prodist.gamlss {gamlss}

Extracting Fitted or Predicted Probability Distributions from gamlss Models

Description

Methods for gamlss model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.

Usage

## S3 method for class 'gamlss'
prodist(object, ...)

Arguments

object

A model object of class gamlss.

...

Arguments passed on to predictAll, e.g., newdata.

Details

To facilitate making probabilistic forecasts based on gamlss model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predictAll method is used first to obtain the distribution parameters (mu, sigma, tau, nu, or a subset thereof). Subsequently, the corresponding distribution object is set up using the GAMLSS class from the gamlss.dist package, enabling the workflow provided by the distributions3 package (see Zeileis et al. 2022).

Note that these probability distributions only reflect the random variation in the dependent variable based on the model employed (and its associated distributional assumption for the dependent variable). This does not capture the uncertainty in the parameter estimates.

Value

An object of class GAMLSS inheriting from distribution.

References

Zeileis A, Lang MN, Hayes A (2022). “distributions3: From Basic Probability to Probabilistic Regression.” Presented at useR! 2022 - The R User Conference. Slides, video, vignette, code at https://www.zeileis.org/news/user2022/.

See Also

GAMLSS, predictAll

Examples

## packages, code, and data
library("gamlss")
library("distributions3")
data("cars", package = "datasets")

## fit heteroscedastic normal GAMLSS model
## stopping distance (ft) explained by speed (mph)
m <- gamlss(dist ~ pb(speed), ~ pb(speed), data = cars, family = "NO")

## obtain predicted distributions for three levels of speed
d <- prodist(m, newdata = data.frame(speed = c(10, 20, 30)))
print(d)

## obtain quantiles (works the same for any distribution object 'd' !)
quantile(d, 0.5)
quantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)
quantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)

## visualization
plot(dist ~ speed, data = cars)
nd <- data.frame(speed = 0:240/4)
nd$dist <- prodist(m, newdata = nd)
nd$fit <- quantile(nd$dist, c(0.05, 0.5, 0.95))
matplot(nd$speed, nd$fit, type = "l", lty = 1, col = "slategray", add = TRUE)

## moments
mean(d)
variance(d)

## simulate random numbers
random(d, 5)

## density and distribution
pdf(d, 50 * -2:2)
cdf(d, 50 * -2:2)

## Poisson example
data("FIFA2018", package = "distributions3")
m2 <- gamlss(goals ~ pb(difference), data = FIFA2018, family = "PO")
d2 <- prodist(m2, newdata = data.frame(difference = 0))
print(d2)
quantile(d2, c(0.05, 0.5, 0.95))

## note that log_pdf() can replicate logLik() value
sum(log_pdf(prodist(m2), FIFA2018$goals))
logLik(m2)