quantregGrowth (version 1.7-1)

logLik.gcrq: Log Likelihood, AIC and BIC for gcrq objects

Description

The function returns the log-likelihood value(s) evaluated at the estimated coefficients

Usage

# S3 method for gcrq
logLik(object, summ=TRUE, ...)
# S3 method for gcrq
AIC(object, ..., k=2, bondell=FALSE)

Value

The log likelihood(s) of the model fit object

Arguments

object

A gcrq fit returned by gcrq()

summ

If TRUE, the log likelihood values (and relevant edf) are summed over the different taus to provide a unique value accounting for the different quantile curves. If FALSE, tau-specific values are returned.

k

Optional numeric specifying the penalty of the edf in the AIC formula. k < 0 means k=log(n).

bondell

Logical. If TRUE, the SIC according to formula (7) in Bondell et al. (2010) is computed.

...

optional arguments (nothing in logLik.gcrq). For AIC.gcrq, summ=TRUE or FALSE can be set.

Author

Vito Muggeo

Details

The 'logLikelihood' is computed by assuming an asymmetric Laplace distribution for the response as in logLik.rq, namely \(n (\log(\tau(1-\tau))-1-\log(\rho_\tau/n))\), where \(\rho_\tau\) is the minimized objective function. When there are multiple quantile curves \(j=1,2,...,J\) (and summ=TRUE) the formula is

\(n (\sum_j\log(\tau_j(1-\tau_j))-J-\log(\sum_j\rho_{\tau_j}/(n J)))\)

AIC.gcrq simply returns -2*logLik + k*edf where k is 2 or log(n).

References

Bondell HD, Reich BJ, Wang H (2010) Non-crossing quantile regression curve estimation, Biometrika, 97: 825-838.

See Also

logLik.rq

Examples

   # \donttest{
## logLik(o) #a unique value (o is the fit object  from gcrq)
## logLik(o, summ=FALSE) #vector of the log likelihood values
## AIC(o, k=-1) #BIC
   # }