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Table 2 Bayesian Information Criterion (BIC) computed for Models (810)

From: Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis

Model \(2ln(\widehat{{\mathcal {L}}})\) \(\# \theta _F\) \(\# \theta _R\) BIC
(8) 1761 \(2^\text {a}/1^\text {b}\) \(4^\text {a}/5^\text {b}\) \(1778^\text {a}/1775^\text {b}\)
(9) 1801 3 4 1822
(10) 1759 \(2^\text {a}/1^\text {b}\) \(8^\text {a}/9^\text {b}\) \(1784^\text {a}/1782^\text {b}\)
  1. Since the definition of the BIC depends on the decomposition of individual parameters between fixed parameters and random parameters [37, 38], the computation of the BIC is ambiguous for Models (8) and (10). In these models, \(\rho _C^{pop}\) determines jointly the population values of \(\rho _C\) (which is fixed), \(\delta _{SC}\) and \(\delta _{CB}\) (which are random). Consequently, we can compute two different values of the BIC, depending on whether we consider \(\rho _C^{pop}\) as the fixed effect of a fixed parameter (a), or as the fixed effect of two random parameters (b). In practice, this consideration does not seem to affect the outcome of the selection