Table 2.

Model selection for PRLT performance in the two-groups sample

Model	Fixed factors	df	AIC	χ2	p
Sat. (0.a)	Group, Phase, Log-trial, 2-way interactions, 3-way interaction	19	10,422
1	Saturated minus 3-way interaction	16	10,419	2.418	0.490 (1 ≥ 0.a)
2.1	Model 1 minus Group × Log-trial	15	10,418	1.418	0.227 (2.1 ≥ 1)
2.2b	Model 1 minus Phase × Log-trial	13	10,432	18.978	< 0.001 (1 > 2.2)
2.3	Model 1 minus Phase × Group	13	10,418	4.973	0.174 (2.3 ≥ 1)
2.4	Model 1 minus Group × Log-trial and Phase × Group	12	10,417
3a	Model 2.4 minus Group	11	10,416	0.592	0.459 (3 ≥ 2.4)

Significant p values are in italics

^aBest fitting model

^bAlmost singular fit (given the risk of overfitting, parameters will be estimated both for Model 1 and Model 3) (Although singular models are statistically well defined, singular fits may correspond to overfitted models with low power, and inferential procedures such as likelihood ratio tests may be inappropriate. In our case, singularity is due to the inclusion of Log-trial as a random slope in the model. Although it is theoretically sensible to assume that there are random individual differences in learning rates across participants, random slopes are not necessary to capture statistical dependency between repeated measures and thus to properly estimate within-participant effects. In view of that, and for the sake of consistency, alternative analyses without random slopes in the models are provided in the Additional file)

Sat Saturated