Participants complete a survey at all 3 waves. At Survey 1 (S1) I collected a variety of baseline measures (Baseline Var A, Baseline Var B, etc.). At all 3 surveys (S1, S2, S3) I give the same measures that are thought to change across time (Repeated Var X, Repeated Var Y, etc.) – i.e. Repeated Var X is given 3 times, Repeated Var Y is given 3 times, etc.

In between S1 and S2 (approx. 48 hours), a "treatment" (Tx) is applied to all participants. In between S2 and S3 (approx. 48 hours), the Tx is removed and participants go back to life as usual.

Written another way:

- S1 – Baseline Var A, Baseline Var B, Repeated Var X, Repeated Var Y

- Tx (48 hrs)

- S2 – Repeated Var X, Repeated Var Y

- Tx Removed (48 hrs)

- S3 – Repeated Var X, Repeated Var Y

I want to ask the following kinds of questions:

1. Does Repeated Var X (or Repeated Var Y) change across the course of the study in response to the Tx?

2. HOW does Repeated Var X change across the course of the study in response to treatment? e.g. Does it increase in response to Tx and then return to baseline? Or is there a kind of "rebound effect" once Tx is removed? etc.

3. Does Baseline Var A/B predict how Repeated Var X/Y changes across the study?

4. Does the interaction of Baseline Var A and Baseline Var B predict how Repeated Var X/Y changes across the study?

5. Does Wave 1 Repeated Var X/Y predict Wave 2 Repeated Var X/Y?

6. Does Wave 2 Repeated Var X/Y predict Wave 3 Repeated Var X/Y?

7. Does Wave 1 Repeated Var X/Y predict Wave 3 Repeated Var X/Y?

8. Does the interaction of Wave 1/2 Repeated Var X and Repeated Var Y predict Wave 2/3 Repeated Var X/Y?

9. Can Baseline Var A/B and/or Repeated Var A/B predict who adheres to the Tx, or how strongly they adhere to Tx?

10. Does the interaction of Baseline Var A/B and Repeated Var A/B predict who adheres to Tx, or how strongly they adhered to Tx?

11. I want to control for a variety of covariates when asking the above questions.

To be more specific:

--

**Tx**= participants are asked to stop smoking cigarettes for the 2 days b/w S1 and S2, then they can return to smoking as usual b/w S2 and S3

--

**Repeated Vars**= measure of wellness; number of cigarettes smoked (I assume people will smoke when they're not supposed to, so I am curious to see who actually stops)

--

**Baseline Vars**= smoking motives; quit motives; level of tobacco dependence; etc.

-- Basically, I want to know:

Will stopping smoking affects people's wellbeing?

Will changes in wellbeing trigger changes in smoking behavior (e.g. if wellbeing goes does when the person stops smoking, when the person can return to smoking will they smoke more than usual in an attempt to reinstate wellbeing)?

Is this relation between wellbeing and smoking affected by one's smoking motives (i.e. will I only find that changes in smoking behavior affects wellbeing if someone endorses smoking motives aimed at achieving wellbeing)?

Can smoking motives (or wellness, etc.) predict who will actually stop smoking during the Tx phase, how much someone reduces their smoking during the Tx phase, or how much they smoke when they can return to smoking?

Do smoking motives interact with quit motives in predicting the above outcomes? Etc.

**MY QUESTION TO THIS FORUM**: I am having trouble identifying exactly what kind of statistical approach I should use to answer the above questions…I have read many things that are close to what I need, but are not exactly what I need. I have also gotten a variety of answers – Path Analysis, Multilevel Modeling, even T-tests, etc. Any insight on what statistical approach to use would be appreciated. Or I would even appreciate it if you could give me a better way of describing my study so I could be more effective when searching for the type of analysis to use...its like an ABA Design, but with 100 participants, what do you call that?

I primarily use SPSS and SAS to analyze the data. SPSS is preferred.

No answers involving Bayesian statistics please.