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You get biased and inconsistent coefficient estimates, and biased standard errors. Bias in standard errors can be in both directions and the probability of types I and II errors could increase.

You can tackle non-linearity by introducing different functional forms of the predictor that had a non-linear relationship with Y. Common functional forms are quadratic, logarithmic, cubic, square roots, among others. You can also think about including splines and possibly interactions between two or more predictors. A last possibility is to use a different link function for the binary relationship, as functions such as probit and clog-log have slightly different shapes, albeit all of them following a synodal shape.

You get biased and inconsistent coefficient estimates, and biased standard errors. Bias in standard errors can be in both directions and the probability of types I and II errors could increase.

You can tackle non-linearity by introducing different functional forms of the predictor that had a non-linear relationship with Y. Common functional forms are quadratic, logarithmic, cubic, square roots, among others. You can also think about including splines and possibly interactions between two or more predictors.

You get biased and inconsistent coefficient estimates, and biased standard errors. Bias in standard errors can be in both directions and the probability of types I and II errors could increase.

You can tackle non-linearity by introducing different functional forms of the predictor that had a non-linear relationship with Y. Common functional forms are quadratic, logarithmic, cubic, square roots, among others. You can also think about including splines and possibly interactions between two or more predictors. A last possibility is to use a different link function for the binary relationship, as functions such as probit and clog-log have slightly different shapes, albeit all of them following a synodal shape.

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You get biased and inconsistent coefficient estimates, and biased standard errors. Bias in standard errors can be in both directions and the probability of types I and II errors could increase.

You can tackle non-linearity by introducing different functional forms of the predictor that had a non-linear relationship with Y. Common functional forms are quadratic, logarithmic, cubic, square roots, among others. You can also think about including splines and possibly interactions between two or more predictors.