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Link function literally ?links? the linear predictor and the parameter for probability distribution. In the case of Poisson regression, the typical link function is the log link function. This is because the parameter for Poisson regression must be positive (explained later).

Probabilities are strictly defined between zero and one. The logit link maps the probability of the individual having the disease to the entire real line. The log-link function maps the probability of disease onto the negative real line, requiring the constraint that a linear predictor must be negative.

For log link will be u=e^(po+p1x) For the estimation of y, using signal function and estimator of p to get y. For log transform y=e^(po+p1x), for log link is only depend on the which exponential family choose.

The log link exponentiates the linear predictors. It does not log transform the outcome variable. Where ?=predicted value of Y given X, exp(?0) = the effect on the mean of ? when X=0, and exp(?1)= the multiplicative effect on the mean of Y for a one-unit increase in X. e is a constant value of approximately 2.72.

Regression with log-link or Poisson regression is a model that can be used to study the relative change in an outcome variable. In the log-link regression model, the antilog of each coefficient describes the relative difference in the outcome variable associated with each one-unit difference in the predictor variable.

Regression with log-link or Poisson regression is a model that can be used to study the relative change in an outcome variable. In the log-link regression model, the antilog of each coefficient describes the relative difference in the outcome variable associated with each one-unit difference in the predictor variable.

The purpose of the logit link is to take a linear combination of the covariate values (which may take any value between ±?) and convert those values to the scale of a probability, i.e., between 0 and 1. The logit link function is defined in Eq.