gamlss2

Extracting Fitted or Predicted Probability Distributions from gamlss2 Models

Description

Methods for gamlss2 model objects for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions as distributions3 objects.

Usage

## S3 method for class 'gamlss2'
prodist(object, ...)

Arguments

object A model object of class gamlss2.

… Arguments passed on to predict.gamlss2, e.g., newdata.

Details

To facilitate making probabilistic forecasts based on gamlss2 model objects, the prodist method extracts fitted or predicted probability distribution objects. Internally, the predict.gamlss2 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/.

Examples

library("gamlss2")


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

## fit heteroscedastic normal GAMLSS model
## stopping distance (ft) explained by speed (mph)
m <- gamlss2(dist ~ s(speed) | s(speed), data = cars, family = NO)

GAMLSS-RS iteration  1: Global Deviance = 407.3647 eps = 0.125474     
GAMLSS-RS iteration  2: Global Deviance = 406.1879 eps = 0.002888     
GAMLSS-RS iteration  3: Global Deviance = 406.1521 eps = 0.000088     
GAMLSS-RS iteration  4: Global Deviance = 406.1491 eps = 0.000007

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

                                  1                                   2 
"GDF NO(mu = 23.29, sigma = 10.11)" "GDF NO(mu = 58.71, sigma = 18.60)" 
                                  3 
"GDF NO(mu = 94.13, sigma = 34.21)"

## obtain quantiles (works the same for any distribution object 'd' !)
quantile(d, 0.5)

       1        2        3 
23.28681 58.70678 94.12851

quantile(d, c(0.05, 0.5, 0.95), elementwise = FALSE)

     q_0.05    q_0.5    q_0.95
1  6.660745 23.28681  39.91288
2 28.117328 58.70678  89.29623
3 37.863044 94.12851 150.39398

quantile(d, c(0.05, 0.5, 0.95), elementwise = TRUE)

         1          2          3 
  6.660745  58.706778 150.393985

## 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)

       1        2        3 
23.28681 58.70678 94.12851

variance(d)

        1         2         3 
 102.1703  345.8508 1170.1173

## simulate random numbers
random(d, 5)

        r_1          r_2      r_3       r_4        r_5
1  31.46146  -0.03983743 36.22054  28.28792   3.230608
2  46.03940  81.83797745 65.79318  44.30638  54.715483
3 112.66001 116.30619679 76.26833 119.85856 105.993169

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

        d_-100        d_-50          d_0        d_50        d_100
1 1.957744e-34 1.517418e-13 0.0027779484 0.001201193 1.226794e-14
2 3.287990e-18 8.163864e-10 0.0001470760 0.019225098 1.823375e-03
3 1.183451e-09 1.628516e-06 0.0002645741 0.005074764 1.149206e-02

cdf(d, 50 * -2:2)

        p_-100        p_-50          p_0       p_50     p_100
1 1.611730e-34 2.077317e-13 0.0106164934 0.99588875 1.0000000
2 7.070541e-18 2.527177e-09 0.0007976179 0.31982786 0.9868047
3 6.929792e-09 1.257638e-05 0.0029640291 0.09851764 0.5681420

## Poisson example
data("FIFA2018", package = "distributions3")
m2 <- gamlss2(goals ~ s(difference), data = FIFA2018, family = PO)

GAMLSS-RS iteration  1: Global Deviance = 355.3922 eps = 0.045332     
GAMLSS-RS iteration  2: Global Deviance = 355.3922 eps = 0.000000

d2 <- prodist(m2, newdata = data.frame(difference = 0))
print(d2)

                   1 
"GDF PO(mu = 1.237)"

quantile(d2, c(0.05, 0.5, 0.95))

[1] 0 1 3

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

[1] -177.6961

logLik(m2)

'log Lik.' -177.6961 (df=2.005144)