Summarise a copregbayes fit

summary() tabulates the posterior mean, median, standard deviation and credible interval of the regression coefficients, the residual variance and the endogeneity correlations; print() on the result formats that table.

Usage

# S3 method for class 'copregbayes'
summary(object, level = 0.95, ...)

# S3 method for class 'summary.copregbayes'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

object

An object of class "copregbayes", as returned by CopRegBAYES.

level

Credible level for the reported interval, e.g. 0.95 for a 95% interval. Defaults to 0.95.

...

Not used; present for S3 method consistency.

x

An object of class "summary.copregbayes", as returned by summary.copregbayes.

digits

Number of significant digits to print.

Value

For summary.copregbayes, an object of class "summary.copregbayes", a list with coefficients (the posterior mean/median/sd/credible-interval table for the regression coefficients), sigma2 (the same for the residual variance), rho (the same for the endogeneity correlations named in object$rho.names; correlations among the regressors themselves are nuisance parameters and are not shown here, though they remain in object$Sigma.draws), n.other (how many of those nuisance correlations there are), restricted (names of the correlations held at exactly zero by the exogeneity restriction), acceptance, horseshoe, n, ndraws, level, iterations, burnin, thin, call and method.

For print.summary.copregbayes, x is returned invisibly; called for its side effect of printing.

References

Haschka, R. E. (2025). Bayesian inference for joint estimation models using copulas to handle endogenous regressors. Oxford Bulletin of Economics and Statistics. doi:10.1111/obes.70023

Examples

set.seed(1)
n <- 60
x <- rnorm(n); z <- x + rnorm(n); y <- 1 + z + x + rnorm(n)
fit <- CopRegBAYES(y ~ z | x, data = data.frame(y, z, x),
                    iterations = 200, burnin = 50, thin = 5, verbose = FALSE)
summary(fit)
#> 
#> Bayesian copula correction (Haschka 2025)
#> 
#> Call:
#> CopRegBAYES(formula = y ~ z | x, data = data.frame(y, z, x), 
#>     iterations = 200, burnin = 50, thin = 5, verbose = FALSE)
#> 
#> Regression coefficients:
#>             P. Mean  P. Median Sd       2.5%     97.5%   
#> (Intercept)  0.85584  0.82703   0.18691  0.53041  1.12715
#> z            1.75252  1.85036   0.50721  0.67135  2.37521
#> x            0.39360  0.27318   0.39014 -0.04615  1.18508
#> 
#> Structural error variance:
#>        P. Mean P. Median Sd     2.5%   97.5% 
#> sigma2 1.9613  1.8970    0.7394 0.9596 3.7874
#> 
#> Endogeneity: rho(P*, xi*) is the correlation between the normal score 
#>   of an endogenous regressor and that of the structural error.
#>              P. Mean P. Median Sd      2.5%    97.5%  
#> rho(z*, xi*) -0.4564 -0.5433    0.2409 -0.7113  0.1041
#>   1 further correlations among the regressors are estimated jointly and
#>   sit in $Sigma.draws; 1 more are held at zero, which is what makes
#>   the exogenous regressors exogenous.
#> 
#> The two quantile columns are 95% credible intervals: no asymptotic
#>   argument is involved, and the marginal CDFs are estimated jointly rather
#>   than plugged in.
#> 
#> 60 observations. 30 draws kept from 200 iterations (burn-in 50, thinning 5).
#> Prior on the coefficients: horseshoe. Acceptance coefficients 0.835, sigma2 0.865.