distributions3 (version 0.2.0)

prodist: Extracting fitted or predicted probability distributions from models

Description

Generic function with methods for various model classes for extracting fitted (in-sample) or predicted (out-of-sample) probability distributions3 objects.

Usage

prodist(object, ...)

Value

An object inheriting from distribution.

Arguments

object

A model object.

...

Arguments passed on to methods, typically for calling the underlying predict methods, e.g., newdata for lm or glm objects or n.ahead for arima objects.

Details

To facilitate making probabilistic forecasts based on regression and time series model objects, the function prodist extracts fitted or predicted probability distribution objects. Currently, methods are provided for objects fitted by lm, glm, and arima in base R as well as glm.nb from the MASS package. All methods essentially proceed in two steps: First, the standard predict method for these model objects is used to compute fitted (in-sample, default) or predicted (out-of-sample) distribution parameters. Typically, this includes the mean plus further parameters describing scale, dispersion, shape, etc.). Second, the distributions objects are set up using the generator functions from distributions3.

See Also

predict, lm, glm, arima

Examples

## Model: Linear regression
## Fit: lm
## Data: 1920s cars data
data("cars", package = "datasets")

## Stopping distance (ft) explained by speed (mph)
reg <- lm(dist ~ speed, data = cars)

## Extract fitted normal distributions (in-sample, with constant variance)
pd <- prodist(reg)
head(pd)

## Compute corresponding medians and 90% interval
qd <- quantile(pd, c(0.05, 0.5, 0.95))
head(qd)

## Visualize observations with predicted quantiles
plot(dist ~ speed, data = cars)
matplot(cars$speed, qd, add = TRUE, type = "l", col = 2, lty = 1)


## Model: Poisson generalized linear model
## Fit: glm
## Data: FIFA 2018 World Cup data
data("FIFA2018", package = "distributions3")

## Number of goals per team explained by ability differences
poisreg <- glm(goals ~ difference, data = FIFA2018, family = poisson)
summary(poisreg)
## Interpretation: When the ratio of abilities increases by 1 percent,
## the expected number of goals increases by around 0.4 percent

## Predict fitted Poisson distributions for teams with equal ability (out-of-sample)
nd <- data.frame(difference = 0)
prodist(poisreg, newdata = nd)

## Extract fitted Poisson distributions (in-sample)
pd <- prodist(poisreg)
head(pd)

## Extract log-likelihood from model object
logLik(poisreg)

## Replicate log-likelihood via distributions object
sum(log_pdf(pd, FIFA2018$goals))
log_likelihood(pd, FIFA2018$goals)


## Model: Autoregressive integrated moving average model
## Fit: arima
## Data: Quarterly approval ratings of U.S. presidents (1945-1974)
data("presidents", package = "datasets")

## ARMA(2,1) model
arma21 <- arima(presidents, order = c(2, 0, 1))

## Extract predicted normal distributions for next two years
p <- prodist(arma21, n.ahead = 8)
p

## Compute median (= mean) forecast along with 80% and 95% interval
quantile(p, c(0.5, 0.1, 0.9, 0.025, 0.975))