I conducted an experiment where subjects made two decisions. the first (Pre) decision was unaffected by any treatment, whereas subjects made their second decision (Post) after being randomly allocated to a treatment condition. I define
D=Post−Pre
I am primarily interested in how Pre predicts D differently based on treatment assignment, i.e. the interaction.
To answer this question I estimate the following regression model
(1) D_i=b0+b1Treat_i+b2Pre_i+b3Treat_i∗Pre_i+e_i
Now, the variables Pre and Post are monetary donation amounts. In the experiment, donations had lower and upper limits of 0 and 100, both in the pre- and post-test.
Consequently, the lower and upper limits for the variable D
depend on the Pre donations.
For example, if a subject donated Pre=25, then −25
Without censoring, model (1) and model (2) are equivalent, with b1 from model (1) equal to b1 - 1 from model (2). I haven't thought too closely about this, but I don't think censoring changes much about that, except for the fact that it's more difficult to get the censoring right in model (1).
That's why I would fit model (2), and then do e.g. instead of a hypothesis test for b1 = 0 in model (1), a test for b1 = 1 in model (2), which should give the same result.
So I would not care about the answers to questions (a) and (b), and say yes to (c).
Hendrik,
I would not be too concerned with the "censoring". I would not refer to this as "censoring", but as floor and ceiling effects. The impact will certainly depend on the proportion of observations that are censored. I would not use a regression model, as you have, but would use ANCOVA with Treatment and Baseline and the interaction of Treatment and Baseline included in the model This will provide a direct between-treatment comparison and the interaction will provide the information regarding the "slope" that you are considering in your proposed models.
As Stefan noted, the inference will be the same, whether Post or Difference are analyzed. However, the estimates from ANCOVA will only pertain to the variable that is analyzed. My preference is to analyze Difference, since the model-based estimates are usually of greater interest. The summary statistics should also be provided for Post.
David
Thank you both for your replies.
David: I'm not really seeing your point for an ANCOVA. Since we have a categorical-continuous interaction, the interaction-coefficients tell us the difference of the slope in the respective category vs. the slope of the base-category, including its significance.
I am not an expert on AN(C)OVA, but I was under the impression that the interaction term there would test the omnibus hypothesis of there being no interaction, but not really which exactly. For those, you would have to run ex-post tests, whereas in the regression I can just set my baseline category to the one I am interested in and do the other tests also with ex-post F-tests.
I might be wrong. In that case feel free to correct me.
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