glm.hP: Fit a hyper-Poisson Double Generalized Linear Model

Description

The glm.hP function is used to fit a hyper-Poisson double generalized linear model with a log-link for the mean (mu) and the dispersion parameter (gamma).

Usage

glm.hP(
  formula.mu,
  formula.gamma,
  init.beta = NULL,
  init.delta = NULL,
  data,
  weights,
  subset,
  na.action,
  maxiter_series = 1000,
  tol = 0,
  offset,
  opts = NULL,
  model.mu = TRUE,
  model.gamma = TRUE,
  x = FALSE,
  y = TRUE,
  z = FALSE
)

Value

glm.hP returns an object of class "glm_hP". The function summary can be used to obtain or print a summary of the results.

The generic accessor functions coef,

fitted.values and residuals can be used to extract various useful features of the value returned by

glm.hP.

weights extracts a vector of weights, one for each case in the fit (after subsetting and na.action).

An object of class "glm_hP" is a list containing at least the following components:

coefficients: a named vector of coefficients.
residuals: the residuals, that is response minus fitted values.
fitted.values: the fitted mean values.
linear.predictors: the linear fit on link scale.
call: the matched call.
offset: the offset vector used.
weights: the weights initially supplied, a vector of 1s if none were.
df.residual: the residual degrees of freedom.
df.null: the residual degrees of freedom for the null model.
y: if requested (the default) the y vector used.
matrix.mu: if requested, the mu model matrix.
matrix.gamma: if requested, the gamma model matrix.
model.mu: if requested (the default) the mu model frame.
model.gamma: if requested (the default) the gamma model frame.
nloptr: an object of class "nloptr" with the result returned by the optimizer nloptr

Arguments

formula.mu: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
formula.gamma: regression formula linked to log(gamma)
init.beta: initial values for regression coefficients of beta.
init.delta: initial values for regression coefficients of delta.
data: an optional data frame, list or environment (or object that can be coerced by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which glm.hP is called.
weights: an optional vector of ‘prior weights’ to be used in the fitting process. Should be NULL or a numeric vector.
subset: an optional vector specifying a subset of observations to be used in the fitting process.
na.action: a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.
maxiter_series: Maximum number of iterations to perform in the calculation of the normalizing constant.
tol: tolerance with default zero meaning to iterate until additional terms to not change the partial sum in the calculation of the normalizing constant.
offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See model.offset.
opts: a list with options to the optimizer, nloptr, that fits the model. See, the opts parameter of nloptr for further details.
model.mu: a logical value indicating whether the mu model frame should be included as a component of the returned value.
model.gamma: a logical value indicating whether the gamma model frame should be included as a component of the returned value.
x: logical value indicating whether the mu model matrix used in the fitting process should be returned as a component of the returned value.
y: logical value indicating whether the response vector used in the fitting process should be returned as a component of the returned value.
z: logical value indicating whether the gamma model matrix used in the fitting process should be returned as a component of the returned value.

Details

Fit a hyper-Poisson double generalized linear model using as optimizer the NLOPT_LD_SLSQP algorithm of function nloptr.

References

Antonio J. Saez-Castillo and Antonio Conde-Sanchez (2013). "A hyper-Poisson regression model for overdispersed and underdispersed count data", Computational Statistics & Data Analysis, 61, pp. 148--157.

S. G. Johnson (2018). The nlopt nonlinear-optimization package

Examples

Run this code

## Fit model
Bids$size.sq <- Bids$size ^ 2
fit <- glm.hP(formula.mu = numbids ~ leglrest + rearest + finrest +
              whtknght + bidprem + insthold + size + size.sq + regulatn,
              formula.gamma = numbids ~ 1, data = Bids)

## Summary of the model
summary(fit)

## To see the termination condition of the optimization process
fit$nloptr$message

## To see the number of iterations of the optimization process
fit$nloptr$iterations

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