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)
