tweedie.profile {tweedie}R Documentation

Tweedie Distributions: mle estimation of p

Description

Maximum likelihood estimation of the Tweedie index parameter power.

Usage

tweedie.profile(formula, p.vec, link.power=0, fit.glm=FALSE, do.smooth=FALSE,
do.plot=FALSE, do.ci=do.smooth,
eps=1/6, do.points=do.plot, method="series", conf.level=0.95, 
phi.method=ifelse(method == "saddlepoint", "saddlepoint", "mle"), verbose=TRUE)

Arguments

formula a formula expression as for other regression models and generalized linear models, of the form response ~ predictors. For details, see the documentation for lm, glm and formula
p.vec a vector of p values for consideration. The values must all be larger than one (if the response variable has exact zeros, the values must all be between one and two). See the DETAILS section below for further details.
link.power the power link function to use. These link functions g() are of the form g(eta) = eta^link.power, and the special case of link.power=0 (the default) refers to the logarithm link function. See the documentation for tweedie also.
fit.glm logical flag. If TRUE, the Tweedie generalized linear model is fitted using the value of p found by the profiling function. If FALSE (the default), no model is fitted.
do.smooth logical flag. If TRUE, a spline is fitted to the data to smooth the profile likelihood plot. If FALSE (the default), no smoothing is used (and the function is quicker). Note that p.vec must contain at least five points for smoothing to be allowed.
do.plot logical flag. If TRUE, a plot of the profile likelihood is produce. If FALSE (the default), no plot is produced.
do.ci logical flag. If TRUE, the nominal 100*conf.level is computed. If FALSE, no confidence interval is computed. By default, do.ci is the same value as do.smooth, since a confidence interval will only be accurate if smoothing has been performed. Indeed, if do.smooth=FALSE, confidence intervals are never computed and do.ci is forced to FALSE if it is given as TRUE.
eps the offset in computing the variance function. The default is eps=1/6 (as suggested by Nelder and Pregibon, 1987). Note eps is ignored unless the method="saddlepoint" as it makes no sense otherwise.
do.points plot the points on the plot where the (log-) likelihood is computed for the given values of p; defaults to the same value as do.plot
method the method for computing the (log-) likelihood. One of "series" (the default), "inversion", "interpolation" or "saddlepoint". If there are any troubles using this function, often a change of method will fix the problem. Note that method="saddlepoint" is only an approximate method for computing the (log-) likelihood. Using method="interpolation" may produce a jump in the profile likelihood as it changes computational regimes.
conf.level the confidence level for the computation of the nominal confidence interval. The default is conf.level=0.95.
phi.method the method for estimating phi, one of "saddlepoint" or "mle". A maximum likelihood estimate is used unless method="saddlepoint", when the saddlepoint approximation method is used. Note that using phi.method="saddlepoint" is equivalent to using the mean deviance estimator of phi.
verbose the amount of feedback requested: 0 or FALSE means minimal feedback, 1 or TRUE means some feedback (the default), or 2 means to show all feedback. Since the function can be slow and sometimes problematic, feedback can be good; but it can also be unnecessary when one knows all is well.

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 the value of p is found, the distribution within the class of Tweedie distribution is identified.

Value

The main purpose of the function is to estimate the value of the Tweedie index parameter, p, which is produced by the output list as p.max. Optionally (if do.plot=TRUE), a plot is produced that shows the profile log-likelihood computed at each value in p.vec (smoothed if do.smooth=TRUE). This function can be tempermental (for theoretical reasons involved in numerically computing the density), and this plot shows the values of p requested on the horizontal axis (using rug); there may be fewer points on the plot, since the likelihood some values of p requested may have returned NaN, Inf or NA.
A list containing the components: y and x (such that plot(x,y) (partially) recreates the profile likelihood plot); ht (the height of the nominal confidence interval); L (the estimate of the (log-) likelihood at each given value of p); p (the p-values used); phi (the computed values of phi at the values in p); p.max (the estimate of the mle of p); L.max (the estimate of the (log-) likelihood at p.max); phi.max (the estimate of phi at p.max); ci (the lower and upper limits of the confidence interval for p); method (the method used for estimation: series, inversion, interpolation or saddlepoint); phi.method (the method used for estimation of phi: saddlepoint or phi).
If glm.fit is TRUE, the list also contains a component glm.obj, a glm object for the fitted Tweedie generalized linear model.

Note

The estimates of p and phi are printed. The result is printed invisibly.

If the response variable has any exact zeros, the values in p.vec must all be between one and two.

The function is sometimes unstable and may fail. It may also be very slow. One solution is to change the method. The default is method="series" (the default); then try method="inversion", method="interpolation" and method="saddlepoint" in that order. Note that method="saddlepoint" is an approximate method only. Also make sure the values in p.vec are suitable for the data (see above paragraph).

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.

Author(s)

Peter Dunn (pdunn2@usc.edu.au)

References

Dunn, P. K. & Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing, 18, 73–86.

Dunn, Peter K and Smyth, Gordon K (2001). Tweedie family densities: methods of evaluation. Proceedings of the 16th International Workshop on Statistical Modelling, Odense, Denmark, 2–6 July

Jorgensen, B. (1987). Exponential dispersion models. Journal of the Royal Statistical Society, B, 49, 127–162.

Jorgensen, B. (1997). Theory of Dispersion Models. Chapman and Hall, London.

Nelder, J. A. and Pregibon, D. (1987). An extended quasi-likelihood function. Biometrika 74(2), 221–232.

Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families. Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference (Eds. J. K. Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical Institute.

See Also

dtweedie dtweedie.saddle tweedie

Examples

library(statmod) # Needed to use  tweedie.profile
# Generate some fictitious data
test.data <- rgamma(n=200, scale=1, shape=1)
# The gamma is a Tweedie distribution with power=2;
# let's see if the profile plot shows this
## Not run: 
        out <- tweedie.profile( test.data ~ 1, p.vec=seq(1.7, 2.3, length=6),
       do.plot=TRUE, method="interpolation", do.smooth=TRUE, do.ci=TRUE)
## End(Not run)

[Package tweedie version 1.6.2 Index]