EstDiscrete {CopulaGAMM}

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,
  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).

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

rot

rotation

dfC

Degrees of freedom for the Student copula

model

Name of the margins

disc

Discrete margin number

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(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)