1. Generate flexion by time curves using GAMLSS with a variety of candidate distributions (e.g. Normal, Gamma, Box-Cox).|
2. Determine whether the addition of smoothing splines to median, variance, skewness and kurtosis improve fit of the models, using the Schwarz Bayesian Criterion (SBC) as a numerical guide.
3. Optimize the number of knots of smoothing splines and power transformation of time using the find.hyper function.
4. Compare model fit for different candidate distributions using SBC and Mean Squared Error (MSE) by 5-fold cross validation. The best model minimizes these metrics.
5. Examine reference charts for each of the candidate distributions to determine the percentage of data captured below each of the specified centiles. The best model accurately represents the observed data (e.g. 5% below the 5th percentile, etc.).
6. For similar models, a less-complex approach (fewer degrees of freedom) is preferred.