Research Article

Stochastic Mixed-Effects Parameters Bertalanffy Process, with Applications to Tree Crown Width Modeling

Table 3

Estimation goodness of fit statistics for all the used fixed-effects models applied to the estimation and validation dataset.

Models
(number of parameters)
EstimationValidation
, m
(PB, %)
RMS, m
(PRMSE, %)
AIC
(BIC)
, m
(PB, %)
RMSE, m (PRMSE, %)AIC

Fixed
(4)
−0.0504
(−6.70)
0.7104
(21.80)
10922.1
(10943.79)
0.6584−0.0236
(−5.18)
0.6686
(20.46)
4012.63
(4030.82)
0.7066

Fixed +
(5)
−0.0477
(−4.74)
0.6516
(20.00)
10634.64
(10661.61)
0.71230.1117
(−6.21)
0.6909
(21.14)
4059.46
(4082.20)
0.6867

Mixed
(5)
0.0350
(−3.41)
0.6414
(19.67)
10590.63
(10617.60)
0.72150.0344
(−2.01)
0.6390
(19.55)
3950.60
(3973.74)
0.7319

Mixed +
(6)
0.0374
(−2.68)
0.6238
(19.13)
10501.09
(10533.46)
0.73660.1105
(−0.70)
0.6716
(19.98)
4020.96 
(4048.25)
0.7270

The best values of the performance statistics for all scenarios of stand variables are in bold, the mean prediction bias and the percentage mean prediction bias , the root mean squared error and the percentage root mean squared error , an adjusted coefficient of determination , and is the number of parameters in the model, is the total number of observations used to fit the model, is the number of stands, is the number of trees in th stand, and , , and are the measured, estimated, and average values of the dependent variable (crown width).