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

prof.dev {gamlss} | R Documentation

## 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, ...)

### 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
`...` | for extra arguments

### 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 mikis.stasinopoulos@gamlss.org 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.

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, http://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 http://www.gamlss.org/).

### 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)

[Package gamlss version 5.0-2 Index]