yhteysfunktio

Yhteysfunktio, known in English as a connection function or linking function, is a mathematical concept used primarily in the field of statistics and machine learning. It plays a crucial role in generalized linear models (GLMs). The core idea of a yhteysfunktio is to transform the expected value of a response variable, which may be constrained to a specific range (e.g., probabilities must be between 0 and 1), into a linear predictor that can take any real value. This transformation allows for a more flexible modeling approach than traditional linear regression.

In a generalized linear model, the relationship between the expected value of the response variable, E(Y), and the predictor variables, X, is modeled as E(Y) = g⁻¹(Xβ), where g is the yhteysfunktio, g⁻¹ is its inverse, X is the matrix of predictor variables, and β is the vector of coefficients. The yhteysfunktio g links the mean of the distribution of the response variable to a linear combination of the predictor variables. Common examples of yhteysfunktiot include the logit function for binary data (logistic regression), the logarithm for count data (Poisson regression), and the identity function for continuous data (which reduces to standard linear regression). The choice of yhteysfunktio is often dictated by the assumed distribution of the response variable.