# How to interpret transformed predictor variable in GLM regression?

Recently encountered a research paper which included a GLM regression with a binary dependent variable. One of the predictor variables, x_t, (or independent variable), is transformed by the following:

log(x_t)^2, where x_t is actually the ratio of two count variables at time t, g_t/G_t.


How is one supposed to interpret the coefficient generated by the GLM regression? In other words, if I change my predictor variable by p%, the expected change in Y is ... (something involving Beta, the regression coefficient).

I know that when a predictor variable is transformed by the log function within an OLS model, the following interpretation is needed: [100 + p]/100 * Beta change in Y is expected for a p% change in x. But I can't seem to think of similar way to interpret this novel transformation.

• Be careful: that predictor depends on two values, not just one like in a $log$ transform. – Dave Apr 22 at 18:22
• Good catch. Looked at the regression again, and it seems G is the average of g_t for all time t. So G is a constant. – Tony C Apr 22 at 18:42