Log Linear Models
- Analyzes relationships among two or more categorical variables.
- Models the dependent variable using a logarithmic transformation of independent variables.
- Allows examination of interactions and detection of non-linear or curvilinear patterns in categorical data.
Definition
Section titled “Definition”A log-linear model is a statistical method used to analyze and understand the relationship between multiple categorical variables. It is a type of regression analysis used to model the relationship between two or more variables, where the dependent variable is a logarithmic transformation of the independent variable.
Explanation
Section titled “Explanation”Log-linear models apply regression techniques to categorical data by expressing the dependent variable on a logarithmic scale relative to independent variables. They are suitable for examining relationships among multiple categorical variables, including interactions between those variables. By modeling on the log scale, these models can reveal patterns such as non-linear or curvilinear effects and quantify the strength of associations.
Examples
Section titled “Examples”Gender and voting behavior
Section titled “Gender and voting behavior”A log-linear model can analyze the relationship between gender and voting behavior in a presidential election. Here, the dependent variable is the likelihood of an individual to vote for a particular candidate, and the independent variable is the individual’s gender. Log-linear analysis can determine whether there is a significant relationship between gender and voting behavior and measure the strength of that relationship. Researchers can also assess interactions, for example between gender and political party affiliation, and how such interactions affect voting likelihood.
Income level and purchasing behavior
Section titled “Income level and purchasing behavior”A log-linear model can analyze the relationship between income level and purchasing behavior in a retail store. In this scenario, the dependent variable is the likelihood of an individual to make a purchase at the store, and the independent variable is the individual’s income level. Log-linear analysis can determine whether a significant relationship exists and its strength. It can also identify non-linear relationships, such as a threshold effect where individuals with higher incomes are more likely to make purchases than those with lower incomes.
Related terms
Section titled “Related terms”- Regression analysis
- Categorical variables
- Interaction effects