Log-Linear Regression

Definition

In statistic, log-linear regression is a powerful regression technique that models relationship between a dependent variable or regressand Y, explanatory variable or regressor X = {x₁, … , x_I} and a random term ε by fitting a log-linear model,

$$ \ln Y={\alpha}_{+}{\alpha}_1 \ln {x}_1+{\alpha}_2 \ln {x}_2+\dots .\\ {}+{\alpha}_I \ln {\alpha}_I+\varepsilon $$

where α₀ is the constant term, the α_i s are the respective parameters of independent variables, and I is the number of parameters to be estimated in the log-linear regression.

Key Points

The goal of log-linear regression is to explore effect a set of covariance X = {x₁, … , x_I} on the expected rate [1]. It assumes that a linear relationship exists between the log of the regressand Y and the regressor X = {x₁, … , x_I}. The log-linear regression is appropriate for categorical variables.

When applied to continuous variables, discretization is an essential step for preprocessing. There are two basic steps to using log-linear...