glm.good: Maximum Likelihood Estimation and Good Regression

In good: Good Regression

Maximum Likelihood Estimation and Good Regression

Description

glm.good is used to fit generalized linear models with a response variable following a Good distribution with parameters z and s. glm.good allows incorporating predictors in the model with a link function (log, logit and identity) that relates parameter z and predictors. A summary method over an object of class glm.good provides essential information regarding the fitted model such as parameters estimates, standard errors, and some goodness-of-fit measures. A prediction method over an object of class glm.good provides the fitted values with the estimated model and optionally standard errors and predictions for a new data set.

Usage

glm.good ( formula , data , link = "log" , start = NULL )

Arguments

formula	symbolic description of the model to be fitted. A typical predictor has the form response ~ terms where the response is the integer-valued response vector following a Good distribution with parameters s and z, and terms is a series of predictors.
data	an optional data frame with the variables in the model.
link	character specification of link function: "logit", "log" or "identity". By default link="log".
start	a vector with the starting values for the model parameters. Used for numerically maximize the likelihood function for parameters estimation. By default start = NULL.

Value

glm.good returns an object of class glm.good that is a list including:

coefs	The vector of coefficients.
loglik	Log-likelihood of the fitted model.
vcov	Variance-covariance matrix of all model parameters (derived from the Hessian matrix returned by nlm() ).
hess	Hessian matrix, returned by nlm().
fitted.values	The fitted mean values. These are obtained by transforming the linear predictors by the link function inverse.

Author(s)

Jordi Tur, David Moriña, Pere Puig, Alejandra Cabaña, Argimiro Arratia, Amanda Fernández-Fontelo

References

Good, J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40: 237–264.

Zörnig, P. and Altmann, G. (1995). Unified representation of zipf distributions. Computational Statistics & Data Analysis, 19: 461–473.

Kulasekera, K.B. and Tonkyn, D. (1992). A new distribution with applications to survival dispersal anddispersion. Communication in Statistics - Simulation and Computation, 21: 499–518.

Doray, L.G. and Luong, A. (1997). Efficient estimators for the good family. Communications in Statistics - Simulation and Computation, 26: 1075–1088.

Johnson, N.L., Kemp, A.W. and Kotz, S. Univariate Discrete Distributions. Wiley, Hoboken, 2005.

Kemp. A.W. (2010). Families of power series distributions, with particular reference to the lerch family. Journal of Statistical Planning and Inference, 140:2255–2259.

Wood, D.C. (1992). The Computation of Polylogarithms. Technical report. UKC, University of Kent, Canterbury, UK (KAR id:21052).

See Also

See also polylog from copula, dgood, and pgood, qgood and rgood from good, and maxLik from maxLik.

Examples

strikes <- c ( rep ( 0, 46 ) , rep ( 1, 76 ) , rep ( 2, 24 ) , rep ( 3, 9 ) , rep ( 4, 1 )  )
mle <- glm.good ( strikes ~ 1 , link = "log" )
names ( mle )
mle$coefficients
mle$fitted.values
mean ( strikes )
summary ( mle )
predict ( mle , newdata = NULL , se.fit = TRUE )

good documentation built on May 29, 2024, 11:50 a.m.