# A question about applying GAMLSS models

I want to make the growth chart by using age and height as predictors. As the scatter plots show a nonlinear relationship between age and y, I need to use the P-spline to make the statistical equation. We need to make sure that age would contribute any information. So I used the following function in R

m4 <- gamlss(y ~ log(Ph1_Groesse) + pb(log(Ph1_Alter_2)),
sigma.fo =~pb(log(Ph1_Alter_2)), nu.fix=T, nu.start=1,
family = BCCGo(mu.link = "log"), data=DAT1.F)


The summary of the model shows that the pb(log(Ph1_Alter_2)) is not significant for sigma spline.

Family:  c("BCCGo", "Box-Cox-Cole-Green-orig.")

Call:  gamlss(formula = y ~ log(Ph1_Groesse) +
pb(log(Ph1_Alter_2)),
sigma.formula = ~pb(log(Ph1_Alter_2)),
family = BCCGo(mu.link = "log"),      data = DAT1.F,
nu.start = 1, nu.fix = T)

Fitting method: RS()

------------------------------------------------------------------
Mu link function:  log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)          -11.085097   0.134985  -82.12   <2e-16 ***
log(Ph1_Groesse)       2.409092   0.028776   83.72   <2e-16 ***
pb(log(Ph1_Alter_2))   0.055320   0.005212   10.61   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

------------------------------------------------------------------
Sigma link function:  log
Sigma Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)          -2.27211    0.06733 -33.745   <2e-16 ***
pb(log(Ph1_Alter_2))  0.03401    0.02082   1.633    0.103
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

------------------------------------------------------------------
Nu parameter is fixed
Nu =  1


So, I was wondering if I should accept this model or reduce the model to A4 by considering simga spline as a constant.

A4<- gamlss(y ~ log(Ph1_Groesse) + pb(log(Ph1_Alter_2)),
sigma.fo =~log(Ph1_Alter_2), nu.fix=T, nu.start=1,
family = BCCGo(mu.link = "log"), data=DAT1.F)