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Table 4 Characteristics of GAMLSS models fit with smoothing splines for the median and variance, following optimization of smoothing spline knots and the power transformation of time. The best GAMLSS distribution for each metric is bolded. Results reflect within sample performance (i.e., within the development set)

From: Reference chart for knee flexion following total knee arthroplasty: a novel tool for monitoring postoperative recovery

GAMLSS Distribution Model Degrees of Freedom SBC MSE Percentage of observed values captured below model centiles
5th 25th 50th 75th 95th
NO 7.45 9298.6 166.0 6.05 23.53 47.49 73.49 97.1
GA 7.45 9364.7 165.6 6.05 22.59 45.69 73.83 98.04
TF 8.45 9303.0 171.1 6.05 24.47 48.34 73.49 97.19
BCCG 8.45 9266.5 166.4 5.12 25.15 49.87 74.51 95.14
BCT 9.45 9273.5 167.4 5.12 25.15 49.87 74.51 95.14
BCPE 9.45 9271.0 166.3 5.29 24.55 49.79 74.85 95.06
  1. Abbreviations: SBC Schwarz Bayesian Criterion, MSE Mean Squared Error, NO Normal, GA Gamma, TF t-Family, BCCG Box Cox Cole and Green, BCT Box Cox t-distribution, BCPE Box Cox Power Exponential