Talk:General linear model
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- No, the generalized linear model is considerably more general than the general linear model. (This is obviously not the greatest terminology, but it is standard.) -- Walt Pohl 22:36, 1 January 2007 (UTC)
Why is the "Application" section give one example from neuroimaging that is less-than-obvious, when the GLM underlies almost all simple statistical tests and therefore has a plentiful supply of clear and easy-to-understand examples? --user: NotTires —Preceding unsigned comment added by 184.108.40.206 (talk) 01:04, 12 July 2008 (UTC)
- In functional neuroimaging analysis the general linear model is well-known and it is probably used in thousands of articles where it is specifically written "general linear model". If you have other appropriate examples you can add them. — fnielsen (talk) 08:49, 3 April 2009 (UTC)
- I ditto the skepticism about mention of neuroimaging details. Firstly, I think it may have let to a factual error. A "mass-univariate" hypothesis test is merely several independent univariate tests. The real distinction, therefore, is between the univariate approach and the multivariate approach. Since this is a distinction that is not particular to GLMs but is, rather, a general thing is statistical inference, it hardly bears mention and certainly not in a way that might imply this was something particular about GLMs. Secondly, does anyone beyond Karl Friston (SPM guru) or imaging folks even use the term "mass-univariate"? Google it with flags "-fmri -PET" and you will quickly see that it is field specific jargon and not suitable to a general encyclopedia article. Similarly, SPMs are mostly referred to as SPMs by users of the SPM software package. This bit is not wrong per se, just misleading: There are more SPM users than AFNI users, FSL users, etc., validating the "often" part of the statement. I think most folks, even SPM users, really just talk about results as maps, volumes or images, as in, t-maps, F-maps, beta-images, etc. 220.127.116.11 (talk) 18:46, 9 December 2009 (UTC)
More on terminology
The above says "it is standard" but there is no citation. Kendall&Stuart use "general linear regression model" for what is is otherwise called "multiple regression" ie a univariate independent variable. I believe I have seem "multivariate regression" used generally for the problem as described in the article: for example by Zellner(1971) An introduction to Bayesian Inference in Econometrics, Wiley ISBN 0-471-98165-6. But I cannot find this in my stats dictionaries. However "General linear model" does not appear either. So, any citations for the term "General linear model" used in the sense of the present article? Melcombe (talk) 16:37, 13 March 2009 (UTC)
- Kanti Mardia and his co-authors use "general linear model" in their Multivariate Analysis book, but it is given as a specialization of multivariate regression (if I remember correctly). Maybe we need to clearify the terminology. — fnielsen (talk) 08:49, 3 April 2009 (UTC)
OK, I have found a basic early explicit definition in the introductory text book by Mood & Graybill, which only covers the univariate nultiple regression case, and some of the references in the first list above do extend this meaning to cover multivariate regression but without I formal definition. (Some of the other lists are not publically accessible.) But what is the supposed distinction between "general linear model" and "generalized linear model": ie what supposedly makes "generalized linear model" more general? The definition of Mood & Graybill allows for non-normal additive residuals and I suppose something could be constructed to show that "generalized linear model" is more general, but does someone have a citation that does explicitly make an acceptable statement of why "generalized linear models" are more general? As for "general linear model", if too many people are using the terminology in too many different senses, perhaps this needs to be recognised. Of course there is also the question of "general linear model hypothesis" which seems not yet covered on wikipedia and which is again subtly different in meaning. Melcombe (talk) 09:06, 3 April 2009 (UTC)
I made a change that may answer this and discusses how I play/hope to develop this. My understanding is based partly on the initial formula attributed to Mardia. In this case we have multiple independent variables. So we have multiple linear regression generalized to allow for multiple independent variables. This is also the term used in.
Regardless of what it is called, we can consider the number of dependent variables, consider correlated error terms, non-normality, and heterogeneity the number of independent variables, and the use of non-linear link functions.
On this page, I plan to start with linear regression with multiple dependent variables and generalize to multiple independent variables as in .
I noticed Seber refers to generalized least squares when dealing with correlated errors—weighted least squares, this seems to match what Mood and Graybill.
I do not see a simple development of multiple linear regression with one independent variable, on wikipedia Please tell me if I'm wrong.
Having said that, You see my initial plan, but I'm not 100% sure what should go on this page.
What do you reckon?
You mean that multiple dependent variables are the difference between the general linear model (aka multivariate linear regression) and multiple linear regression.