Choosing whether to eliminate or keep a predictor in a GAMLSS model I need to calculate the centile curve for y using a GAMLSS model with age and height as predictors.
The plots below depict the relationship between log(y) and each of the independent variables.


I incorporated log of age and log of height into the model to make the relationship between these variables more linear. The findings reveal that age does not influence all factors.The R2=0.8 and RMSE=0.3. Do you recommend me to remove sigma.fo =~pb(log(Ph1_Alter_2)) from the model and put sigma.fo =~1? Is it necessary for age and height to be significant for all parameters when the goal of a project is centile estimation?
m8 <- gamlss(y ~ log(Ph1_Groesse) + pb(log(Ph1_Alter_2)), sigma.fo =~pb(log(Ph1_Alter_2)), nu.fo =~1, family = BCCGo(mu.link = "log"), data=DAT1.F)



The p-value 0.2768 is just for the linear term in log(Ph1_Alter_2),
and does not tell you if the smoothing term is significant.
There is  good example of centile estimation for Y based on 2 X variables
in Rigby et al. (2019) Section 5.9, pages 100-108
NOTE:
The p-value after pb(log(Alter_age)) in the output is the significance of the LINEAR term in log(Alter_age).
It is NOT the significance of the whole nonlinear smooth pb term.
