Is there a difference between a general linear model (GLM) and general regression model (GRM)?

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    $\begingroup$ Can you provide some context for this? Where did you see these terms? I'm not familiar w/ "general regression model (GRM)". $\endgroup$ Apr 24, 2017 at 14:56
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    $\begingroup$ I am not familiar with general regression model as a formal statistical term. $\endgroup$ Apr 24, 2017 at 14:56
  • $\begingroup$ I'm voting to close this question as off-topic because it is too brief and refers to a non-standard term. $\endgroup$ Apr 24, 2017 at 14:58

1 Answer 1


I think you might have some terminology mixed up here. The acronym "GLM" is used to refer to a generalized linear model, which is not to be confused with a general linear model. Statisticians are bad at naming things.

Here is the major difference:

  1. A GLM is so-called generalized since $Y$ need not be normal, or even continuous. It could, for instance, be Bernoulli or something.
  2. A general linear model generalized the covariance structure of the error term. Traditional OLS lets the error term $\mathbf{\varepsilon} \sim N(\mathbf{0}, \sigma^2 I)$, where in a general linear model, you may let $\varepsilon \sim N(\mathbf{0}, \mathbf{\Sigma})$, where $\mathbf{\Sigma}$ can have some strange, sometime nondiagonal structure.
  • $\begingroup$ But what do you have to say about general regression model? $\endgroup$ Apr 24, 2017 at 15:01
  • $\begingroup$ Can you tell us where you heard such a term? It seems everyone posting here so far agrees it is a nonstandard term. My guess was that you were confusing it with something else - likely the two "GLM"s. $\endgroup$ Apr 24, 2017 at 15:38
  • $\begingroup$ What you say is a valid statement about the GLM terminology but the OP is asking about general regression model and there is no way to answer this unless the OP explains what he thinks that term means. $\endgroup$ Apr 24, 2017 at 15:42
  • $\begingroup$ Whoops - sorry. I'm new to CV and thought you were OP. Looks like he just joined to ask this one question so it's doubtful he'll return. $\endgroup$ Apr 24, 2017 at 15:47
  • $\begingroup$ yes i am new here. it is ok i think it is only about name, but the meaning is the same. linear regression model is a model used to test the possible effect of two fixed factors and their interaction on the response variables. $\endgroup$
    – meriem
    May 2, 2017 at 13:22

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