länkfunktion

Länkfunktion, a Swedish term, translates to "link function" in English and is a core concept in statistical modeling, particularly within generalized linear models (GLMs). It serves as a bridge between the expected value of the response variable and the predictor variables. In essence, the link function transforms the expected value of the response variable so that it can be modeled as a linear combination of the predictors.

The choice of link function depends on the nature of the response variable and the assumed distribution of the errors. For example, in linear regression with normally distributed errors, the identity link function is used, where the expected value is directly modeled as a linear combination of predictors. For binary outcomes, the logit or probit link functions are common, transforming the probability of success into a linear predictor. When modeling count data, the log link function is often employed.

The link function is a crucial component that allows GLMs to handle a wide range of response variable types and distributions, extending the flexibility of traditional linear regression. It ensures that the linear predictor remains within the valid range of the transformed expected value, for instance, ensuring probabilities are between 0 and 1.