prof.term: Plotting the Profile: deviance or information criterion for...

In gamlss: Generalized Additive Models for Location Scale and Shape

Plotting the Profile: deviance or information criterion for one of the terms (or hyper-parameters) in a GAMLSS model

Description

This functions plots the profile deviance for a chosen parameter included in the linear predictor of any of the mu,sigma, nu or tau models so profile confidence intervals can be obtained. In can also be used to plot the profile of a specified information criterion for any hyper-parameter when smooth additive terms are used.

Usage

prof.term(model = NULL, criterion = c("GD", "GAIC"), penalty = 2.5, 
          other = NULL, min = NULL, max = NULL, step = NULL, 
          length = 7, xlabel = NULL, plot = TRUE, perc = 95, 
          start.prev = TRUE, col="darkgreen")

Arguments

model	this is a GAMLSS model, e.g. model=gamlss(y~cs(x,df=this),sigma.fo=~cs(x,df=3),data=abdom), where this indicates the (hyper)parameter to be profiled
criterion	whether global deviance ("GD") or information criterion ("GAIC") is profiled. The default is global deviance criterion="GD"
penalty	The penalty value if information criterion is used in criterion, default penalty=2.5
other	this can be used to evaluate an expression before the actual fitting of the model (Make sure that those expressions are well define in the global environment)
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	if the step is left NULL then length is considered for evaluating the grid for the parameter. It has a default value of 11
xlabel	if a label for the axis is required
plot	whether to plot, plot=TRUE the resulting profile deviance (or GAIC)
perc	what % confidence interval is required
start.prev	whether to start from the previous fitted model parameters values or not (default is TRUE)
col	the color of the profile line

Details

This function can be use to provide likelihood based confidence intervals for a parameter involved in terms in the linear predictor(s). These confidence intervals are more accurate than the ones obtained from the parameters' standard errors. The function can also be used to plot a profile information criterion (with a given penalty) against a hyper-parameter. This can be used to check the uniqueness in hyper-parameter determination using for example find.df.

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	the 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)

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.dev

Examples

data(aids)
# fitting a linear model
gamlss(y~x+qrt,family=NBI,data=aids)
# testing the linear beta parameter
mod<-quote(gamlss(y ~ offset(this * x) + qrt, data = aids, family = NBI))
prof.term(mod, min=0.06, max=0.11)
# find the hyper parameter using cubic splines smoothing
mod1<-quote(gamlss(y ~ cs(x,df=this) + qrt, data = aids, family = NBI))
prof.term(mod1, min=1, max=15, step=1, criterion="GAIC", penalty=log(45))
# find a break point in x
mod2 <- quote(gamlss(y ~ x+I((x>this)*(x-this))+qrt,family=NBI,data=aids))
prof.term(mod2, min=1, max=45, step=1, criterion="GD")
rm(mod,mod1,mod2)

gamlss documentation built on May 29, 2024, 6:08 a.m.