The diagnostics for GAMLSS models are based on the residuals of the fitted model.The GAMLSS models use the normalised quantile residuals for continuous response variables and randomised normalised quantile residuals for discrete response variables.

The main advantage of the normalised (randomised) quantile residuals is that, whatever the distribution of the response variable their true values r always have a standard normal distribution given that the assumptions the model is correct. Since within the statistical literature checking the normality assumption is well established the normalised (randomised) quantile residuals provide us an easy way to check the adequacy of a GAMLSS fitted model.

There are several functions in the R implementation of GAMLSS using the residuals.

- The plot() function displaying the residuals
- The worm plot function wp()
- The detrended Own’s plot function dtop()
- The Q-statistics function Q.stats()
- The randomised residual plot function rqres.plot()