Table 1
Fit quality evaluation criteria for 16 competing model functions.
| Model no. | Fitting function | p | A | B | C | χ2 | d.o.f. |  |
AIC | ΔAIC | BIC | ΔBIC |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | A+Bt | 2 | 2.535 × 101 | –1.060 × 10−2 | 10.494 | 18 | 0.58 | –8.19 | 3.50 | –6.91 | 4.01 | |
| 2 | A+Bt2 | 2 | 1.517 × 101 | –2.755 × 10−6 | 10.555 | 18 | 0.59 | –8.08 | 3.62 | –6.79 | 4.13 | |
| 3 | At+Bt2 | 2 | 1.579 × 10−2 | –6.858 × 10−6 | 10.658 | 18 | 0.59 | –7.88 | 3.81 | –6.60 | 4.33 | |
| 4 | A+Bt+Ct2 | 3 | 1.101 × 102 | –9.900 × 10−2 | 2.301 × 10−5 | 10.254 | 17 | 0.60 | –5.86 | 5.84 | –4.37 | 6.55 |
| 5 | A exp(Bt) | 2 | 3.065 × 102 | –2.148 × 10−3 | 10.280 | 18 | 0.57 | –8.61 | 3.09 | –7.32 | 3.60 | |
| 6 | A exp(Bt)+C | 3 | –2.784 × 101 | 2.399 × 10−4 | 4.913 × 101 | 10.520 | 17 | 0.62 | –5.35 | 6.35 | –3.86 | 7.06 |
| 7 | A exp[B/(t+C)] | 3 | 1.184 × 102 | –2.148 × 10−3 | –4.427 × 102 | 10.280 | 17 | 0.60 | –5.81 | 5.88 | –4.32 | 6.60 |
| 8 | A exp(B/t) | 2 | 8.106 × 10−2 | 7.888 × 103 | 10.171 | 18 | 0.57 | –8.82 | 2.88 | –7.53 | 3.39 | |
| 9 | A exp(B/t)+C | 3 | –1.778 × 102 | –2.508 × 102 | 1.610 × 102 | 10.387 | 17 | 0.61 | –5.60 | 6.09 | –4.12 | 6.81 |
| 10 | A exp[B/(t+C)] | 3 | 2.836 × 100 | 1.482 × 102 | –1.635 × 103 | 9.732 | 17 | 0.57 | –6.91 | 4.79 | –5.42 | 5.50 |
| 11 | t/(A+t) | 1 | –1.526 × 103 | 9.973 | 19 | 0.52 | –11.70 | 0.00 | –10.92 | 0.00 | ||
| 12 | At/(B+t) | 2 | 9.733 × 10−1 | –1.537 × 103 | 9.941 | 18 | 0.55 | –9.28 | 2.42 | –7.99 | 2.93 | |
| 13 | A+Bt/(C+t) | 3 | 2.513 × 100 | 2.690 × 10−1 | –1.691 × 103 | 9.698 | 17 | 0.57 | –6.98 | 4.72 | –5.49 | 5.43 |
| 14 | A+B ln(t) | 2 | 1.590 × 102 | –2.037 × 101 | 10.435 | 18 | 0.58 | –8.30 | 3.39 | –7.02 | 3.90 | |
| 15 | (A+Bt) ln(t) | 2 | 3.440 × 100 | –1.447 × 10−3 | 10.513 | 18 | 0.58 | –8.16 | 3.54 | –6.87 | 4.05 | |
| 16 | (A+Bt+Ct2) ln(t) | 3 | 1.496 × 101 | –1.345 × 10−2 | 3.125 × 10−6 | 10.262 | 17 | 0.60 | –5.85 | 5.85 | –4.36 | 6.56 |
Notes. A, B, and C are the values of the optimized parameters for each model. The quoted number of degrees of freedom (d.o.f.) is equal to the number of data points, n, minus the number of independent fitting parameters, p. ΔAIC (ΔBIC) is the pairwise difference with respect to the value of the AIC (BIC) of the most likely model. (see text for details).
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