Table 1.
Goodness of fit and generalizability of models differing in complexity
| Model | M1 (true model) | M2 | M3 |
|---|---|---|---|
| Goodness of fit | 4.28 (0%) | 3.84 (25%) | 3.67 (75%) |
| Generalizability | 5.37 (59%) | 5.62 (23%) | 5.78 (18%) |
Mean squared error (MSE) of the fit of each model to the data and the percentage of samples in which the particular model fitted the data best (in parentheses). The three models were as follows: M1: y = θ0 + θ1x + error, M2: y = θ0 + θ1xθ2 + θ3exp(x) + error, and M3: y = θ0 + θ1x + θ2x2 + θ3x3 + error. The error was normally distributed with a mean of zero and a standard deviation of 5. One thousand pairs of samples were generated from the model M1 using (θ0 = 1, θ1 = 2) on the same 10 points for x, which ranged from 0.1 to 4.6 in increments of 0.5.