Fitting bivariate mixed MGL and MGL-EV copula regression models.

MGL.reg.mixed is used to fit bivariate MGL and MGL-EV copula regression models for continuous and semi-continuous variables.

MGL.reg.mixed(
  obs,
  U,
  U_,
  f,
  X,
  copula = c("MGL", "MGL180", "MGL-EV", "MGL-EV180", "Gumbel", "MGB2"),
  umin = 0,
  hessian = TRUE,
  initpar,
  ...
)

Arguments

obs: two-dimensional matrix for observations.
U: two-dimensional matrix for pseudo copula data with values in $[0,1]$ for (F(y1), F(y2)).
U_: two-dimensional matrix for pseudo copula data for the data (F(y1), F(y2-1)).
f: two-dimensional matrix for the density function of marginal distributions.
X: design matrix.
copula: 'MGL', 'MGL180', "MGL-EV", "MGL-EV180"
umin: threshold value used in the semi-continuous data.
hessian: Logical. Should a numerically differentiated Hessian matrix be returned?
initpar: Initial values for the parameters to be optimized over.
...: additional arguments, see optim for more details.

Value

A list containing the following components:

loglike: the value of the estimated maximum of the loglikelihood function.
copula: the name of the fitted copula. "MGL180" and "MGL-EV180" denote the survival MGL and MGL-EV copula respectively.
estimates: the point at which the maximum value of the loglikelihood is obtained.
se: the standard errors of the estimators.
AIC, BIC: the goodness fit of the regression models.
hessian: the hessian at the estimated maximum of the loglikelihood (if requested).

Details

The estimation method is performed via optim function. Y1 and Y2 are both continuous variables.

Y1: continuous data.
Y2: semi-continuous data where Y2>umin is continuous and Y2<=umin is discrete.

copula: "MGL180" and "MGLEV180" denote the survival MGL and survival MGL-EV copula respectively.

For "Gumbel" regression model, the copula parameter $$\delta_i = \exp(X\beta) + 1.$$
For "MGL", "MGL180", "MGL-EV", "MGL-EV180" regression model, the copula parameter $$\delta_i = \exp(X\beta),$$ where $\beta$ is the vector of coefficients to be estimated in the copula regression.

Examples

library(rMGLReg)
u <- cbind(earthqCHI$u1, earthqCHI$u2)
u_ <- cbind(earthqCHI$u1, earthqCHI$u2_)
y <- cbind(earthqCHI$y1, earthqCHI$y2)
f <- cbind(earthqCHI$f1, earthqCHI$f2)
obs <- y
U <- u
U_ <- u_
umin <- 20
library(splines)
X <- ns(earthqCHI$year, knots = quantile(earthqCHI$year, c(0.333, 0.667)), intercept = TRUE)
m.MGL180 <- MGL.reg.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f, X = X,
copula = "MGL180",
                         method = "Nelder-Mead",
                        control = list(maxit = 100000),
                        initpar = c(0.64, 1.2, 1, -0.2))

m.MGLEV180 <- MGL.reg.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f, X = X,
                           copula = "MGL-EV180",
                           method = "Nelder-Mead",
                          control = list(maxit = 100000),
                          initpar = c(-0.32, 1, 1, 1))
m.MGL180
#> $loglike
#> [1] -3002.216
#> 
#> $copula
#> $copula$name
#> [1] "MGL180"
#> 
#> 
#> $estimates
#> [1]  0.6335636  1.7222609  1.8482879 -0.2495413
#> 
#> $se
#> [1] 0.3331746 0.2919771 0.3862413 0.3407179
#> 
#> $hessian
#>            [,1]        [,2]       [,3]        [,4]
#> [1,] -15.255498  -7.0269080  -8.299759   1.7418354
#> [2,]  -7.026908 -17.7331530  -8.965614  -0.4904041
#> [3,]  -8.299759  -8.9656143 -14.412310  -3.2798214
#> [4,]   1.741835  -0.4904041  -3.279821 -10.6878692
#> 
#> $AIC
#> [1] 6012.431
#> 
#> $BIC
#> [1] 6027.124
#> 
m.MGLEV180
#> $loglike
#> [1] -3004.762
#> 
#> $copula
#> $copula$name
#> [1] "MGL-EV180"
#> 
#> 
#> $estimates
#> [1]  0.3334915  1.3270662  1.0505622 -0.2111104
#> 
#> $se
#> [1] 0.3892632 0.3113927 0.3553789 0.3571050
#> 
#> $hessian
#>            [,1]       [,2]       [,3]       [,4]
#> [1,] -15.675946  -7.633866  -8.261542   4.374247
#> [2,]  -7.633866 -15.716414  -6.014448  -2.002361
#> [3,]  -8.261542  -6.014448 -13.660477  -1.447256
#> [4,]   4.374247  -2.002361  -1.447256 -11.533344
#> 
#> $AIC
#> [1] 6017.524
#> 
#> $BIC
#> [1] 6032.217
#>