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I apologize if this question is very simple but I have found a lot of information on how to interpret log transformed variables (http://www.ats.ucla.edu/stat/mult_pkg/faq/general/log_transformed_regression.htm, Interpretation of log transformed predictor) but not on logit transformations and I am confused.

I have a linear mixed effect model in which the dependent variable is the proportion of home range overlap (logit transformed), and two predictor variables, home range size and season (untransformed):

logit(overlap proportion) ~ 1 + Home range size + season + 1|indiv_code

I want to know how to interpret the effect of the home range size on home range overlap. The beta coefficient of home range size is -0.00​19829​. My question then is:

​Can I interpret the effect of home range size as I would do in any logistic regression?

And if so, could I then say that for every unit increase in home range size there w​ill be​ ​a ​99.80% increase in the odds of ​home range ​overlap, ​given that exp(-0.0019829) = 0.9980​ (99.80%​)​. This was my understanding after reading about how to interpret the effect of continuous variables in logistic regression (http://www.ats.ucla.edu/stat/mult_pkg/faq/general/odds_ratio.htm)

Many thanks!

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For a unit change in home range size, the odds change by a factor of exp(-0.0019829)=0.9980 so the overlap expressed (in terms of the odds) decreases by 1 - 0.998 = 0.2%.

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