Variance-Covariance Matrix for a CPN Model

Computes the variance-covariance matrix of parameter estimates from a fitted Compound Poisson-Normal (CPN) regression model using the numerical Hessian of the negative log-likelihood.

Usage

# S3 method for class 'cpn'
vcov(object, ...)

Arguments

object: An object of class "cpn" returned by the cpn function.
...: Additional arguments (currently unused).

Value

A variance-covariance matrix of the model parameters. Rows and columns are named according to the model parameters (regression coefficients, mu, and sigma). If the Hessian is singular, contains NA values, or is otherwise invalid, a matrix of NA values is returned with an appropriate warning.

Details

The Hessian matrix of the negative log-likelihood is computed using numerical finite differences (via the hessian function). The variance-covariance matrix is then obtained by inverting this Hessian. The result reflects local curvature and can be used to compute standard errors and confidence intervals for the parameters.

Examples

set.seed(123)
df <- data.frame(x = rnorm(100))
df$y <- sapply(exp(0.5 * df$x), function(lam) {
  k <- rpois(1, lam)
  if (k == 0) return(0)
  sum(rnorm(k, mean = 1, sd = 1))
})
fit <- cpn(y ~ x, data = df)
vcov(fit)
#>              (Intercept)             x           mu         sigma
#> (Intercept)  0.019229096 -0.0053012925 -0.007015153 -0.0042571726
#> x           -0.005301292  0.0169143475 -0.002521948  0.0008552595
#> mu          -0.007015153 -0.0025219477  0.016074768  0.0035950679
#> sigma       -0.004257173  0.0008552595  0.003595068  0.0145751698