How to deal with missing values in summated scales in a logistic regression? I am carrying out a logistic regression analysis in entrepreneurship research, in which one of the main independent variables, "innovativeness", is a company trait based on two different questions ("product's/service's potential to change the market" and "product/service novelty"). As these two were internally consistent with a high Cronbachs alpha score, it was decided to create one variable with a 9 point Likert scale instead of the 5 point scale of the individual variables. The final value is the two respective values added together and divided by two ((X+Z)/2).
The problem is that there is a range of missing values for one or the other variable (32), meaning that the entrepreneur "didn't know" or just didn't answer the question. This is unfortunate as the complete sample (182) is not very big in the first place. 
Is it legitimate to take one of the values, if the other is missing, and use it as a proxy for the underlying construct (innovativeness)? Or would this create a bias greater than the missing values might potentially lead to?
 A: The answer will be subjective but surely it will be informed by the magnitude of Cronbach's alpha, or, alternatively, of the linear association between the two survey items that make up the innovation score.  It's hard to imagine anyone objecting to your approach if alpha > .90.  It's easy to imagine an objection in the face of an alpha < .50.  In between, it's really a matter of preference.  You may be able to persuade your readers or stakeholders that the benefits of increasing the sample size outweigh whatever imprecision of measurement is introduced by substituting a single-item score for a scale score.
In fact, you could conduct a simulation to assess the potential bias resulting from applying your proposed substitution.  That would be useful to report in conjunction with your primary results.  As to bias from missing data, that is a larger matter.  You haven't mentioned what information you may have as to the differences, on other variables, between those who answered one vs. two innovation items.  This is certainly worth evaluating to the extent your data and your situation allow.
