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I understand that the fitted values for Logistic Regression can be expressed as:

$$P(Y_i=1) = \left(1+\exp(-\hat{\theta}^TX_i)\right)^{-1}$$

where $X_i$ is the feature vector, which will work well when the features take only numeric values.

However, when the features are non-numerical, can we use the same approach as given here for a Linear Regression model? Or is there a better way which we can use for Logistic Regression?

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Coding of regressors are done exactly the same way in logistic regression as in linear regression. And, by the way, the same way in Poisson regression---all of the GLM's (generalized linear models). In fact, for a lot of other kind of models too. There may be some other considerations in addition, but the same principles apply.

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