Table 4.

Results of models with and without cross-level interactions predicting number of daily steps.

Parameter	Model 1a			Model 2b
	Estimate (SE)	P value	Estimate (SE)		P value
Intercept	14,003.0 (1233.7)	N/Ac	14,063.9 (1240.4)		N/A
BMId	−178.0 (38.9)	<.001 e	−177.1 (39.02)		<.001
Age	35.9 (18.9)	.06	36.0 (18.92)		.06
Timef	−1261.9 (308.0)	<.001	−1259.60 (307.95)		<.001
Timeg	332.5 (81.4)	<.001	332.4 (81.36)		<.001
Timeh	−21.2 (6.1)	<.001	−21.2 (6.08)		<.001
Gamification	856.9 (211.4)	<.001	541.9 (241.7)		.03
Nudging	−690.9 (326.6)	.04	−751.5 (359.0)		.04
Follow-up	−1475.3 (406.7)	<.001	−1520.2 (441.2)		<.001
Intervention	−16.0 (374.8)	.97	−222.3 (416.4)		.59
Intervention × gamification	N/A	N/A	634.0 (244.8)		.005
Intervention × nudging	N/A	N/A	98.2 (325.5)		.76
Intervention × follow-up	N/A	N/A	53.49 (381.7)		.89

^aModel 1: γ_ij=β0_j + β1BMI_j + β2Age_j + β3Time_ij + β4Time_ij² + β5Time_ij³ + β6Gamification_ij + β7Nudging_ij + β8Follow-up_ij + β9Intervention_j + ε_ij+ μ_ij. Model 1 (Akaike Information Criteria: 269682) refers to the model without cross-level interactions between the intervention and study phases.

^bModel 2: γ_ij=β0_j + β1BMI_j + β2Age_j + β3Time_ij + β4Time_ij² + β5Time_ij³ + β6Gamification_ij + β7Nudging_ij + β8Follow-up_ij + β9Intervention_j + β10Intervention_jGamification_ij + β11Intervention_jNudging_ij + β12Intervention_jFollow-up_ij + ε_ij + μ_0j+ μ_1j Gamification_ij + μ_2j Nudging_ij + μ_3j Follow-up_ij. Model 2 (Akaike Information Criteria: 269679) refers to the model with cross-level interactions between the intervention and study phases. Model 2 significantly improved the model fit (χ²₃=8.6; P=.04).

^cN/A: not applicable.

^dCalculated from self-reported height and weight.

^eItalics indicates statistical significance (P<.05).

^fTime is rescaled to represent 2-week intervals.

^gRepresents the quadratic function of time.

^hRepresents the cubic function of time.