tweedie_profile: Profile Likelihood Estimate of Tweedie Variance Index...

In tweedie: Evaluation of Tweedie Exponential Family Models

Profile Likelihood Estimate of Tweedie Variance Index Parameter

Description

This function profiles the (log-)likelihood over a vector of Tweedie power-index parameter (denoted p or \xi) to find the maximum likelihood estimate (MLE) of the index parameter p (or equivalently \xi).

Usage

tweedie_profile(formula, p.vec = NULL, xi.vec = NULL, link.power = 0, 
  data, weights = 1, offset = 0, fit.glm = FALSE, do.smooth = TRUE, 
  do.plot = FALSE, do.ci = do.smooth, eps = 1/6, 
  control = list( epsilon = 1e-09, maxit = stats::glm.control()$maxit, 
  trace = glm.control()$trace ),
  do.points = do.plot, method = "inversion", conf.level = 0.95, 
  phi.method = ifelse(method == "saddlepoint", "saddlepoint", "mle"), 
  verbose = FALSE, add0 = FALSE)

tweedie.profile(
  formula,
  p.vec = NULL,
  xi.vec = NULL,
  link.power = 0,
  data,
  weights = 1,
  offset = 0,
  fit.glm = FALSE,
  do.smooth = TRUE,
  do.plot = FALSE,
  do.ci = do.smooth,
  eps = 1/6,
  control = list(epsilon = 1e-09, maxit = stats::glm.control()$maxit, trace =
    glm.control()$trace),
  do.points = do.plot,
  method = "inversion",
  conf.level = 0.95,
  phi.method = ifelse(method == "saddlepoint", "saddlepoint", "mle"),
  verbose = FALSE,
  add0 = FALSE
)

Arguments

formula	a formula expression as for other regression models and generalized linear models, of the form response ~ predictors.
p.vec	a vector of p values for consideration. The values must all be larger than one. If the response has zeros, values must be 1 < p < 2. If NULL (default), p.vec is set automatically.
xi.vec	a synonym for p.vec, as some authors use the \xi notation.
link.power	the power link function to use in the tweedie glm family. These link functions g(\cdot) are of the form g(\eta)=\eta^{link.power}, where link.power = 0 (default) refers to the logarithm link function.
data	an optional data frame, list or environment containing the variables.
weights	an optional vector of weights to be used in the fitting process.
offset	an a priori known component included in the linear predictor. See model.offset.
fit.glm	logical; if TRUE, the Tweedie glm is fitted using the value of p found by the profiling function. The default is FALSE.
do.smooth	logical; if TRUE (default), a spline is fitted to the data to smooth the profile likelihood plot. Note that p.vec must contain at least five points for smoothing.
do.plot	logical; if TRUE, a plot of the profile likelihood is produced. The default is FALSE.
do.ci	logical; if TRUE, the nominal 100*conf.level is computed. Defaults to the value of do.smooth. Confidence intervals are only computed if do.smooth = TRUE.
eps	the offset in computing the variance function. Default is 1/6 (as recommended by Nelder and Pregibon, 1987). eps is ignored unless method = "saddlepoint".
control	a list of parameters for controlling the fitting process;
do.points	logical; if TRUE, the points used to compute the likelihood as given by p.vec (or equivalently, xi.vec) are explicitly shown by points. The defaults is the value of do.plot.
method	the method of evaluation; one of saddlepoint, interpolation, series or inversion (the default).
conf.level	the level of confidence for the confidence intervals; the default is 0.95 (for 95\% confidence intervals).
phi.method	the method used to estimate \phi; one of saddlepoint, mle (the default).
verbose	logical; if TRUE, some details of the calculations are shown. The default is FALSE.
add0	logical; if TRUE, adds P(Y = 0) to the plot. The default is FALSE.

Details

For each value in p.vec, the function computes an estimate of \phi and then computes the value of the log-likelihood for these parameters. The plot of the log-likelihood against p.vec allows the maximum likelihood value of p to be found. Once p is found, the distribution within the class of Tweedie distributions is identified.

Note

The estimates of p and \phi are printed invisibly. If the response variable has any exact zeros, the values in p.vec must all be between one and two.

The function can be temperamental (for theoretical reasons involved in numerically computing the density; see Dunn and Smyth (2005)) and may be very slow or fail. One solution is to change the method. The default is method = "inversion"; then try "series", "interpolation", and "saddlepoint" in that order. Note that method = "saddlepoint" is an approximate method only.

It is recommended that for the first use with a data set, use p.vec with only a small number of values and set do.smooth = FALSE, do.ci = FALSE. If this is successful, a larger vector p.vec and smoothing can be used.

References

Dunn, P. K. and Smyth, G. K. (2018). Generalized linear models with examples in R. Springer. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-1-4419-0118-7")}

Examples

data(Loblolly)
out <- tweedie_profile(height~age, data = Loblolly, 
          do.plot = FALSE, p.vec = seq(3.5, 4.5, length = 7) )
# The estimate for the variance power index (p, or xi) is:
out$p.max

tweedie documentation built on Feb. 7, 2026, 5:07 p.m.