Genmodellen

Genmodellen refers to generalized linear models, a flexible class of statistical models. They extend the familiar linear regression model to accommodate response variables that have different distributions and to allow the mean of the response to depend on the predictors through a link function.

A generalized linear model consists of three components: a random component, a systematic component, and a link function. The random component specifies the probability distribution of the response variable, which can belong to the exponential family, such as the normal, binomial, Poisson, or gamma distributions. The systematic component is a linear combination of the predictor variables, often denoted as η = β₀ + β₁x₁ + ... + βₚxₚ. The link function, g(.), connects the expected value of the response variable, E(Y) = μ, to the linear predictor: g(μ) = η.

Common examples of genmodellen include linear regression (where the distribution is normal and the link is identity), logistic regression (for binary outcomes, with binomial distribution and logit link), and Poisson regression (for count data, with Poisson distribution and log link). These models are widely used in various fields, including biostatistics, econometrics, and social sciences, for analyzing data where the assumptions of standard linear regression are not met. The estimation of parameters in genmodellen is typically done using maximum likelihood estimation.