compute_ICA_OrdCont: Compute Individual Causal Association for a given D-vine copula model in the Ordinal-Continuous Setting

Description

The compute_ICA_OrdCont() function computes the individual causal association for a fully identified D-vine copula model in the setting with a continuous surrogate endpoint and an ordinal true endpoint.

Usage

compute_ICA_OrdCont(
  copula_par,
  rotation_par,
  copula_family1,
  copula_family2 = copula_family1,
  n_prec,
  q_S0,
  q_T0,
  q_S1,
  q_T1,
  marginal_sp_rho = TRUE,
  seed = 1,
  ICA_estimator = NULL
)

Value

(numeric) A Named vector with the following elements:

ICA
Spearman's rho, $\rho_s (\Delta S, \Delta T)$ (if asked)
Marginal association parameters in terms of Spearman's rho (if asked): $$\rho_{s}(T_0, S_0), \rho_{s}(T_0, S_1), \rho_{s}(T_0, T_1), \rho_{s}(S_0, S_1), \rho_{s}(S_0, T_1), \rho_{s}(S_1, T_1)$$

Arguments

copula_par: Parameter vector for the sequence of bivariate copulas that define the D-vine copula. The elements of copula_par correspond to $(c_{12}, c_{23}, c_{34}, c_{13;2}, c_{24;3}, c_{14;23})$.
rotation_par: Vector of rotation parameters for the sequence of bivariate copulas that define the D-vine copula. The elements of rotation_par correspond to $(c_{12}, c_{23}, c_{34}, c_{13;2}, c_{24;3}, c_{14;23})$.
copula_family1: Copula family of $c_{12}$ and $c_{34}$. For the possible options, see loglik_copula_scale(). The elements of copula_family correspond to $(c_{12}, c_{34})$.
copula_family2: Copula family of the other bivariate copulas. For the possible options, see loglik_copula_scale(). The elements of copula_family2 correspond to $(c_{23}, c_{13;2}, c_{24;3}, c_{14;23})$.
n_prec: Number of Monte Carlo samples for the computation of the mutual information.
q_S0: Quantile function for the distribution of $S_0$.
q_T0: Quantile function for the distribution of $T_0$.
q_S1: Quantile function for the distribution of $S_1$.
q_T1: Quantile function for the distribution of $T_1$.
marginal_sp_rho: (boolean) Compute the sample Spearman correlation matrix? Defaults to TRUE.
seed: Seed for Monte Carlo sampling. This seed does not affect the global environment.
ICA_estimator: Function that estimates the ICA between the first two arguments which are numeric vectors. Defaults to NULL which corresponds to using estimate_ICA_OrdCont().