resid_semiconti {assessor}

Residuals for regression models with semicontinuous outcomes

Description

Calculates the DPIT residuals for regression models with semi-continuous outcomes. The semi-continuous regression model such as a Tweedie regression model from tweedie package or a Tobit regression model from VGAM, AER packages is used in this function.

Usage

resid_semiconti(model, plot=TRUE, scale = "normal")

Arguments

model

Model object (e.g., tweedie, vglm, and tobit)

plot

A logical value indicating whether or not to return QQ-plot

scale

You can choose the scale of the residuals between normal and uniform scales. The default scale is normal.

Details

The DPIT residual for the ith semicontinuous observation is defined as follows:

\hat{r}_i = \frac{\hat{F}(Y_i|X_i)}{n}\sum_{j=1}^{n}I\bigg(\hat{p}_0(X_j) \leq \hat{F}(Y_i|X_i)\bigg),

which has a null distribution of uniformity. \hat{F} refers to the fitted cumulative distribution function, and \hat{p}_0 refers to the fitted probability of being zero.

Value

Residuals. If plot=TRUE, also produces a QQ plot.

References

Lu Yang (2024). Diagnostics for Regression Models with Semicontinuous Outcomes, Biometrics, https://arxiv.org/abs/2401.06347

See Also

resid_2pm()

Examples

## Tweedie model
library(tweedie)
library(statmod)
n <- 500
x11 <- rnorm(n)
x12 <- rnorm(n)
beta0 <- 5
beta1 <- 1
beta2 <- 1
lambda1 <- exp(beta0 + beta1 * x11 + beta2 * x12)
y1 <- rtweedie(n, mu = lambda1, xi = 1.6, phi = 10)
# Choose parameter p
# True model
model1 <-
  glm(y1 ~ x11 + x12,
    family = tweedie(var.power = 1.6, link.power = 0)
  )
resid.tweedie <- resid_semiconti(model1)

## Tobit regression model
library(VGAM)
beta13 <- 1
beta14 <- -3
beta15 <- 3

set.seed(1234)
x11 <- runif(n)
x12 <- runif(n)
lambda1 <- beta13 + beta14 * x11 + beta15 * x12
sd0 <- 0.3
yun <- rnorm(n, mean = lambda1, sd = sd0)
y <- ifelse(yun >= 0, yun, 0)

# Using VGAM package
# True model
fit1 <- vglm(formula = y ~ x11 + x12, tobit(Upper = Inf, Lower = 0, lmu = "identitylink"))
# Missing covariate
fit1miss <- vglm(formula = y ~ x11, tobit(Upper = Inf, Lower = 0, lmu = "identitylink"))

resid.tobit1 <- resid_semiconti(fit1, plot = TRUE)
resid.tobit2 <- resid_semiconti(fit1miss, plot = TRUE)

# Using AER package
library(AER)
# True model
fit2 <- tobit(y ~ x11 + x12, left = 0, right = Inf, dist = "gaussian")
# Missing covariate
fit2miss <- tobit(y ~ x11, left = 0, right = Inf, dist = "gaussian")
resid.aer1 <- resid_semiconti(fit2, plot = TRUE)
resid.aer2 <- resid_semiconti(fit2miss, plot = TRUE)