How to asess the importance of variables in a logit-transformed model

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My dependent variable is the share of workers on long-term contracts and I run a fixed-effects regression on the panel dataset to assess the relative importance of various variables, such as the availability of alternative jobs, unemployment, distance from a major city etc. By definition the dependent variable share is bounded between 0 and 1, and I use logistic transformation
logit(share)= log(share / 1 - share)
to move a continuous variable. Now I have the regression coefficients for logit(share). How can I use them to assess the relative contribution of independent variables to explaining the variation in the original variable share?

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