Why do we use logit transformation?

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The logit function serves a pivotal purpose in statistical modeling, particularly in the realm of logistic regression. Its primary application lies in transforming probabilities, which inherently reside within the unit interval, onto the real line. This transformation facilitates the analysis and interpretation of probabilities in a more intuitive and mathematically tractable manner.

Logistic regression, a widely employed statistical technique, relies heavily on the logit function. It enables researchers and analysts to model the likelihood of binary outcomes, such as success or failure, occurrence or non-occurrence, and so forth. By transforming probabilities into logits, logistic regression can effectively estimate the odds of these binary events occurring under various conditions.

One of the notable properties of the logit function is its ability to preserve symmetry around 0.5. This means that the logit transformation treats probabilities below and above 0.5 equally, ensuring that the analysis remains unbiased and balanced. This symmetry is crucial in accurately capturing the nuances and complexities of binary outcomes.