great, I am very grateful for your advice

thank you so much for time and kindness. I just did not understand how you could make the plot of standardized residuals based on the centiles results. Could you please share the programming function or formula with me? Agian, thank you so much

@ COOLSerdash, thanks for the reply. I have two predictors (age and hight) in this project and Q statitics of exproximately all models (by using: BCCGO and No distributions, such as m4 <- gamlss(y ~ log(W) + pb(log(Age)), sigma.fo =~pb(log(Age)), nu.fo=~log(Age), family = BCCGo(mu.link = "log"), data=DAT1.F)) ) ) identifies a region of age and weight when the model is inadequate. So, I decide to compare them based on their centiles.

@ whube, thanks for the reply. I have around 3000 observations.

@ Henry, thanks for the reply, You are right, The LMS method is equivalent to Box-Cox Cole and Green distribution (BCCG), and BCCG parameters (μ, σ, υ) are the approximate median, coefficient of variation and skewness.

@ thanks for the reply. We need to present the equations. Forexample, when we use LMS method with long link function for Mu, the formula for mu would be: (forexample: mu = exp(-10.56310 + 2.27937·log(height) + 0.04112·log(age) + mu-spline). However, I have no idea how we can present the equation for mu when we use logitSST.

@ Alex, Thanks for the reply. For the manuscript. Can I just report the pvalue and the coeffient of the main variables? Or I need to provide the full table including all info regarding main and confounders>

Robert, Thank you so much for the help. Regarding calcualting the percentile curves and LMS method, what is the difference between Vgam and Gamlss?