I currently read a paper in which the author has asked people 3 different questions regarding their life satisfaction, all of which are to be rated on a four point scale: 1) very low, 2) low, 3) high, 4) very high. The author then takes the average of the answers to the three questions for each individual and then uses this individual average as dependent variable in an OLS regression with binary and continuous explanatory variables.
This does not make sense to me from an interpretation point of view. What does $\beta = 0.12$ tell me in this case given the nature of the dependent variable?
So here are my other questions:
- Is OLS even unbiased and consistent for such outcome variables?
- Would it be possible to first standardize the answers into the unit interval and then take the average to form a measure of life satisfaction?
For the second question I thought it might make sense to standardize the answers $j$ for individual $i$ as $$\tilde{X}_{i} = \frac{X_{ij}-X_{min}}{X_{max}-X_{min}}$$ and then take the average of that, such that $$\overline{\tilde{X}}_{i} = \frac{1}{N}\sum^N_{i=1}\tilde{X}_{i}$$ could be used as the dependent variable. Given that this measure of life satisfaction is between 0 and 1 this should give more interpretable OLS parameters, right?
Thanks in advance.