Table 2.

Model selection for the random effects portion of the smooth model fit to pre-challenge data.

Model number	Random effects	Extra df	nlL	ΔAIC
1	Study, challenge date, subject	3	6,720.09	2.00
2	Study, subject	2	6,720.09	0.00
3	Challenge date, subject	2	6,721.05	1.91
4	Subject	1	6,723.44	4.70

Extra degrees of freedom (df) refers to the number of random effects. Negative log-likelihood (nlL) reflects goodness of fit with smaller values indicating better fit. AIC differences (ΔAIC) indicate the best-supported model having ΔAIC = 0.00, models with ΔAIC < 2.00 considered to have good support, and those with ΔAIC ≥ 2.00 considered to have poor support (Burnham and Anderson, 2003).