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Many people get confused between these two terms :

**General Linear Model**and**Generalized Linear Model**. Do they really mean the same thing ? If not, what is the difference between them?**General Linear Model**

When we try to establish mathematical relationship between dependent and independent variables assuming linear relationship between them then the mathematical model that we get is called a general linear model.

It is the foundation for the t-test, Analysis of Variance (ANOVA), Analysis of Covariance (ANCOVA), regression analysis, and many of the multivariate methods including factor analysis, cluster analysis, multidimensional scaling, discriminant function analysis, canonical correlation, and others.

**Generalized Linear Model**

The Generalized Linear Model is a generalization of the general linear model. In general linear model, a dependent variable must be linearly associated with values on the independent variables. Whereas the relationship in the generalized linear model between dependent variable and independent variables can be non-linear.

In generalized linear model, due to categorical dependent variable we cannot find out the linear relationship between dependent and independent variables. Therefore, we need a function called “Link function” through which we can establish a linear relation with independent variables.

1. In general linear model, the dependent variable is continuous. While, dependent variable in the generalized linear model is non-continuous.

In generalized linear model, due to categorical dependent variable we cannot find out the linear relationship between dependent and independent variables. Therefore, we need a function called “Link function” through which we can establish a linear relation with independent variables.

**Key Differences**1. In general linear model, the dependent variable is continuous. While, dependent variable in the generalized linear model is non-continuous.

2. In general linear model, the relationship between dependent variable and independent variables is linear. While, relationship in the generalized linear model between dependent variable and independent variable can be non-linear.

Hi Mayank! Thanks for the article.

ReplyDeleteAll the tests that you mentioned like t-test,ANNOVA,ANCOVA etc. Can they be used only on General Linear Models? What tests can be used on Generalized Linear Models. Also can you give some examples of Generalized Linear Models used frequently in industries?