Table 3.
LMMs using maximum likelihood on mean group contributions depending on the information shown in the first game (3 levels) and the restart treatment (4 levels) (N = 20 groups per restart treatment, 10 or 5 for the first game information level)
| Term \ Model | M1 P-value | M2*P-value | M3 P-value | M4 P-value |
|---|---|---|---|---|
| Stage† | <0.001 | <0.001 | <0.001 | <0.001 |
| Restart treatment‡ | 0.023 | 0.023 | 0.020 | 0.045 |
| First game info.§ | / | / | 0.217 | 0.210 |
| Stage*Restart treatment | / | <0.001 | <0.001 | <0.001 |
| Stage*First game info. | / | / | / | 0.094 |
| Restart treatment* First game info. | / | / | / | 0.952 |
| Stage*Restart treatment* First game info. | / | / | / | 0.108 |
| Number of observations¶ | 160 | 160 | 160 | 160 |
| Number of independent units# | 80 | 80 | 80 | 80 |
| Number of parameters | 7 | 10 | 12 | 26 |
| AIC | 1,372 | 1,357 | 1,358 | 1,370 |
| BIC | 1,393 | 1,388 | 1,395 | 1,450 |
| Significance of more complicated model|| | NA | <0.001 | 0.217 | 0.317 |
*This is the optimal model.
†Stage specifies the final round of the first game or the first round of the restarted game.
‡Specifies Classic Replay, Blind Replay, Computer Replay, or Computer Rewind
§Specifies Payoffs only, Payoffs plus group average contribution, or Payoffs plus individual contributions.
¶Each group contributed two data points, the end of the first game and the start of the restarted game.
#Models controls for group identity as a random effect.
||Model comparisons performed with a likelihood ratio test.