![]() How intuitive are odds ratios?īecause the log odds scale is so hard to interpret, it is common to report logistic regression results as odds ratios. And what does that mean? I’ve never met anyone with any intuition for log odds. 05, that means that a one-unit increase in X 1 is associated with a. The logistic model is less interpretable. Just about everyone has some understanding of what it would mean to increase by 5 percentage points their probability of, say, voting, or dying, or becoming obese. 05, that means that a one-unit increase in X 1 is associated with a 5 percentage point increase in the probability that Y is 1. The major advantage of the linear model is its interpretability. The linear model assumes that the probability p is a linear function of the regressors, while the logistic model assumes that the natural log of the odds p/(1- p) is a linear function of the regressors. Ln = b 0 + b 1 X 1 + b 2 X 2 + … + b kX k ( logistic) P = a 0 + a 1 X 1 + a 2 X 2 + … + a kX k ( linear) Then the linear and logistic probability models are: If the outcome Y is a dichotomy with values 1 and 0, define p = E( Y| X), which is just the probability that Y is 1, given some value of the regressors X. Let’s start by comparing the two models explicitly. ![]() LEARN MORE IN ONE OF OUR SHORT SEMINARS Interpretability While there are situations where the linear model is clearly problematic, there are many common situations where the linear model is just fine, and even has advantages. Which probability model is better, the linear or the logistic? It depends. Yet economists, though certainly aware of logistic regression, often use a linear model to model dichotomous outcomes. ![]() In both the social and health sciences, students are almost universally taught that when the outcome variable in a regression is dichotomous, they should use logistic instead of linear regression. But he neglected to consider the merits of an older and simpler approach: just doing linear regression with a 1-0 dependent variable. In his April 1 post, Paul Allison pointed out several attractive properties of the logistic regression model. ![]()
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