Fit a Mean Parametrized Conway-Maxwell Poisson Generalized Linear Model with constant dispersion.

This is a workhorse function in which glm.cmp to call upon to fit a mean-parametrized Conway-Maxwell Poisson generalized linear model with constant dispersion.

Usage

fit_glm_cmp_const_nu(
  y = y,
  X = X,
  offset = offset,
  betastart = betastart,
  lambdalb = lambdalb,
  lambdaub = lambdaub,
  maxlambdaiter = maxlambdaiter,
  tol = tol
)

Arguments

y

the response y vector.

X

the design matrix for regressing the mean

offset,

this can be used to specify an a priori known component to be included in the linear predictor for mean during fitting. This should be NULL or a numeric vector

betastart

starting values for the parameters in the linear predictor for mu.

lambdalb, lambdaub

numeric: the lower and upper end points for the interval to be searched for lambda(s). The default value for lambdaub should be sufficient for small to moderate size nu. If nu is large and required a larger lambdaub, the algorithm will scale up lambdaub accordingly.

maxlambdaiter

numeric: the maximum number of iterations allowed to solve for lambda(s).

tol

numeric: the convergence threshold. A lambda is said to satisfy the mean constraint if the absolute difference between the calculated mean and a fitted values is less than tol.

Value

A fitted model object of class cmp similar to one obtained from glm or glm.nb.

Details

If X is not of full column rank, the aliased (linearly dependent) columns are dropped before fitting – identified via the same pivoted QR decomposition that glm.fit uses – and the corresponding coefficients are reported as NA, mirroring the behaviour of glm for rank-deficient designs.

Examples

## For examples see example(glm.cmp)