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Linear regression model parameters, statistics, and global validation statistics are presented in Additional file 1: Table S2.
A typical curve fitting example for the triplet of trajectories (mathbf {x}_1,mathbf {y}_1) and (mathbf {z}_1) appears in Figs. 2 and 3, with ((x_0,y_0,z_0) = (0.15,0.10,0.55)), where the associated goodness of fit and model parameters statistics are presented in Tables 2 and 3 for the single exponential model and in Tables 4 and 5 for the double exponential model.
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The procedure for updating the mechanical model, probabilistic model, distribution parameter statistics and reliability is illustrated for the fatigue reliability problem.
Model parameters and tree statistics were summarized in MrBayes and posterior probabilities higher than 0.75 were mapped to the maximum likelihood best tree manually.
The resulting relationships between model parameters and summary statistics are shown in Figure S3.
Table 1 shows the varying prior specifications of the MCMC chains and posterior results for model parameters and summary statistics.
Having done this, there are strong relationships between model parameters and the summary statistics, which means that inference via ABC on the basis of these statistics should provide good statistical power to infer parameter values.
The corresponding model parameters and other summary statistics can be found in Table 2.
Due to the clustered data structure in ICILS 2013 (i.e., teachers are nested in schools), we adjusted the standard errors of the model parameters and the χ2 statistics, using the MLR estimator and the 'TYPE = Coption' optinn in Mplus for the moderation analyses.
Additional file 1 contains full results for all model parameters and model diagnostic statistics.
We used simulated data to investigate the relationship between the model parameters and the summary statistics.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com