dglars (version 2.1.7)

phihat: Estimate the Dispersion Parameter

Description

phihat returns the estimates of the dispersion parameter.

Usage

phihat(object, type = c("pearson", "deviance", "mle", "grcv"), g = NULL, ...)

Value

phihat returns a vector with the estimates of the dispersion parameter.

Arguments

object

fitted dglars object.

type

a description of the used estimator.

g

vector of values of the tuning parameter.

...

further arguments passed to the function grcv.

Author

Luigi Augugliaro
Maintainer: Luigi Augugliaro

Details

phihat implements four different estimators of the dispersion parameter, i.e, the generalized Pearson statistic (type = "pearson"), the deviance estimator (type = "deviance"), the maximum likelihood estimator (type = "mle") and general refitted cross-Validation estimator (type = "grcv") proposed in Pazira et al. (2018). For regression models with Gamma family, the maximum likelihood estimator of the dispersion parameter is computed using the approximation proposed in Cordeiro et al. (1997).

References

Cordeiro G. M. and McCullagh P. (1991) <doi:10.2307/2345592> Bias Correction in Generalized Linear Models, Journal of the Royal Statistical Society. Series B., Vol 53(3), 629--643.

Jorgensen B. (1997, ISBN:0412997188) The Theory of Dispersion Models, Chapman and Hall, Great Britain.

Pazira H., Augugliaro L. and Wit E.C. (2018) <doi:10.1007/s11222-017-9761-7> Extended differential-geometric LARS for high-dimensional GLMs with general dispersion parameter, Statistics and Computing, Vol 28(4), 753-774.

See Also

grcv, coef.dglars, logLik.dglars, AIC.dglars and BIC.dglars.

Examples

############################
# y ~ Gamma

library("dglars")
set.seed(321)
n <- 100
p <- 50
X <- matrix(abs(rnorm(n*p)),n,p)
eta <- 1 + 2 * X[, 1L]
mu <- drop(Gamma()$linkinv(eta))
shape <- 0.5
phi <- 1 / shape
y <- rgamma(n, scale = mu / shape, shape = shape)
fit <- dglars(y ~ X, Gamma("log"))
g <- seq(range(fit$g)[1L], range(fit$g)[2L], length = 10)

# generalized Pearson statistic
phihat(fit, type = "pearson")
phihat(fit, type = "pearson", g = g)

# deviance estimator
phihat(fit, type = "deviance")
phihat(fit, type = "deviance", g = g)

# mle
phihat(fit, type = "mle")
phihat(fit, type = "mle", g = g)

# grcv
phihat(fit, type = "grcv")
phihat(fit, type = "grcv", g = g)