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I'm comparing several GAMLSS models and was wondering how I might use the term.plot to identify the best model/fit. What type of information can we get from this graph? Can I argue that the model with a wider confidence interval performs worse (just looking at this plot, how do you determine on the model's performance)?

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Selecting the best model can be

(i) by choosing the fitted model with lowest generalized Akaike information criterion GAIC(k) for a user chosen penalty k for each effective degree of freedom in the model. [e.g k=2 for AIC or k=log(n) for BIC, although I prefer k=4 for a Chi-squared test (Chi-Sq with 1 df at 5% =3.84, approx 4]

(ii) looking at the residual (multiple) worm plots and Q-statistics. This especially highlights problems in the tails of the fitted models.

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  • $\begingroup$ thanks so much for the reply. I made the question more clear here, stats.stackexchange.com/questions/601860/… so I would be so thankful if you share your thouth with me regarding the question. I am using GAMLSS to calculate the centile curves based on LMS method including two independent variables. For the several dependent variables, the worm plots look fine but not the Q-statitics (as there are the Z-score >2) $\endgroup$
    – stats
    Jan 13, 2023 at 10:39

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