I know that in logistic regression we assume a linear relationship between the independent variables and the logits. Can you explain why is this a reasonable assumption?


2 Answers 2


I think this could be answered a few different ways. One interpretation would be to say that it is NOT reasonable (I'd probably land in this camp if you pushed me hard enough). Linearity is the simplest assumption we can make about the effects of the variables, and so we make it. The reason the assumption is about linearity on the log odds scale and not on the natural scale is to avoid unrealistic predictions. Note that the range of the logits is the entire real line. Modelling the effects of the covariates on an unbounded scale prevents us from having to deal with cases where we predict the mean is less than 0 or greater than 1.

A different argument would be that in a neighbourhood of the covariates, the function is approximately linear. In the case where we believe we are examining a sufficiently small neighbourhood of the possible covariate space, maybe this assumption is good enough.


The assumption of linearity in logistic regression (and other glm's), as in linear regression, is linearity as a function of the unknown, to-be-estimated, parameters.

Linearity as a function of the predictors is not assumed, as witnessed by quadratic and other polynomial regressions. See What does linear stand for in linear regression?

So if you believe that linearity of the logodds as a function of $x$ is unreasonable (it often is), you can use $x^2$, or spline $x$. See for instance

Do statisticians assume one can't over-water a plant, or am I just using the wrong search terms for curvilinear regression?

How to achieve linear relationship between predictors and logit of outcome?. Also

How should I check the assumption of linearity to the logit for the continuous independent variables in logistic regression analysis?,

Investigating robustness of logistic regression against violation of linearity of logit,

Correcting nonlinear relationship between continuous predictor and logit of dependent variable (Binary logistic regression),

Logit Linearity Assumption Violated. What now? and many, many more.


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