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Table 7 Matrix Π of the variance decomposition and conditioning indices for Mitscherlich model and thinned model: Collinear parameters were identified in the variance decomposition matrix Π deduced from the correlation matrix of \(\tilde {X}\) (Belsley et al. 1980), whose lines correspond to conditioning indices, and columns correspond to parameters

From: Bayesian inference of biomass growth characteristics for sugi (C. japonica) and hinoki (C. obtusa) forests in self-thinned and managed stands

Conditioning Variance proportion
Mitscherlich model
Indices \(\phantom {\dot {i}\!}S_{Y_{max_{th_{m}}}}\) \(\phantom {\dot {i}\!}S_{\omega _{yth_{m}}}\) \(\phantom {\dot {i}\!}S_{\gamma _{yth_{m}}}\)
η1=1 0 0 0
η2=10.89 0.031 0 0.008
η3=151.35 0.97 1 0.99
Thinned model
Indices \(\phantom {\dot {i}\!}S_{Y_{max_{{th}}}}\) \(\phantom {\dot {i}\!}S_{\omega _{{yth}}}\) \(\phantom {\dot {i}\!}S_{\gamma _{{yth}}}\)
η1=1 0.001 0.011 0.001
η2=3.44 0.013 0.296 0.002
η3=25.42 0.99 0.69 0.99
  1. For a large conditioning index ηj, parameters are collinear if their contributions to the variance are high