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. Author manuscript; available in PMC: 2020 Sep 9.

Published in final edited form as: Psychol Methods. 2019 Jul 18;25(1):1–29. doi: 10.1037/met0000219

Table 3:

Expected Outcome for Each Time Point for Each Embedded Adaptive Intervention (AI) Based on the Piecewise Linear Regression Model in (3)

Embedded AI	Month	Expected Outcome
AI #1: Later choice ( $A_{1} = - 1$ , $A_{2} = 1$ )	1	$β_{0}$
	2	$(β_{S_{1}} - β_{S_{1} A_{1}})$
	3	$(β_{S_{1}} - β_{S_{1} A_{1}}) + (β_{S_{2}} - β_{S_{2} A_{1}} + β_{S_{2} A_{2}} - β_{S_{2} A_{1} A_{2}})$
AI #2: Choice throughout ( $A_{1} = 1$ , $A_{2} = 1$ )	1	$β_{0}$
	2	$(β_{S_{1}} + β_{S_{1} A_{1}})$
	3	$(β_{S_{1}} + β_{S_{1} A_{1}}) + (β_{S_{2}} + β_{S_{2} A_{1}} + β_{S_{2} A_{2}} + β_{S_{2} A_{1} A_{2}})$
AI #3: No Choice ( $A_{1} = - 1$ , $A_{2} = - 1$ )	1	$β_{0}$
	2	$(β_{S_{1}} - β_{S_{1} A_{1}})$
	3	$(β_{S_{1}} - β_{S_{1} A_{1}}) + (β_{S_{2}} - β_{S_{2} A_{1}} - β_{S_{2} A_{2}} + β_{S_{2} A_{1} A_{2}})$
AI #4: Initial Choice ( $A_{1} = 1$ , $A_{2} = - 1$ )	1	$β_{0}$
	2	$(β_{S_{1}} + β_{S_{1} A_{1}})$
	3	$(β_{S_{1}} + β_{S_{1} A_{1}}) + (β_{S_{2}} + β_{S_{2} A_{1}} - β_{S_{2} A_{2}} - β_{S_{2} A_{1} A_{2}})$