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Linear regression models are commonly used to obtain estimates of parameter significance as well as forecasting of the response variable at random points in the design space.
Because the data had a hierarchical structure (i.e. growth rings within discs, within trees, within stands), a mixed-modelling approach was adopted to ensure that appropriate estimates of parameter standard errors were obtained and tests of parameter significance were valid (Pinheiro and Bates [2000]).
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This makes it impossible to perform a rigorous statistical treatment of the model goodness-of-fit and of the parameter significance, which would otherwise be a natural part of practical identifiability analysis.
The method supplies a tool to estimate model parameters from observed data through the analysis of the relative parameter significance.
Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance.
Looking beyond the usual measures of fit and adequacy, residual analysis revealed nothing out of the ordinary and tests of parameter coefficients significance all looked satisfactory.
There was no distinctive difference between the standard and robust estimates in terms of parameters and significance levels.
Asterisks denote the level of significance of parameter values: *** indicating significance at 1% level, ** at 5% level and * at 10% level.
To compensate for this, we advise that interpretation of parameter tests of significance should be done with extreme caution.
For more details on the significance of parameter influence see Additional file 1: Section "Significance of parameter influence".
Analysis of variance was applied to determine the significance of parameter influence (see also Additional file 1: Section "Significance of parameter influence" and Table 1).
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