Using the "Divide by 4 Rule" to Interpret Logistic Regression Coefficients

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I was recently reading a bit about logistic regression in a book on hierarchical/multilevel modeling when I first learned about the “divide by 4 rule” for quickly interpreting coefficients in a logistic regression model in terms of the predicted probabilities of the outcome. The idea is pretty simple. The logistic curve (predicted probabilities) is steepest at the center where a+ßx=0, where logit

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