Table 3:

Scientific questions about distal effects and model parameters for a hybrid factorial-MRT

Scientific question about distal effects		Type	Model (1) parameters
A	Is it beneficial (in terms of month 6 weight loss) to add (or not to add) coaching at the beginning of the program?	Main effect of factor assigned at program entry, averaging the other factor assigned at program entry and the time-varying factor	2θ1
B	Is it beneficial (in terms of month 6 weight loss) to add (or not to add) meal replacement at the beginning of the program?	Main effect of factor assigned at program entry, averaging the other factor assigned at program entry and the time-varying factor	2θ2
C	Is adding coaching more beneficial (in terms of month 6 weight loss) with or without adding meal at the beginning of the program?	Two-way interaction between two factors that were assigned at program entry, averaging over the time-varying factor	2θ3
D	Does the effect of (i.e., difference between) adding (vs. not adding) coaching at the beginning of the program vary by the rate of prompt delivery?	Two-way interaction between a factor assigned at program entry and the rate of the time-varying factor, averaging over the other factor assigned at program entry.	${\theta }_5(\stackrel{-}{a}-{\stackrel{-}{a}}^{\prime })$
E	Does the effect of (i.e., difference between) adding (vs. not adding) meal replacement at the beginning of the program vary by the rate of prompt delivery?	Two-way interaction between a factor assigned at program entry and the rate of the time-varying factor, averaging over the other factor assigned at program entry.	${\theta }_6(\stackrel{-}{a}-{\stackrel{-}{a}}^{\prime })$
F	Does the interaction between Add Coaching and Add Meal varies by the rate of prompt delivery?	Three-way interaction between factors assigned at program entry and the time-varying factor	${\theta }_7(\stackrel{-}{a}-{\stackrel{-}{a}}^{\prime })$