Fit the Gaussian-copula marginal regression by maximum likelihood

Fits the model of nll_copula() by BFGS (Nelder-Mead is unstable on this likelihood surface; see the paper's pitfall 6), starting from the independence-model fit, then computes standard errors from the numerical Hessian with a relative step of 1e-3 (the numDeriv default, d = 0.1, can push an autoregressive coefficient outside the stationary region near the boundary; see the paper's pitfall 16).

Usage

fit_copula(y, X, Z, p = 0, q = 0, family = "kuma", tau = 0.5)

Arguments

y

Numeric response vector in (0, 1).

X

Location-submodel design matrix.

Z

Shape-submodel design matrix.

p, q

Non-negative integers, the ARMA orders.

family

"kuma" (default) or "beta".

tau

Quantile level for the Kumaraswamy margin (ignored if family = "beta").

Value

A list with components par (named numeric vector), se (standard errors, NA if the Hessian is not invertible), loglik, npar, aic, bic, family, p, q, tau, the inputs X, Z, y, and convergence (as returned by stats::optim()).

Details

At tau other than the median, prefer fit_copula_multi_tau(): the likelihood surface can have more than one interior stationary point at a given tau, with different values, and a bare single-start fit_copula() call is not guaranteed to land on the one with the higher likelihood (see the paper's pitfall 1).

See also

fit_copula_multi_tau(), qresiduals(), sim_copula()