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Introduction to assessor

Source: vignettes/assessor.Rmd
assessor.Rmd

assessor

The goal of assessor is to provide assessment tools for regression models with discrete and semicontinuous outcomes proposed in Yang (2024) and and Yang(2024). It calculates the double probability integral transform (DPIT) residuals, constructs QQ plots of residuals for model diagnostics, and constructs the ordered curve for assessing mean structures.

General function arguments

In assessor, there are functions for calculating DPIT residuals for the various type of models: discrete, zero-inflated, and semi-continuous outcome regression models. resid_disc(), resid_zeroinfl(), resid_semiconti(), and resid_2pm() are functions evaluating DPIT residuals for discrete, zero-inflated discrete, semicontinuous, and two-part outcomes, respectively. They share the same arguments:

  • model: Each function supports certain types of model objects. Check below on which model objects are applicable.

  • plot: If you set plot=TRUE, the function will return a QQ-plot of DPIT residuals. Some users may only need the QQ-plot. In that case, qqresid() only returns the QQ-plot without returning the DPIT residuals.

  • scale: You can choose the scale of the residuals among normal and uniform scales. The sample quantiles of the residuals are plotted against the theoretical quantiles of a standard normal distribution under the normal scale, and against the theoretical quantiles of a uniform (0,1) distribution under the uniform scale. The default scale is normal.

Real data example

The solder data, extracted from the faraway package, lends itself to fitting through either Poisson regression or Negative Binomial regression. The selection between these models depends on the underlying distribution characteristics of the data. To validate the distribution assumption, a comprehensive approach involves assessing the DPIT residuals and scrutinizing the QQ plot derived from these residuals.

library(assessor)
library(faraway) 
library(MASS)
data("solder") # from faraway package


## Negative Binomial
modpnb <- glm.nb(skips~.,data=solder)
modp <- glm(skips~.,famil=poisson(link="log"),data=solder)

## QQ-plot
par(mfrow=c(1,3))
poi.resid <- resid_disc(modp,plot = TRUE)
norm.resid <- resid_disc(modpnb,plot = TRUE, scale = "normal")
unif.resid <- resid_disc(modpnb,plot = TRUE, scale = "uniform")

The left panel of the figure above presents the QQ plot of the DPIT residuals when we use a Poisson GLM (modp). The residuals display a pronounced S-shaped pattern, hinting at potential overdispersion.

The second and third panels present the of DPIT residuals of the negative binomial regression (modpnb) on different scales. Both plots align closely along the diagonal line, suggesting that the assumption of negative binomial distribution appears appropriate. The only distinction between them lies in the scale parameter; the middle panel displays the plot on the normal scale, with the \(x\) and \(y\) axes spanning beyond (0,1), while the right panel limits the axes to a range of 0 to 1.