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How to code a predictor in logistic regression when some values are purposefully unknown

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I decides to post my question here because, strictly speaking, it has to do with coding.

The problem is as follows. In a psychological experiment involving two conditions, an independent variable - made up of numeric values - was present in one condition but not in the 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 second condition - where participants were not provided with such information - I coded the variable as NA. However, when I run my logistic model, setting na.action = na.omit causes the model to fail.

In principle, the NAs in my data are not missing values but, in accordance with the experimental design, would like to reflect the absence of this 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.

Is there any strategy to code such unknown values and cope with this problem?

Any help would be much appreciated. Thank you very much!


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