Impact of experimental designs with increased amounts of data.

Whole pp-plot graph classification results and average normalized distances from the pp-plot graphs to the diagonal for three illustrative benchmark models. The outcome for the originally published design , and two artificial designs and with increased temporal sampling is shown. The respective number of estimated parameters, total number of data points and their ratio is given below.</p

All pp-plots graphs of the estimated model parameters, separated by their identifiability status.

(A) identifiable parameters and (B) practically non-identifiable based on their profile likelihoods. All graphs are classified in perfect (red), conservative (yellow), anti-conservative (blue) or alternating (purple) cases.</p

Parametric bootstrapping procedure for empirical likelihood ratios.

Parametric bootstrapping procedure for empirical likelihood ratios.</p

Average distance of pp-plot graphs from the diagonal.

Distances are normalized by the maximal possible distance value, i.e. a graph lying on the upper x-axis at pemp = 1 for all pemp in the pp-plot. Models are ordered according to the ranking of the classification results from Fig 4A. The histogram on the right shows the distribution of average distances from the diagonal summarized for all parameters.</p

Classification results of whole pp-plots graphs compared to the -distribution.

Results are sorted by the percentage of non-problematic, i.e. conservative and perfect consensus cases. The anti-conservative and alternating fraction of cases is indicated by a negative sign. (A) Overall results for all model parameters and (B-E) results separately for each model parameter type.</p

Profile likelihood for identifiability analysis.

(A) Illustrative profile likelihood as blue solid line for an identifiable parameter. For analyses of the identifiability status, the intersection with statistical threshold value (red line) at is crucial. Furthermore, profile likelihood-based confidence intervals can be constructed from the projections of the intersections on the parameter axis, defining the lower θlb and upper bound θub of the confidence interval, if these intersections exist. The MLE is indicated by the black asterisk. (B) Profile likelihood of a practically non-identifiable parameter that is open to the left resulting in an unbounded (C) Likelihood profile of a structural non-identifiability indicated by a flat line with unbounded confidence interval in both directions.</p

Classification results of pp-plots graphs at the 95% confidence level.

Results are sorted by the percentage of non-problematic, i.e. conservative and perfect consensus cases. The model ranking remains similar to the whole pp-plot graph analysis (cf. Fig 4).</p

Appropriateness of the -distribution for empirical likelihood ratios at specific confidence levels.

(A) Heatmap of conservativeness ratio CR, i.e. fraction of non-problematic cases in the respective parameter group or model. CR-values close to 1 indicate a good agreement with asymptotic theory, while lower values occur in situations where the asymptotic approximation might not be appropriate. (B) Parameter groups or models with CR larger than 95% at the confidence level are indicated by black tiles in the upper panel. (C) A less strict criterion checks if the CR value is larger than 1 − α% of the respective confidence level and parameter groups or model.</p

Overview of benchmark model properties and identifiability status.

(A) Estimated parameters of all 19 models and distribution of parameter types. (B) Identifiability of model parameters based on the profile likelihood using the original data and a threshold of Δα=0.05 = 3.84. Either identifiable parameters with finite profile likelihood-based confidence intervals (darker colors) or practically non-identifiable parameters (lighter colors) were identified. Structural non-identifiability was not observed.</p

Bartlett correction results of pp-plot classifications at the 95% confidence level.

Heatmap colors according to pp-plot classification for each Bartlett correction factor as indicated on the y-axis. Black tiles show optimal Bartlett correction factor closest to 1 of the individual parameter in each column. Since columns are ordered by this correction factor, the x-axis corresponds to the approximative conservativeness ratio aCR. White line and black bold numbers indicate the uncorrected outcome for C = 1, whereas green line and numbers show overall optimal Bartlett correction for a CR ≈ 95%. Deviations from 0.95 on x-axis originate from binning issues. (A) Results for all 768 parameters, (B) same results grouped by parameter type and (C) identifiability status. (D) Outcome for individual models reveal that a comprehensive overall optimal correction factor is difficult to determine. (E) Overall optimal Bartlett correction factors C* from exhaustive search with resulting thresholds for the likelihood ratio statistic.</p