1d:T79c,# Graphical normality testing for quantile residuals Derives quantile residuals of the input model and creates two plots: the first compares density of a standard normal distribution to the residuals' empirical density while the other one is a **QQplot**. ```r Qresiduals(model, plot.it = TRUE) ``` ## Arguments - `model`: a model supported by `glmxdiag`. - `plot.it`: logical, whether to plot the results or not. ## Details Quantile residuals are defined on a continuous cumulative distribution function; for binomial, beta-binomial, poisson and negative binomial regression models the **Randomized quantile residuals** are used. Residuals have an important role inside the global diagnostic of a regression model. Any departure from the standard normal distribution can be considered as a warning that one or more aspects of the model are misspecified. Quantile residuals are particullary useful with models that do not have a continuous response variable, such as a binomial or poisson models; see examples. ## Returns Called for side effects but invisibly returns the calculated quantile residuals. ## Author(s) Giuseppe Reale ## References Peter K. Dunn and Gordon K. Smyth (1996). Randomized Quantile Residuals. Journal of Computational and Graphical Statistics. ## Examples ```r # Simulate the data set.seed(10) n <- 100 x1 <- rt(n, df = 4) x2 <- rnorm(n, sd = 2) b <- c(1, .5, .5) eta <- b[1] + b[2] * x1 + b[3] * x2 prob <- exp(eta)/(1 + exp(eta)) y <- rbinom(n, size = 1, prob = prob) # The model is correctly specified mod <- glm(y ~ x1 + x2, family = binomial) res.p <- residuals(mod, type = 'pearson') res.d <- residuals(mod, type = 'deviance') qres <- Qresiduals(mod, plot.it = FALSE) shapiro.test(res.p) # not normal shapiro.test(res.d) # not normal shapiro.test(qres) # normal y.hat <- fitted(mod) plot(y.hat, res.p) # uninformative plot(y.hat, res.d) # uninformative plot(y.hat, qres) Qresiduals(mod) ```

Qresiduals function