Link function logit

Suppose we decide to use the logarithm of the odds ratio as the link function. The logarithm of the odds ratio is called the logit. We set it equal to the linear function of... 

There are several possible link functions that are commonly used. The logit link that we will use leads to the logistic regression model. The inverse of the normal cumulative distribution function 0o + Pix = (tr) is called the probit link and leads to the probit model. The complementary log-tog link is given... 

The mean function of the observations is linked to a linear function of the predictor variable. For logistic regression the logit link function is used. 

In the logistic regression model, the observations are independent binomial observations where each observation has its own probability of success that is related to a set of predictor variables by setting the logarithm of the odds ratio equal to an unknown linear function of the predictor variables. This is known as the logit link function. The coefficients of the linear predictor are the unknown parameters that we are interested in. 

The logistic regression model is an example of a generalized linear model. The observations come from a member of one-dimensional exponential family, in this case binomial. Each observation has its own parameter value that is linked to the linear predictor by a link function, in this case the logit link. The observations are all independent. 

The logit is linked to the linear predictor, an unknown linear function of the predictor variables. 

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