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Can I calculate Odds Ratios from a linear regression model?

Or is it only possible / allowed on a logistic model?

I have a linear mixed-effects model and I use R and the lmer command to run a regression and then the following code calculates odds ratios:

fit <- lmer(formula, data = reg_SwisciRuralUrban_bin)

OR <- exp(fixef(fit))

whuber
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B. Rentrug
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    What would you be calculating the odds ratio on? Does your $y$ value (response) represent a value between 0 and 1? A better question might even be, what are you trying to do and why? – StatsStudent Jan 20 '19 at 18:59
  • Y variables is NOT 0 and 1. Its a continious variable with values between 0 and 100. I guess I could then directly interpret the output from the fit. Correct? – B. Rentrug Jan 20 '19 at 20:23
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    It's hard to see how you could interpret anything in your model as an odds ratio when the response is a continuous variable between 0 and 100 and you use linear regression. – whuber Jan 20 '19 at 20:55
  • You could perform a beta regression. Or it may be easier for you to transform your variable into the range of real numbers between 0 and 1 (by dividing by 100) and using a generalized linear model with the logistic transform as your link variable. There are a few other options too It all depends on what you are trying to do. See here: https://stats.stackexchange.com/questions/43366/extending-logistic-regression-for-outcomes-in-the-range-between-0-and-1?rq=1 – StatsStudent Jan 20 '19 at 21:22
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    Looks like an instance of the [XY-problem](https://en.wikipedia.org/wiki/XY_problem) – kjetil b halvorsen Jan 21 '19 at 10:58

1 Answers1

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What you are (almost) doing is calculating some transformation (inverse logit, but it should be $e^x/(1+e^x)$) of the regression coefficient that for logistic regression would transform to an odds ratio. For alinear regression I am not aware of any useful interpretation of this quantity.

The one useful link between a linear model and an odds ratio occurs when you want to know what the probability of the outcome being greater than some threshold. That one can usually estimate from the linear model much better than by dichtomizing the data into above/below threshold and looking at that.

Björn
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