Glossary of statistical terms

facebook LinkedIn twitter Google+ Email

General Linear Model:

General (or generalized) linear models (GLM), in contrast to linear models, allow you to describe both additive and non-additive relationship between a dependent variable and N independent variables. The independent variables in GLM may be continuous as well as discrete. (The dependent variable is often named "response", independent variables - "factors" and "covariates", depending on whether they are controlled or not).

Consider a clinical trial investigating the effect of two drugs on survival time. Each drug is tested at three levels - "not used", "low dose", "high dose", and all the 9 (=3x3) combinations of the three levels of the two drugs are tested. The following general linear model might have been used:

Yij = A + B X + Ci + Dj + Rij + N; i,j = 1,2,3;

where Y is survival time (response), i and j correspond to the three levels of drug I and drug II respectively, X is age, Ci are additive effects (called "main effects") of each level of drug I, Dj are main effects of drug II, Rij are non-additive effects (called interaction effects or simply "interactions") of drugs I and II, N is random deviation.

We have here three independent variables: two discrete factors - "drug I" and "drug II" with three levels each, and a continuous covariate "age".

In this particular case, because each of the two factors (drugs) has a zero level i,j=1 ("not used"), main effects C1, B1, and interactions R1j, j=1,2,3; Ri1, i=1,2,3 are zeros. The remaining unknown coefficients - A, B, Ci, Dj, Rij - are estimated from the data. The main effects Ci, Dj of the two drugs and their interaction effects Rij are of primary interest. For example, their positive values would indicate a positive effect - longer survival time due to use of the drug(s).

Browse Other Glossary Entries

Want to learn more about this topic? 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.

Generalized Linear Models

This course will explain the theory of generalized linear models (GLM), outline the algorithms used for GLM estimation, and explain how to determine which algorithm to use for a given data analysis. GLM allows the modeling of responses, or dependent variables, that take the form of counts, proportions, dichotomies (1/0), positive continuous values, as well as values that follow the normal Gaussian distribution. Logistic, Poisson, and negative binomial regression models are three of the most noteworthy GLM family members.

Note:  Detailed study of model specification and the interpretation of software output is handled in's individual courses on regression, logistic regression, count data modeling, etc.

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?

Student comments