EstDiscrete function

Copula-based estimation of mixed regression models for discrete response

This function computes the estimation of a copula-based 2-level hierarchical model.

EstDiscrete(
  y,
  model,
  family,
  rot = 0,
  clu,
  xc = NULL,
  xm = NULL,
  start,
  LB,
  UB,
  nq = 25,
  dfC = NULL,
  offset = NULL,
  prediction = TRUE
)

Arguments

• y: n x 1 vector of response variable (assumed continuous).
• model: margins: "binomial" or "bernoulli","poisson", "nbinom" (Negative Binomial), "geometric", "multinomial".
• family: copula family: "gaussian" , "t" , "clayton" , "frank" , "fgm", gumbel".
• rot: rotation: 0 (default), 90, 180 (survival), or 270
• clu: variable of size n defining the clusters; can be a factor
• xc: covariates of size n for the estimation of the copula, in addition to the constant; default is NULL.
• xm: covariates of size n for the estimation of the mean of the margin, in addition to the constant; default is NULL.
• start: starting point for the estimation; could be the ones associated with a Gaussian-copula model defined by lmer.
• LB: lower bound for the parameters.
• UB: upper bound for the parameters.
• nq: number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 25.
• dfC: degrees of freedom for a Student margin; default is 0.
• offset: offset (default is NULL)
• prediction: logical variable for prediction of latent variables V (default is TRUE).

Returns

• coefficients: Estimated parameters

• sd: Standard deviations of the estimated parameters

• tstat: T statistics for the estimated parameters

• pval: P-values of the t statistics for the estimated parameters

• gradient: Gradient of the log-likelihood

• loglik: Log-likelihood

• aic: AIC coefficient

• bic: BIC coefficient

• cov: Covariance matrix of the estimations

• grd: Gradients by clusters

• clu: Cluster values

• Matxc: Matrix of covariates defining the copula parameters, including a constant

• Matxm: Matrix of covariates defining the margin parameters, including a constant

• V: Estimated value of the latent variable by clusters (if prediction=TRUE)

• cluster: Unique clusters

• family: Copula family

• thC0: Estimated parameters of the copula by observation

• thF: Estimated parameters of the margins by observation

• rot: rotation

• dfC: Degrees of freedom for the Student copula

• model: Name of the margins

• disc: Discrete margin number

Examples

data(sim.poisson) #simulated data with Poisson margins
start=c(2,8,3,-1); LB =    c(-3,  3,  -7,  -6);UB=c( 7, 13,   13,   4)
y=sim.poisson$y; clu=sim.poisson$clu;
xc=sim.poisson$xc; xm=sim.poisson$xm
model = "poisson"; family="frank"
out.poisson=EstDiscrete(y,model,family,rot=0,clu,xc,xm,start,LB,UB,nq=31,prediction=TRUE)

References

Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models

Author(s)

Pavel Krupskii, Bouchra R. Nasri and Bruno N. Remillard