Unbalanced dependent sample and intercept correction


I’m running a logistic regression analysis in SPSS and wanted to ask about the sample values for the dependent variable (landslide presence). My dependent variable is binary and has observed values of 1, or presence of landslides (252,204 cases, 86% of the sample), and 0, or absence of landslides (38,541 cases, 14%).

I would like to ask if this sample of the dependent variable is too unbalanced for logistic regression. I’m asking because when I run the LR the model has a 0% specificity and a 100% sensitivity, meaning that, globally, the model predicts 86% of the cases correctly (the same value as the 0 cases).

From reading on the internet, a possible solution is to apply an intercept correction. Is this a good idea? How can this be done in SPSS?

Many thanks in advance!!

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I've been reading around sinces posting this and have come across a couple of possible solutions. Firstly, King & Zeng's method (http://pan.oxfordjournals.org/content/9/2/137.abstract) which is dismissed by Paul Allison in this blog (http://www.statisticalhorizons.com/logistic-regression-for-rare-events), where he opts for Firth's method. According to Allison I shouldn't have any problems with my sample as I have a sufficient number of 0s. However, I would like to try either King and Zeng's method or Firth's just to see if it has any effect on the model.

Has anybody had any experience of applying these corrections, particularly in SPSS?