fitMvdc {copula}

Estimation of Multivariate Models Defined via Copulas

Description

Fitting copula-based multivariate distributions ("mvdc") to multivariate data, estimating both the marginal and the copula parameters.

If you assume (non parametric) margins, in other words, take the empirical distributions for all margins, you can use fitCopula(*, pobs(x)) instead.

Usage

loglikMvdc(param, x, mvdc)
fitMvdc(data, mvdc, start, optim.control = list(), method = "BFGS",
        lower = -Inf, upper = Inf,
        estimate.variance = fit$convergence == 0, hideWarnings = TRUE)

## S3 method for class 'fittedMV'
coef(object, SE = FALSE, orig = TRUE, ...)
## S3 method for class 'fittedMV'
logLik(object, ...)
## S3 method for class 'fittedMV'
vcov(object, orig = TRUE, ...)

Arguments

param

a vector of parameter values. When specifying parameters for mvdc objects, the parameters must be ordered with the marginals first and the copula parameters last. When the mvdc object has marginsIdentical = TRUE, only the parameters of one marginal must be specified.

x

a data matrix.

mvdc

a "mvdc" object.

data

a data matrix.

start

a vector of starting value for "param". See "param" above for ordering of this vector.

optim.control

a list of controls to be passed to optim.

method

the method for optim.

lower, upper

bounds on each parameter, passed to optim, typically “box constraints” for method = "L-BFGS-B".

estimate.variance

logical; if true (as by default, if the optimization converges), the asymptotic variance is estimated.

hideWarnings

logical indicating if warning messages from likelihood maximization, e.g., from evaluating at invalid parameter values, should be suppressed (via suppressWarnings).

object

an R object of class "fitMvdc".

SE

for the coef method, a logical indicating if standard errors should be returned in addition to the estimated parameters (in a matrix). This is equivalent, but more efficient than, e.g., coef(summary(object)).

orig

logical, relevant currently only for mixCopula fits with free weights. orig indicates if the weights should be shown in original scale (orig=TRUE) or in the transformed log- aka lambda-space.

...

potentially further arguments to methods.

Value

The return value loglikMvdc() is the log likelihood evaluated for the given value of param.

The return value of fitMvdc() is an object of class "fitMvdc" (see there), containing slots (among others!):

estimate

the estimate of the parameters.

var.est

large-sample (i.e., asymptotic) variance estimate of the parameter estimator (filled with NA if estimate.variance = FALSE).

mvdc

the fitted multivariate distribution, see mvdc.

The summary() method for "fitMvdc" objects returns a S3 “class” "summary.fitMvdc", simply a list with components method, loglik, and convergence, all three from corresponding slots of the "fitMvdc" objects, and

coefficients

a matrix of estimated coefficients, standard errors, t values and p-values.

Note

User-defined marginal distributions can be used as long as the "{dpq}" functions are defined. See vignette("AR_Clayton", package="copula").

When covariates are available for marginal distributions or for the copula, one can construct the loglikelihood function and feed it to "optim" to estimate all the parameters.

Finally, note that some of the fitting functions generate error messages because invalid parameter values are tried during the optimization process (see optim). This should be rarer since 2013, notably for likelihood based methods (as the likelihood is now rather set to -Inf than giving an error).

Previously, loglikMvdc() had an argument hideWarnings; nowadays, do use suppressWarnings(..) if you are sure you do not want to see them.

See Also

mvdc and mvdc; further, Copula, fitCopula, gofCopula.

For fitting univariate marginals, fitdistr().

Examples

G3 <- gumbelCopula(3, dim=2)
gMvd2  <- mvdc(G3, c("exp","exp"),
               param = list(list(rate=2), list(rate=4)))
## with identical margins:
gMvd.I <- mvdc(G3, "exp",
               param = list(rate=3), marginsIdentical=TRUE)

(Xtras <- copula:::doExtras()) # determine whether examples will be extra (long)
n <- if(Xtras) 10000 else 200 # sample size (realistic vs short for example)

set.seed(11)
x <- rMvdc(n, gMvd2)
## Default:     hideWarnings = FALSE .. i.e. show warnings here
fit2 <- fitMvdc(x, gMvd2, start = c(1,1, 2))
fit2
confint(fit2)
summary(fit2) # slightly more
## The estimated, asymptotic var-cov matrix [was used for confint()]:
vcov(fit2)

## with even more output for the "identical margin" case:
fitI <- fitMvdc(x, gMvd.I, start = c(3, 2),
                optim.control=list(trace= TRUE, REPORT= 2))
summary(fitI)
coef(fitI, SE = TRUE)
stopifnot(is.matrix(coef(fitI, SE = TRUE)),
          is.matrix(print( confint(fitI) )) )

## a wrong starting value can already be *the* problem:
f2 <- try(fitMvdc(x, gMvd.I, start = c(1, 1),
           optim.control=list(trace= TRUE, REPORT= 2)))
##--> Error in optim( ... ) : non-finite finite-difference value [2]

##==> "Solution" :  Using a more robust (but slower) optim() method:
fI.2 <- fitMvdc(x, gMvd.I, start = c(1, 1), method = "Nelder",
                optim.control=list(trace= TRUE))
fI.2