Zählwertregressionen

Zählwertregressionen, also known as count regressions, are statistical models used when the dependent variable represents a count of events. These counts are non-negative integers (0, 1, 2, ...), and their distribution often differs from the normal distribution. Standard linear regression, which assumes a normally distributed dependent variable and constant variance, is generally not appropriate for count data.

Commonly used models for zählwertregressionen include the Poisson regression and the negative binomial regression. Poisson regression assumes that the mean and variance of the count variable are equal. This assumption is often violated in practice, as count data frequently exhibit overdispersion, meaning the observed variance is greater than the mean. When overdispersion is present, negative binomial regression is a more suitable choice, as it allows for a variance that is greater than the mean.

The independent variables in zählwertregressionen can be continuous or categorical, and they are used to predict the expected count of events. The interpretation of coefficients differs from linear regression. For instance, in a Poisson regression, an exponentiated coefficient represents the multiplicative change in the expected count for a one-unit increase in the predictor.

Applications of zählwertregressionen are found in various fields, including epidemiology (e.g., predicting the number of disease cases), ecology (e.g., modeling the number of species in an area), and marketing (e.g., estimating the number of purchases). The choice of model depends on the characteristics of the count data, particularly its distribution and the presence of overdispersion.