Solved – How to interpret this logistic regression table

Question

As someone without much statistics training it can be very annoying to come across tables like this one (supposedly explaining the relationship between various individual level characteristics, such as age, class and perceptions of immigration rates, and the tendency to vote to leave the EU) in academic papers/books:

There are a couple things bothering me here:

1. Can I compare the regression coefficients in order to rank the
   importance of different variables (e.g., can I say the perception that
   Brexit would reduce immigration is a more important predictor of
   Brexit voting than, say, believing immigrants are a burden on the
   welfare state, because the respective regression coefficients are
   0.71 and 0.27, respectively, with both being statistically significant at the 0.01 level).
2. How can I describe the effect in layman's terms? In linear regression I think I'm right in saying that if the independent and dependent variables are measured in percentage terms then you can say a 1 per cent increase in the independent variable will lead to an X per cent increase in the dependent variable, but how does that work in logistic regression?
3. Why does there appear to be two different sets of regression coefficients (i.e., columns 1 and 3)?

Any help would be much appreciated.

Answer 1

1. You cannot compare the coeffcients that way because they are for a unit change in the predictor and the predictor variable may, in general, be measured on very different scales.
2. I am afraid your understanding of linear regression is awry. A unit change in the predictor leads to a $\hat\beta$ change in the outcome. The position for logistic regression is outlined elsewhere on this site in answers to the question linked below
3. Unless the text tells you then your guess is as good as mine. Note by the way that the coefficients are on the log scale

What is the significance of logistic regression coefficients?