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I ran a psychological experiment involving two conditions. An independent variable - made up of numeric values - was present in one condition but not in the other. Accordingly, in one condition the variable in point provided relevant information, and ranged between 0 and 20. In the other condition participants were simply not provided with such information.

Binding the data together, in the condition where participants received no information, I coded the values of the 'information' variable as NAs. However, when I run my (probit) model in R, setting na.action = na.pass causes the model to fail.

In principle, the NAs in my data are not missing values but, in accordance with the experimental design, reflect the absence of information within one of the conditions.

Therefore, it seems to me that multivariate imputation - as could be implemented with mice or other packages - is not the correct course of action. In fact, if I wanted, I could simply retrive the values of interest, but including them in the data would be improper because, as already mentioned, participants were kept from knowing the values thereof.

I have been told that, to cope with this problem, even though 0 is a possible value in the 'information condition', I can code the values of the 'no information condition' as 0 as well. The argument is that, if the value is 0, the estimator doesn't change and the effect is caught by the estimator of the dummy variable for the treatment of interest, which shows a 1 where the NAs have been before.

I am resorting to the expertise of this community to have a clarification and see whether the argument in point is robust or not. Also, any reference able to shed light on this matter would be highly appreciated.

Thank you so much for your help!

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    $\begingroup$ I would model this as an interaction. You have condition, which is 0, 1, and you value of the variable, which is 0-20 in one condition, and 0 in the other. (Although I'll admit I'm having trouble understanding the design, or the hypothesis being tested.) $\endgroup$
    – Jeremy Miles
    Commented Jan 30, 2020 at 17:24
  • $\begingroup$ I think I see what you mean, I will definitely control for the interaction. Thank you very much! By the way, you can think about it as a design having one independent variable (information) with two levels (absent, present). I expect the subjects to behave differently when information is present. $\endgroup$
    – another_newbie
    Commented Jan 30, 2020 at 17:58
  • $\begingroup$ I tried to check the interaction out. The model returns NA as coefficient. If I am mistaken, this means that the two variables are linearly related and there the interaction add no information to the model, or that there is no unique solution. I am getting it correctly? $\endgroup$
    – another_newbie
    Commented Jan 30, 2020 at 18:33
  • $\begingroup$ I guess you're not, but it's hard to say without seeing your data. $\endgroup$
    – Jeremy Miles
    Commented Jan 30, 2020 at 21:56

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