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Please assume that I have two metric independent variables (e.g., two blood parameters), and a dependent variable (e.g., a disease). On the DV, 0 represents the absence from the disease, 1 represents a weak occurrence ... 10 (max.) represents a very strong occurrence (please ignore the usefulness of such an assessment). The supposed problem comes in because in my sample (N = 80), only 25% score > 0 on the DV (that is, 20 participants).

Anyway, I regressed (OLS and Tobit) the DV on IV1, IV2, and the interaction of IV1 and IV2. The interaction turns out to be significant, no main effects occured. Because of the low baseline (25% > 0 on the DV), is this procedure considered problematically? Is my baseline too low? Are there not enough participants having the disease?

Let us assume, ideally, that all of the 20 participants score between 8-10 (DV) and all 20 have a special pattern of the IVs, e.g., low IV1 and low IV2, so this group, simplified, is compared to # low IV1 and high IV2; # low IV1 and low IV2; # high IV1 and high IV2. So from my understanding, a group of 20 is compared against, ideally, 3 groups of 20 participants, which is quite common in medical research. So do you think there are problems? And any literature suggestions that I am “allowed” (or not allowed) to analyze the data the way I do?

Well, because I'm not an expert I hope that you can turn on the lights for me … Thanks!

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    $\begingroup$ There are several questions with discussions on this site about including interactions in a model when main effects are not found to be statistically significant. You will find arguments on both sides of the issue. I think there are situations where including just an interaction term might make sense. $\endgroup$
    – Michael R. Chernick
    Commented Oct 1, 2012 at 10:40

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Given this distribution of the dependent variable, the assumptions of OLS (normal residuals) are likely to be violated (although it's worth checking). More likely, you need ordinal logistic regression, but that can be problematic with such small samples in some categories: if there are 20 in 8, 9 and 10 combined, then there must be one (at least) with 6 or fewer. This can lead to overfitting.

Although I am usually very against dichotomizing data, here you may have to do so, and then run a regular logistic regression on disease (present vs. absent).

Then you have groups of 80 and 20, and having 2 variables plus an interaction is pushing it a little but you should be ok

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  • $\begingroup$ Did you want to address the issue of a significant interaction with no main effect? I thought that was one of the key issue to the OP regarding his analysis. $\endgroup$
    – Michael R. Chernick
    Commented Oct 2, 2012 at 17:02
  • $\begingroup$ Well, as you pointed out, that's been discussed a lot here. I thought the main point was the small sample size. Perhaps @spfatthe can let us know. $\endgroup$
    – Peter Flom
    Commented Oct 2, 2012 at 20:38

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