Lucid.OsteoNorm.FitModel

This task type fits a statistical distribution model to a table of normative data sample measurements.

Centile curves are modelled using GAMLSS (Generalized Additive Models for Location, Scale and Shape).

Parameters

  • μ (mu): location (median for BCPE)

  • σ (sigma): scale (approximate coefficient of variance for BCPE)

  • ν (nu): skewness (transformation to symmetry for BCPE)

  • τ (tau): kurtosis (power of the exponential for BCPE)

mu and sigma are smoothed with cubic P-splines (cf. Rigby and Stasinopoulos). nu and tau can also be smoothed with cubic P-splines, or can be constant. (GAIC (global optimization of hyperparameters using Generalized Akaike Information Criterion) is not used.)

Distribution family

For now BCPE is always used.

  • NO: Normal (Gaussian) distribution

  • BCCG: Box-Cox Cole and Green distribution

  • BCPE: Box-Cox Power Exponential

  • BCT: Box-Cox t

  • SHASH: Sinh-Arcsinh distribution (Jones, 2005)

  • SHASHo: Sinh-Arcsinh distribution (Jones and Pewsey, 2009)

Scoring algorithms

  • The RS (Rigby and Stasinopoulos) algorithm is a modified version of the Fisher-scoring algorithm.

  • The CG (Cole and Green) algorithm is a Newton-Raphson approach suitable when parameters are highly correlated.