A log-linear model is a mathematical model

Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...

 that takes the form of a function

Function (mathematics)

In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

 whose logarithm

Logarithm

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

 is a first-degree polynomial function of the parameters of the model, which makes it possible to apply (possibly multivariate

Multivariate analysis

Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...

) linear regression

Linear regression

In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...

. That is, it has the general form
in which the are quantities that are functions of the variables , in general a vector of values, while and the stand for the model parameters.

The term may specifically be used for:

• A log-linear plot or graph, which is a type of semi-log plot
• Log-linear modeling (economics), a technique among economists
• Markov random field#Log-linear models, a Markov random field with a log-linear distribution
• Poisson regression
  Poisson regression
  In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown...
  
   for contingency tables

See also

• Multinomial logit
  Multinomial logit
  In statistics, economics, and genetics, a multinomial logit model, also known as multinomial logistic regression, is a regression model which generalizes logistic regression by allowing more than two discrete outcomes...
  
  , also known as a maximum entropy classifier
• General linear model
  General linear model
  The general linear model is a statistical linear model.It may be written aswhere Y is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors or...
  
  
• Generalized linear model
  Generalized linear model
  In statistics, the generalized linear model is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to...
  
  

-->