Residuals for regression models with negative binomial outcomes

Computes DPIT residuals for regression models with negative binomial outcomes using the observed counts (y) and their fitted distributional parameters (mu, size).

Usage

dpit_nb(y, mu, size)

Arguments

y

An observed outcome vector.

mu

A vector of fitted mean values.

size

A dispersion parameter of the negative binomial distribution.

Value

A dpit object containing DPIT residuals.

Details

For formulation details on discrete outcomes, see dpit.

Examples

## Negative Binomial example
library(MASS)
n <- 500
x1 <- rnorm(n)
x2 <- rbinom(n, 1, 0.7)
### Parameters
beta0 <- -2
beta1 <- 2
beta2 <- 1
size1 <- 2
lambda1 <- exp(beta0 + beta1 * x1 + beta2 * x2)
# generate outcomes
y <- rnbinom(n, mu = lambda1, size = size1)

# True model
model1 <- glm.nb(y ~ x1 + x2)
y1 <- model1$y
fitted1 <- fitted(model1)
size1 <- model1$theta
dpit.nb1 <- dpit_nb(y=y1, mu=fitted1, size=size1)
resid.nb1 <- residuals(dpit.nb1)
plot(dpit.nb1)


# Overdispersion
model2 <- glm(y ~ x1 + x2, family = poisson(link = "log"))
y2 <- model2$y
fitted2 <- fitted(model2)
dpit.nb2 <- dpit_pois(y=y2, mu=fitted2)
resid.nb2 <- residuals(dpit.nb2)
plot(dpit.nb2)