. 2019 May 10;1(2):240–258. doi: 10.3390/clockssleep1020021

Table 2.

Statistical outputs of the GLMMs seeking for associations between alertness and attention measures and pupil size measures.

		Steady-State Pupil Size	Circadian Phase	Steady-State Pupil Size x Circadian Phase
Dependent variables	Subjective sleepiness	F_1,199.7 = 0.03 p = 0.87	F_12,158 = 2.65 p = 0.03 *R²_β = 0.17**	F_12,157 = 1.23 p = 0.27
	PVT mean reaction times	F_1,178.8 = 5.69 p = 0.02 *R²_β = 0.03**	F_12,165.1 = 0.98 p = 0.47	F_12,165.1 = 0.65 p = 0.8
	Relative theta power	F_1,147.4 = 1.19 p = 0.28	F_12,143.7 = 1.31 p = 0.22	F_12,143 = 1.00 p = 0.46
	Fatigue	F_1,196.4 = 0.03 p = 0.86	F_12,165.2 = 2.93 p = 0.001 *R²_β = 0.18**	F_12,164.8 = 1.14 p = 0.33
		Pupil size variability	Circadian phase	Pupil size variability x circadian phase
Dependent variables	Subjective sleepiness	F_1,187.6 = 2.75 p = 0.099	F_{12, 159.1} = 3.58 p < 0.001 *R²_β = 0.21**	F_12,157.1 = 0.99 p = 0.46
	PVT mean reaction times	F_1,10,65 = 0.2 p = 0.66	F_12,163.1 = 0.9 p = 0.55	F_12,150.3 = 1.64 p = 0.085
	Relative theta power	F_1,173.9 = 1.22 p = 0.27	F_12,144.4 = 1.80 p = 0.059	F_12,142 = 1.21 p = 0.29
	Fatigue	F_1,183.7 = 1.61 p = 0.21	F_12,167.6 = 8.49 p < 0.0001 *R²_β = 0.38**	F_12,166.1 = 2.54 p = 0.004 *R²_β = 0.16**

Each dependent variable was included in a separate GLMM including pupil measure, circadian phase, and their interaction. Degrees of freedom were computed following Kenward-Roger method. Significant linear links are in bold and statistical trends (p < 0.1) are in italic. R²_β* represents semi-partial R² as proposed by [41] (see methods). GLMMs were set according to dependent variables distribution.