1 Level 1 classes selection

In this analysis, within each time slot of the day carbohydrates intake was defined as:
- not eating;
- eating and carbohydrates contributed less than 50% of energy;
- eating and carbohydrates contributed higher or equal to 50% of energy.
Time slots are defined as:
- Breakfast: 6 am to 9 am;
- Morning snack: 9 am to 12 noon;
- Lunch: 12 noon to 2 pm;
- Afternoon snack: 2 pm to 5 pm;
- Dinner: 5 pm to 8 pm;
- Before bedtime snack: 8 pm to 10 pm;
- Midnight food: 10pm to 6 am;

Level 1 class selection. (All data, n = 6155, 24483 data points)
N of classes	N of free parameters	log-likelihood	AIC	BIC	aBIC	Entropy	Lo-Mendel-Rubin LRT
1	14	-173793.306	347614.612	347728.092	347683.601	–	–
2	29	-172669.771	345397.542	345632.608	345540.447	0.31	< 0.0001
3	44	-172039.204	344166.407	344523.06	344383.229	0.392	0.0001
4	59	-171633.941	343385.883	343864.121	343676.621	0.51	< 0.0001
5	74	-171377.292	342902.585	343502.409	343267.239	0.481	< 0.0001
6	89	-171237.476	342652.953	343374.363	343091.524	0.497	0.0577
Note:
Abbreviation: N, number; AIC, Akaike information criterion; BIC, Bayesian information criterion; aBIC, adjusted BIC; Entropy, a pseudo-r-squared index; Lo-Mendel-Rubin LRT, likelihood ratio test comparing q classes models with q-1 classes models.

1.1 Fit information for each model (combination of level 1 and level 2 classes)

Models Specification
	Number of level 1 classes
Model	1 class	2 classes	3 classes	4 classes	5 classes	6 classes
Fixed effects model
No. of free parameters	14	29	44	59	74	89
Log-likelihood	-173793.306	-172669.771	-172039.204	-171633.941	-171377.292	-171237.476
BIC	347728.092	345632.608	344523.06	343864.121	343502.409	343374.363
Lo-Mendell-Rubun LRT	–	< 0.0001	1e-04	< 0.0001	< 0.0001	0.0577
Entropy	1	0.31	0.392	0.51	0.481	0.497
Random effects model
2 between classes
No. of free parameters		59	89	119
Log-likelihood		-169331.132	-168700.96	-168366.193
BIC		339258.502	338301.338	337934.968
Entropy		0.581	0.569	0.555
3 between classes
No. of free parameters		89	134	179
Log-likelihood		-166936.279	-166348.815	-166062.761
BIC		334771.968	334051.799	333934.448
Entropy		0.677	0.63	0.644
4 between classes
No. of free parameters		119	179
Log-likelihood		-165441.731	-164845.696
BIC		332086.045	331500.318
Entropy		0.729	0.659
Note:
Abbreviation: No, number; BIC, Bayesian information criterion; Entropy, a pseudo-r-squared index; Lo-Mendel-Rubin LRT, likelihood ratio test comparing q classes models with q-1 classes models.