Table 3.

Univariate model-fitting results.

Measure	Model	− 2LL	df	(Δ − 2LL)	AIC	(Δ − AIC)	BIC	p-Value	p
Number Sense accuracy	Saturated	− 12,649.05	4505		3639.05		− 12,009.57	–	10
	ACE	− 12,658.33	4511	− 9.28	3636.33	2.72	− 12,029.34	.10	4
	AE	− 12,658.58	4512	− .25	3634.58	1.75	− 12,033.29	.60	3
	E	− 12,791.82	4513	− 133.49	3765.82	− 129.49	− 11,970.74	.00	1
Weber Fraction	Saturated	− 11,170.54	4415		2340.54		− 12,382.55	–	10
	ACE	− 11,185.37	4421	− 14.83	2343.37	− 2.83	− 12,399.55	.02	4
	AE	− 11,185.37	4422	.00	2341.37	2	− 12,403.62	1.0	3
	E	− 11,282.29	4423	− 96.92	2436.29	− 92.92	− 12,359.23	.00	1

− 2LL = minus log-likelihood; df = degrees of freedom; Δ − 2LL = difference in likelihood; AIC = Akaike's Information Criterion; Δ − AIC = difference in AIC, this is calculated between the Saturated and full ACE model, and between the full ACE model and the AE and E nested models. BIC = Bayesian Information Criterion; p-value = associated with the differences in likelihood ratio between the Saturated and the full ACE model, and between the full ACE model and the AE and E nested models. p = number of parameters estimated. The p-value shows no significant differences in likelihood between the Saturated and the full ACE model for accuracy in the Number Sense Task scores. AIC shows good fit of the ACE model compared to the Saturated model in Number Sense scores (lower AIC of full ACE). The same parameter shows the better fit of the AE model. The goodness of fit for the Weber Fraction model is demonstrated to a lesser extent by the AIC and p-value. The BIC however shows a good fit of the full ACE model to the observed data and, similarly to the accuracy scores, confirms the best fit of the AE model for the Weber Fraction variable. The bold characters indicate the best fitting model.