EstContinuous {CopulaGAMM}

Copula-based estimation of mixed regression models for continuous response

Description

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

Usage

EstContinuous(
  y,
  model,
  family,
  rot = 0,
  clu,
  xc = NULL,
  xm = NULL,
  start,
  LB,
  UB,
  nq = 31,
  dfM = NULL,
  dfC = NULL,
  prediction = TRUE
)

Arguments

y

n x 1 vector of response variable (assumed continuous).

model

function for margins: "gaussian" (normal), "t" (Student with known df=dfM), laplace" , "exponential", "weibull".

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.

dfM

degrees of freedom for a Student margin; default is 0 for non-t distribution,

dfC

degrees of freedom for a Student margin; default is 5.

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 values of clusters

family

Copula family

tau

Kendall's tau by observation

thC0

Estimated parameters of the copula by observation

thF

Estimated parameters of the margins by observation

pcond

Conditional copula cdf

fcpdf

Margin functions (cdf and pdf)

dfM

Degrees of freedom for Student margin (default is NULL)

dfC

Degrees of freedom for the Student copula (default is NULL)

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(normal) #simulated data with normal margins
start=c(0,0,0,1); LB=c(rep(-10,3),0.001);UB=c(rep(10,3),10)
y=normal$y; clu=normal$clu;xm=normal$xm
out=EstContinuous(y,model="gaussian",family="clayton",rot=90,clu=clu,xm=xm,start=start,LB=LB,UB=UB)