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Title: Semiparametric Bayesian Gaussian Copula Estimation and Imputation
Version: 1.0
Date: 2025-06-18
Maintainer: Peter Hoff <peter.hoff@duke.edu>
Description: Estimation and inference for parameters in a Gaussian copula model, treating the univariate marginal distributions as nuisance parameters as described in Hoff (2007) <doi:10.1214/07-AOAS107>. This package also provides a semiparametric imputation procedure for missing multivariate data.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL: https://pdhoff.github.io/
RoxygenNote: 6.0.1
NeedsCompilation: no
Packaged: 2025-06-19 15:03:40 UTC; pdh10
Author: Peter Hoff [aut, cre]
Repository: CRAN
Date/Publication: 2025-06-19 15:40:02 UTC

Semiparametric Bayesian Gaussian Copula Estimation and Imputation

Description

Estimation and inference for parameters in a Gaussian copula model, treating univariate marginal distributions as nuisance parameters as described in Hoff (2007) <doi:10.1214/07-AOAS107>. This pacakge also provides a semiparametric imputation procedure for missing multivariate data.

Details

Package: sbgcop
Type: Package
Version: 0.980
Date: 2018-05-25
License: GPL Version 2 or later

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.

Author(s)

Peter Hoff <peter.hofff@duke.edu>

References

Hoff (2007) “Extending the rank likelihood for semiparametric copula estimation”

Examples



fit<-sbgcop.mcmc(swiss)
summary(fit)
plot(fit)



Log Multivariate Normal Density

Description

Computes the log of the multivariate normal density

Usage

ldmvnorm(Y, S)

Arguments

Y

an n x p matrix

S

a p x p positive definite matrix

Details

This function computes the log density of the data matrix Y under the model that the rows are independent samples from a mean-zero multivariate normal distribution with covariance matrix S.

Value

A real number.

Author(s)

Peter Hoff

Examples


Y<-matrix(rnorm(9*7),9,7) 
ldmvnorm(Y,diag(7))




Plot Confidence Bands for Association Parameters

Description

Plots 95

Usage

plotci.sA(sA, ylabs = colnames(sA[, , 1]), mgp = c(1.75, 0.75, 0))

Arguments

sA

a p x p x nsamp array

ylabs

a p x 1 vector of names for plotting labels

mgp

margin parameters

Author(s)

Peter Hoff

Examples


fit<-sbgcop.mcmc(swiss)

plotci.sA(fit$C.psamp) 


Matrix Quantiles

Description

Computes quantiles along the third dimension of a 3-d array.

Usage

qM.sM(sM, quantiles = c(0.025, 0.5, 0.975))

Arguments

sM

an m x n x s array

quantiles

quantiles to be computed

Value

an array of dimension m x n x l, where l is the length of quantiles

Author(s)

Peter Hoff


Sample from the Wishart Distribution

Description

Generate a random sample from the Wishart distribution.

Usage

rwish(S0, nu)

Arguments

S0

a positive definite matrix

nu

a positive integer

Details

Return the sum of nu i.i.d. rank-one matrices generated as z%*%t(z), where z is a sample from a multivariate normal distribution with covariance S0. The resulting random variable has mean nu*S0.

Value

a positive definite matrix.

Author(s)

Peter Hoff


Compute Regression Parameters

Description

Compute an array of regression parameters from an array of correlation parameters.

Usage

sR.sC(sC)

Arguments

sC

a p x p x nsamp array of, made up of nsamp correlation matrices.

Details

For each of the nsamp correlation matrices C, a matrix of regression parameters is computed via R[j,-j]<- C[j,-j]%*%solve(C[-j,-j])

Value

a p x p x nsamp array of regression parameters.

Author(s)

Peter Hoff

Examples


fit<-sbgcop.mcmc(swiss)

plotci.sA(sR.sC(fit$C.psamp))



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

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.

Author(s)

Peter Hoff

References

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

Examples


fit<-sbgcop.mcmc(swiss)
summary(fit)
plot(fit)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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