Maximum likelihood estimation and Hermite regression
glm.hermite is used to fit generalized linear models with count
responses following a Hermite distribution, specified by giving a symbolic
description of the linear predictor. A
summary method providing the
most meaningful information on the fitted model is available for objects of
symbolic description of the model. A typical predictor has the form
an optional data frame containing the variables in the model.
character specification of link function: "log" or "identity". By default
a vector containing the starting values for the parameters of the specified
model. Its default value is
value for parameter
glm.hermite returns an object of class
glm.hermite, which is a
list including the following components:
coefs the vector of coefficients.
data an optional data frame containing the variables in the model.
loglik log-likelihood of the fitted model.
vcov covariance matrix of all coefficients in the model (derived from the Hessian of the
hessHessian matrix, returned by the
fitted.values the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function.
wLikelihood ratio test statistic.
pvalLikelihood ratio test p-value.
María Oliveira, Manuel Higueras, David Moriña and Pere Puig
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Kotz S. Univariate discrete distributions. Norman L. Johnson 2005.
Puig P. (2003). Characterizing Additively Closed Discrete Models by a Property of Their Maximum Likelihood Estimators, with an Application to Generalized Hermite Distributions. Journal of the American Statistical Association 2003; 98:687–692.
Distributions for some other distributions,
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