This function generates Randomized Quantile Residuals.
rqr(y, pi, xi, m)
| y | vector with the response variable. |
|---|---|
| pi | value or vector with the values for pi parameter. |
| xi | value or vector with the values for pi parameter. |
| m | the maximum value. |
# Example 1, without covariates ------------------------------------------- set.seed(456) y <- rcub(n=1000, pi=0.15, xi=0.6, m=8) mod1 <- cub(pi.fo=y~1, xi.fo=~1, m=8) summary(mod1) # Residuals for the correct model r1 <- rqr(y, pi=mod1$fitted.pi, xi=mod1$fitted.xi, m=8) # Residuals for a wrong model, using arbitrary estimated parameters r2 <- rqr(y, pi=0.8, xi=0.2, m=8) par(mfrow=c(1, 2)) car::qqPlot(r1, dist="norm", mean=0, sd=1, main='Correct model', las=1) car::qqPlot(r2, dist="norm", mean=0, sd=1, main='Wrong model', las=1) ks.test(r1, "pnorm", mean=0, sd=1) ks.test(r2, "pnorm", mean=0, sd=1) # Example 2, with covariates ---------------------------------------------- # Function to generate some random values from a CUB model # pi explained by x1 # xi explained by x2 gendata <- function(n, m) { x1 <- runif(n) x2 <- rpois(n, lambda=4) pi <- pnorm(-1 + 2 * x1) xi <- pnorm( 4 - 1 * x2) y <- rcub(n=n, pi=pi, xi=xi, m=m) data.frame(y, x1, x2) } set.seed(12345) dataset <- gendata(n=500, m=5) # This is the correct model, pi explained by x1 and xi explained by x2 mod3 <- cub(pi.fo=y ~ x1, xi.fo= ~ x2, m=5, data=dataset) # This is the wrong model mod4 <- cub(pi.fo=y ~ x2, xi.fo=~ x1, m=5, data=dataset) # The residuals for both models r3 <- rqr(dataset$y, pi=mod3$fitted.pi, xi=mod3$fitted.xi, m=5) r4 <- rqr(dataset$y, pi=mod4$fitted.pi, xi=mod4$fitted.xi, m=5) par(mfrow=c(1, 2)) car::qqPlot(r3, dist="norm", mean=0, sd=1, main='Correct model', las=1) car::qqPlot(r4, dist="norm", mean=0, sd=1, main='Wrong model', las=1) ks.test(r3, "pnorm", mean=0, sd=1) ks.test(r4, "pnorm", mean=0, sd=1)