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The residual plots of the following models are not normal, while the distribution of residuals between (-3 to 3) is normal in model m17. The worm plot of all equations appears to be correct. The goal of this project is to calculate the reference equation using the LMS approach. 1. Could you please tell me if the BCCGo distribution is adequate for this data? If not, which family would you suggest? > 2. Which of these equations performs the best? Why? Thanks so much for your time and help in advance.

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

m17 <- gamlss(y ~ log(Ph1_Groesse) + pb(Ph1_Alter_2), sigma.fo =~pb(Ph1_Alter_2), nu.fo =~pb(Ph1_Alter_2), family = BCCGo(mu.link = "log"), data=DAT1.F)

m24 <- gamlss(y ~ log(Ph1_Groesse) + pb(log(Ph1_Alter_2)), sigma.fo =~pb(log(Ph1_Alter_2)), nu.fo=~log(Ph1_Alter_2), tau.fo=~log(Ph1_Alter_2), family = BCPE(mu.link = "log"), data=DAT1.F)

The graphs: Model m4

enter image description here enter image description here

Model m17 enter image description here enter image description here

Model m24 enter image description here enter image description here

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    $\begingroup$ These distributions are so extremely close to exhibiting Normality that one is compelled to ask the question, why do these tiny departures from Normality matter in your application? $\endgroup$
    – whuber ♦
    Commented Jan 12, 2023 at 15:20
  • $\begingroup$ @ whuber, Thank you very much for your response. We are more interested in residuals ranging between -3 and 3 and any improvement is primarily beyond +3 and -3 z-scores, is unimportant in clinical practice. Although it appears that these three models are the same, do you recommend that I choose one that is at least normal in the -3 to 3 range? or still normality assumption does not matter? $\endgroup$
    – stats
    Commented Jan 13, 2023 at 9:24
  • $\begingroup$ @ whuber, I made the question more clear here, stats.stackexchange.com/questions/601860/… so I would be so thankful if you share your thoughts on it. $\endgroup$
    – stats
    Commented Jan 13, 2023 at 10:41

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