prof.dev: Plotting the Profile Deviance for one of the Parameters in a...

In gamlss: Generalised Additive Models for Location Scale and Shape

Plotting the Profile Deviance for one of the Parameters in a GAMLSS model

Description

This functions plots the profile deviance of one of the (four) parameters in a GAMLSS model. It can be used if one of the parameters mu, sigma, nu or tau is a constant (not a function of explanatory variables) to obtain a profile confidence intervals.

Usage

prof.dev(object, which = NULL, min = NULL, max = NULL, 
        step = NULL, length = 7, startlastfit = TRUE, 
        plot = TRUE, perc = 95, col="darkgreen")

Arguments

object	A fitted GAMLSS model
which	which parameter to get the profile deviance e.g. which="tau"
min	the minimum value for the parameter e.g. min=1
max	the maximum value for the parameter e.g. max=20
step	how often to evaluate the global deviance (defines the step length of the grid for the parameter) e.g. step=1
length	the length if step is not set, default equal 7
startlastfit	whether to start fitting from the last fit or not, default value is startlastfit=TRUE
plot	whether to plot, plot=TRUE or save the results, plot=FALSE
perc	what % confidence interval is required
col	The colour of the profile line

Details

This function can be use to provide likelihood based confidence intervals for a parameter for which a constant model (i.e. no explanatory model) is fitted and consequently for checking the adequacy of a particular values of the parameter. This can be used to check the adequacy of one distribution (e.g. Box-Cox Cole and Green) nested within another (e.g. Box-Cox power exponential). For example one can test whether a Box-Cox Cole and Green (Box-Cox-normal) distribution or a Box-Cox power exponential is appropriate by plotting the profile of the parameter tau. A profile deviance showing support for tau=2 indicates adequacy of the Box-Cox Cole and Green (i.e. Box-Cox normal) distribution.

Value

Return a profile plot (if the argument plot=TRUE) and an ProfLikelihood.gamlss object if saved. The object contains:

values	the values at the grid where the parameter was evaluated
fun	the function which approximates the points using splines
min	the minimum values in the grid
max	te maximum values in the grid
max.value	the value of the parameter maximising the Profile deviance (or GAIC)
CI	the profile confidence interval (if global deviance is used)
criterion	which criterion was used

Warning

A dense grid (i.e. small step) evaluation of the global deviance can take a long time, so start with a sparse grid (i.e. large step) and decrease gradually the step length for more accuracy.

Author(s)

Calliope Akantziliotou, Mikis Stasinopoulos and Bob Rigby

References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

See Also

gamlss, prof.term

Examples

## Not run: 
data(abdom)
h<-gamlss(y~pb(x), sigma.formula=~pb(x), family=BCT, data=abdom) 
prof.dev(h,"nu",min=-2.000,max=2)
rm(h)
## End(Not run)

gamlss documentation built on Oct. 4, 2023, 5:08 p.m.