EstDiscrete {CopulaGAMM} R Documentation

## Copula-based estimation of mixed regression models for discrete response

### Description

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

### Usage

EstDiscrete(
y,
disc,
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). disc function for margins: 1 (Bernoulli), 2 (Poisson), 3 (Negative Binomial), 4 (Geometric). 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) adj tuning parameter (>= 1) that can be used to prevent overflow when the cluster size n is very large; when n<=100 OR Bernoulli marginals, no adjustment is required; when n>=500 for the Poisson likelihood fails due to overflow problem; adj=3 prevents this in 100% cases prediction logical variable for prediction of latent variables V (default is TRUE).

### Value

 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 disc Discrete margin number rot rotation dfC Degrees of freedom for the Student copula

### Author(s)

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

### References

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

### Examples

data(poisson) #simulated data with poisson margins
start=c(0,0,0); LB=rep(-10,3);UB=rep(10,3)
y=poisson$y; clu=poisson$clu;xm=poisson\$xm
EstDiscrete(y,disc=2,family="clayton",rot=90,clu=clu,xm=xm,start=start,LB=LB,UB=UB)


[Package CopulaGAMM version 0.3.0 Index]