In the GAMLSS implementation in R, the function gamlss() allows modelling all the distribution parameters μ, σ, ν and τ as linear and/or non-linear and/or ‘non- parametric’ smoothing functions of the explanatory variables. This allow the explanatory variables to effect the predictors, (the η’s), of the specific parameters and therefore the parameters themselves. As a result the shape of the distribution of the response variable, (not only the mean), is effected by the explanatory variables.
All the standard linear terms as used in the lm() and glm() functions in R can be used here. In addition the following smoothing additive term functions can be used:
- pb(), pvc() and cy(): based on P-splines,
- cs() and scs(): based on cubic splines,
- fp(): fractional polynomials
- fk(): free knot smoothing (break points)
- lo(): local regression based on the loess() R function
- nn(): neural network based on the nnet() R function
- nl(), non-linear term fitting based on the nlm() R function
- random() : simple random effect
- ri(), ridge(): for ridge regression
- ga(): an iterface for the gam() function of Simon Wood in package mgcv
New additive terms can be added relatively easy to the gamlss() function.