# Glossary of statistical terms

Loglinear models:

Loglinear models are models that postulate a linear relationship between the independent variables and the logarithm of the dependent variable, for example:

 log(y) = a0 + a1 x1 + a2 x2 ... + aN xN

where y is the dependent variable; xi, i=1,...,N are independent variables, and {ai, i=0,...,N} are parameters (coefficients) of the model.

Loglinear models, for example, are widely used to analyze categorical data represented as a contingency table . In this case, the main reason to transform frequencies (counts) or probabilities to their log-values is that, provided the independent variables are not correlated with each other, the relationship between the new transformed dependent variable and the independent variables is a linear (additive) one. For example, a simple bivariate independence model for two categorical variables X and Y

 pij = P(X=i) P(Y=j); i=1,...,M; j=1,...,N

transforms to:

 log(pij) = liX + ljY;

where

 liX = logP(X=i);
 ljY = logP(Y=j).

Browse Other Glossary Entries

# Want to learn more about this topic?

Statistics.com offers over 100 courses in statistics from introductory to advanced level. Most are 4 weeks long and take place online in series of weekly lessons and assignments, requiring about 15 hours/week. Participate at your convenience; there are no set times when you must to be online. Ask questions and exchange comments with the instructor and other students on a private discussion board throughout the course.

Introduction to MCMC and Bayesian Regression via rstan

This course covers the application of Markov Chain Monte Carlo techniques (MCMC) to Bayesian statistical modeling using WinBUGS software.

Categorical Data Analysis

This course will cover the analysis of contingency table data (tabular data in which the cell entries represent counts of subjects or items falling into certain categories). Topics include tests for independence (comparing proportions as well as chi-square), exact methods, and treatment of ordered data. Both 2-way and 3-way tables are covered.

Back to Main Glossary

# Promoting better understanding of statistics throughout the world

To celebrate the International Year of Statistics in 2013, we started a program to provide a statistical term every week, delivered directly to your inbox. The Word of the Week program proved to be quite popular, and continues. The Institute for Statistics Education offers an extensive glossary of statistical terms, available to all for reference and research. Make it your New Year's resolution to improve your own statistical knowledge! Sign up here. Rather not have more email? Simply bookmark our home page and check our “Stats Word of the Week” feature.

Want to be notified of future courses?

Yes
Student comments