glm.good {good} | R Documentation |
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 )