Table 1.
Model fits to subject data for experiment 1
| Model | kj | kc | ko | dj, rad−2 | dc, m−2 | do, rad−2 | dof | BIC | BIC Improvement over No Generalization |
|---|---|---|---|---|---|---|---|---|---|
| No-decay models | |||||||||
| Joint | 1 | — | — | — | — | — | 0 | −212.0 | 63.4 |
| Cartesian | — | 1 | — | — | — | — | 0 | 26.5 | −175.2 |
| Object | — | — | 1 | — | — | — | 0 | −65.6 | −83.1 |
| C+O | — | 0.29 | 0.71 | — | — | — | 1 | −92.5 | −56.2 |
| J+O | 0.71 | — | 0.29 | — | — | — | 1 | −280.9 | 132.2 |
| J+C | 0.82 | 0.18 | — | — | — | — | 1 | −248.5 | 99.8 |
| J+O+C | 0.66 | 0.10 | 0.24 | — | — | — | 2 | −294.3 | 145.6 |
| Decay models | |||||||||
| Joint | 1 | — | — | 0.93 | — | — | 1 | −302.7 | 154.0 |
| Cartesian | — | 1 | — | — | 365.88 | — | 1 | −220.2 | 71.5 |
| Object | — | — | 1 | — | — | 3.01 | 1 | −101.0 | −47.7 |
| C+O | — | 1 | 0 | — | 365.93 | N/A | 3 | −210.6 | 61.9 |
| J+O | 0.88 | — | 0.12 | 0.71 | — | 0 | 3 | −302.3 | 153.6 |
| J+C | 1 | 0 | — | 0.93 | N/A | — | 3 | −293.0 | 144.3 |
| J+O+C | 0.88 | 0 | 0.12 | 0.71 | N/A | 0 | 5 | −292.6 | 143.9 |
The k values are the mixture parameters for the individual coordinate system predictions, which are constrained to sum to 1. The d values are the decay parameters associated with distance from the training configuration in the 3 different coordinate systems (with the units of distance in radians for angles and meters for Cartesian distance). The final 3 columns are the degrees of freedom (dof) of the model, the Bayesian information criterion (BIC), and the BIC improvement compared with the no-generalization model. Dashes are used to indicate parameters that are not fit and are set to zero for the particular model. N/A refers to fitted parameters that do not affect the model predictions, as the corresponding mixing parameter has a fitted value of zero.