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I saw the slides on https://ocw.mit.edu/courses/mathematics/18-655-mathematical-statistics-spring-2016/lecture-notes/MIT18_655S16_LecNote19.pdf

The title of the slide is "gaussian linear models." But it seems the content is just for general linear model. Are the two equivalent?

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  • $\begingroup$ The "Gaussian linear model" is a special case of the generalized linear model that just so happens to be ordinary least squares. $\endgroup$
    – AdamO
    Jul 8, 2020 at 4:23
  • $\begingroup$ @AdamO I had a typo in my OP. I meant to type "general" instead of "generalized." Is the general linear model the same as the gaussian linear model? If so, then I don't think it's correct to say that a general linear model is OLS. OLS is just one (most popular) method to obtain a general model, but there are also other methods. $\endgroup$ Jul 8, 2020 at 4:25
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    $\begingroup$ I see Kempthorne defines the general linear model on page 3 of the notes. It is the standard OLS model except that the error term is allowed to take any flavor -- not stated, but probably assuming IID and mean 0. The Gaussian linear model then would be the version with normally distributed (Gaussian) errors, where the OLS is the maximum likelihood estimator. $\endgroup$
    – AdamO
    Jul 8, 2020 at 4:34
  • $\begingroup$ @AdamO Doesn’t the general linear model, by definition, assume normality of errors? If the error term is allowed to be anything, isn’t that a generalized linear model instead of a general model? The terminology confuses me. $\endgroup$ Jul 8, 2020 at 5:02
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    $\begingroup$ Why are you still stuck on this? The definition is given on slide 3. If you're going to follow the course notes, you have to follow the professor's definitions; read them closely. $\endgroup$
    – AdamO
    Jul 8, 2020 at 15:17

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Answered in comments by AdamO:

I see Kempthorne defines the general linear model on page 3 of the notes. It is the standard OLS model except that the error term is allowed to take any flavor -- not stated, but probably assuming IID and mean 0. The Gaussian linear model then would be the version with normally distributed (Gaussian) errors, where the OLS is the maximum likelihood estimator.

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    $\begingroup$ Thank you for offering an answer. I believe it misinterprets the slides, though, because later on there is a section within this one on models with Gaussian error terms that is referred to as Normal models. "Gaussian linear model" most likely respects Gauss's contributions to OLS theory rather than referring to the error distribution. $\endgroup$
    – whuber
    Jul 25, 2022 at 14:10
  • $\begingroup$ @whuber Thanks - would you like to add that as a separate answer, or to edit this one to correct it? $\endgroup$
    – mkt
    Jul 26, 2022 at 8:58

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