Table 2 LMM analysis for melatonin AUC and melatonin onset (covariate model)

Predictors	Estimates		CI (95%)		Std. error		df		t value		p
	Melatonin AUC	Melatonin onset time	Melatonin AUC	Melatonin onset time	Melatonin AUC	Melatonin onset time	Melatonin AUC	Melatonin onset time	Melatonin AUC	Melatonin onset time	Melatonin AUC	Melatonin onset time
Intercept	179.05	18.45	21.45, 336.88	15.57, 21.33	88.92	1.63	15	15	-	-	-	-
Condition [moderate]	−7.37	0.30	−16.24, 1.43	−0.01, 0.61	4.56	0.16	37	37	−1.62	1.88	0.114	0.068
Condition [bright]	−11.29	0.35	−20.34, −2.49	0.04, 0.67	4.60	0.16	37	37	−2.45	2.17	0.019	0.037
Bright light history [TAT 1000 lx]	5.65	-0.16	1.19, 9.37	−0.28, −0.02	2.07	0.07	43	52	2.73	−2.41	0.009	0.020
*Chronotype [MSFsc]	-30.62	0.70	−66.81, 5.56	0.04, 1.35	20.41	0.37	14	14	−1.50	1.88	0.155	0.081
*Pubertal stage [late pubertal]	38.75	-0.35	−29.26, 106.71	−1.58, 0.88	38.34	0.70	15	14	1.01	−0.50	0.329	0.624
*Pubertal Stage [midpubertal]	-21.37	0.06	−98.36, 55.61	−1.34, 1.45	43.41	0.79	14	14	−0.49	0.07	0.630	0.945
*Pubertal Stage [early pubertal]	20.80	-1.07	−115.71, 157.17	−3.55, 1.41	76.94	1.41	15	14	0.27	−0.76	0.791	0.459
Random effects & Model fit criteria			σ²	τ_{00 subjects}	ICC	N _subjects	Observa-tions	Marginal R² / Conditional R²		AIC
Evening melatonin AUC			207.54	4623.46	0.96	20	60	0.221 / 0.967		530.364
Melatonin onset time			0.26	1.47	0.85	20	60	0.244 / 0.888		162.679

Summary report of linear mixed model (LMM) analyses for melatonin AUC (primary outcome) and melatonin onset (post-hoc analysis), applying the model with theoretically relevant covariates (covariate model). Estimates of the AEE light intervention conditions are given relative to the dim light condition. Estimates of pubertal stage are given relative to 'post pubertal stage'. Please note, that the intercept represents the expected value when all covariates are set to their reference or zero levels. Instead, the intercept of the sparse model (see Table 3) gives the mean melatonin AUC and onset after the 'dim' AEE light condition. P-Values of (p < 0.05) were considered as significant (in bold). The covariates marked with an asterisk (*) were used as passive stratification factors to control for additional variance. Accordingly, these LMM estimates were not interpreted to avoid a 'Table 2 fallacy'¹⁷¹.
Abbreviations: AEE afternoon to early evening, AIC Akaike Information Criterion, AUC area under the curve, CI confidence interval (95%), df degrees of freedom, ICC Intraclass Correlation Coefficient, MSF_SC midpoint of sleep on free days corrected for oversleep, N_subjects number of subjects in the analysis, σ² variance of the residuals of the model, τ_{00 subjects} variance in the random intercepts at the subject level, Std. error standard error of the estimates, TAT 1000 lx time above threshold ( > 1000 lx illuminance, wrist-recorded).

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