Table 2.

Comparing linear and cusp models using information criteria.

Models tested	Loglikelihood	Par	AIC	AICc	BIC
1. Linear	−20651.560	6	41315.11	41315.12	41360.87
2. Logistic	−20579.590	7	41173.18	41173.18	41226.56
3. Quadratic	−20629.389	8	41274.78	41310.37	41335.79
4. Cusp	−19784.772	9	39587.55	39587.56	39656.19

Par, number of freely estimated parameters; AIC, akaike criterion; AICc, corrected AIC; BIC, Bayesian information criterion. Preference is given to the BIC. Its sample-adjusted variant is not included because of the large sample size of the PISA 2018 cohort.