gamlss: prof.dev – R documentation

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prof.dev

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 d.stasinopoulos@londonmet.ac.uk 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/).

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

Generalised Additive Models for Location Scale and Shape

v5.3-4

GPL-2 | GPL-3

Authors

Mikis Stasinopoulos [aut, cre, cph], Bob Rigby [aut], Vlasios Voudouris [ctb], Calliope Akantziliotou [ctb], Marco Enea [ctb], Daniil Kiose [ctb]

Initial release

2021-03-31