

An object of class `psgc` containing the following components:

 `C.psamp ` an array of size p x p x `nsamp/odens`, consisting of posterior samples of the correlation matrix. `Y.pmean ` the original datamatrix with imputed values replacing missing data `Y.impute ` an array of size n x p x `nsamp/odens`, consisting of copies of the original data matrix, with posterior samples of missing values included. `LPC ` the log-probability of the latent variables at each saved sample. Used for diagnostic purposes.

Peter Hoff

## References

http://www.stat.washington.edu/hoff/

## Examples

 ```1 2 3``` ```fit<-sbgcop.mcmc(swiss) summary(fit) plot(fit) ```

sbgcop documentation built on May 30, 2017, 4:24 a.m.