gamlss (version 5.4-12)

getQuantile: Getting the partial quantile function for a term

Description

This function can be used to calculate the partial effect that an explanatory variable has on a specific quantile.

By `partial effect' function we mean how the term influence the quantile given that the rest of explanatory terms are constant.

The function takes a GAMLSS object and for the range of a specified explanatory (by fixing the rest of the terms at specified values), calculates the effect that this term has on the a quantile of the distribution. That is, it shows the effect that the particular term has on the quantile. The `partial' quantile is calculated on a finite grid of values and then the function is approximated (using the splinefun()) and saved.

The saved function can be used to calculate the first derivative. This first derivatives shows the chance of the quantile function for a small change in the explanatory variable, by fixing the rest of the explanatory variables at a constant values.

Usage

getQuantile(obj = NULL, term = NULL, quantile = 0.9, data = NULL,
    n.points = 100, how = c("median", "last"), 
    fixed.at = list(), plot = FALSE)

Value

A function is created which can be used to evaluate the partial effect of the explanatory variable on a specified quantile.

Arguments

obj

A gamlss object

term

an explanatory variable (at the moment works with with continuous)

quantile

the required quantile of the distribution

data

the data.frame (not needed if is declared on obj)

n.points

the number of points in which the quantile function needs evaluation

how

whether for extra continuous explanatory variables should fixed at the median or the last observation in the data

fixed.at

a list indicating at which values the rest of the explanatory terms should be fixed

plot

whether to the plot the partial quantile function and its first derivatives

Author

Mikis Stasinopoulos

Details

The function getQuantile() relies on the predictAll() function to evaluate the distribution parameters at a grid (default 100 points) of the specified term (given that the the rest of the terms are fixed). Then the inverse cdf is used to calculate the partial quantile. The function then is approximated using splinefun()) and saved.

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, getPEF

Examples

library(gamlss)
data(rent)
m1 <- gamlss(R~pb(Fl)+pb(A)+B+loc, data=rent, family=GA)
FF<-getQuantile(m1, quantile=0.9, term="A", plot=TRUE)
FF(1960)
FF(1060, deriv=1)
FF(1060, deriv=2)
if (FALSE) {
# plotting partial quantile
# .05, 0.25, 0.5, 0.75, 0.95
# at the default values
# Fl = median(Fl), B=0, and loc=2
plot(R~A, data=rent,  col="lightgray", pch=20)
for (i in c(.05, 0.25, 0.5, 0.75, 0.95))
{
  Qua <- getQuantile(m1, quantile=i,term="A")
  curve(Qua, 1900, 1985,  lwd=1, lty=1, add=T)
}
# plotting at values Fl=60, B=1, and loc=1.
for (i in c(.05, 0.25, 0.5, 0.75, 0.95))
{
  Qua <- getQuantile(m1, quantile=i,term="A", 
            fixed.at=list(Fl=60, B=1, loc=1))
  curve(Qua, 1900, 1985,  lwd=1, lty=2, col="red", add=T)
}
# plotting at Fl=60, B=1 and loc=1.
for (i in c(.05, 0.25, 0.5, 0.75, 0.95))
{
  Qua <- getQuantile(m1, quantile=i,term="A", 
           fixed.at=list(Fl=120, B=0, loc=3))
  curve(Qua, 1900, 1985,  lwd=1, lty=3, col="blue", add=T)
}

}