Statistics How To

Bilinear Regression: Definition

Regression Analysis >

The term “bilinear regression” is an informal term (i.e. there is no set definition for its meaning). Therefore, it might mean something different depending on who is using the term and in what context.

General Class of Regressions

One way to define bilinear regression is as a membership to the class of regressions on estimated latent variables. Latent variables are “hidden” variables that, unlike observed variables, are not directly measurable. Examples of latent variables include attitude, intelligence or degree of empathy. The two major bilinear regression methods in this context are principal component regression and partial least squares regression.

Bilinear Regression and Bilinear interactions

One of the most common definitions for bilinear regression is in terms of bilinear interactions. A bilinear interaction is where the slope of a regression line for Y and X changes as a linear function of a third variable, Z.

bilinear regression

A scatter plot shows that this particular data set can best be modeled with two regression lines.

The simple act of creating two separate linear regressions is sometimes called bilinear regression. When a latent variable causes a scatter plot to have two distinct lines (as in the above image), two separate linear regressions might be warranted (one for each line).

In terms of matrices, bilinear regression can refer to a set of explanatory variables that form a two-dimensional matrix.

Generalized Bilinear Model

The generalized bilinear model1 can be written as: g(μij ) = α1iβ1j + α2iβ2j. Two specific models are the growth curve model and the extended growth model.

(1) R-project. Introduction to Generalized Linear Models.
Marie Linder, Rolf Sundberg. Precision of Prediction in Second Order Calibration, with Focus on BR Methods. Mathematical Statistics, Stockholm University, SE-106 91 Stockholm, Sweden. Retrieved July 26, 2017 from:


Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. If you'd rather get 1:1 study help, Chegg Tutors offers 30 minutes of free tutoring to new users, so you can try them out before committing to a subscription.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

Comments? Need to post a correction? Please post a comment on our Facebook page.

Check out our updated Privacy policy and Cookie Policy

Bilinear Regression: Definition was last modified: June 1st, 2018 by Stephanie