Distinction of GLM from generalized linear model, GLIM

[TadaoSHIBAYAMA]

How GLM is distinguished from GLIM: this is my first question in SAS Procedures Community.  As a novice to SAS, I wondered so far how GLM is distinguished from generalized linear model by Nelder and Wedderburn (1972) that is abbreviated as GLIM in SAS documentation or abbreviated purposely here GdLM.  Before asking other questions on GLM, I wish to know the distinction correctly.

I think GLM is general in the linear model but specific in the population, normal, as supposed of the observed responses.  Whereas GdLM, i.e. GLIM in SAS documentation, is general in the population allowed to be some other distributions.  I should like to ask generalized linear model, GdLM, i.e. GLIM in SAS documentation, might be read generalized_population or generalized(population) linear model, Gd_pnLM or Gd(pn)LM.  If this is incorrect or inappropriate, I should like to beg you so that you could kindly please correct me rightly.  Yours Very of Respectfully, (2014.10.10), Tadao SHIBAYAMA.

[PaigeMiller · Accepted solution]

I'm not sure about your use of "population" here.

In any statistical estimation, there are parameter estimates you get from the data, and then there is the true underlying values of the parameters (which are usually unknown).

The true underlying values of the parameters could reasonably be called the "population" values, but the parameter estimates from any SAS PROC or any statistical estimation are not the "population" values (except in the extreme case where you have data from every member of the population).

[TadaoSHIBAYAMA]

Thanks to PaigeMiller sincerely for truly reliable advice.  I completely agree with you.

Forgive me of my poor wordings just like a redundant “of’” in the last greeting at the end of the last question.

The “population” values are estimated from any SAS PROC or any procedure, as you mentioned. 

That are only the estimate values and generally shall be never equal to the underlying true values. 

Sure, and here, behind almost any the estimation procedure, a “population” or its form of the distribution function, at the least, is assumed almost arbitrarily but inevitably, ever.  I meant the form by the word “population”.  Yours Very Respectfully (2014.10.11) Tadao SHIBAYAMA

[PaigeMiller]

If you are saying that you want to use the word "population" to mean that there is a distribution function used, I would not use the word "population" in that fashion, the two are not equivalent.

[lvm]

GLM in SAS is strictly for fixed-effects linear models with a normal distribution. It meant "general" in the 1970s when PROC GLM was developed because it handled a wide range of linear fixed-effects models. It is strictly for normal data. However, this nomenclature has led to a lot of confusion over the decades. As stated by Stroup, GLM is not considered general anymore (but the PROC name has stuck, out of tradition). Generalized linear models (as in PROC GENMOD) are for non-normal distributions in the exponential family, but also strictly for fixed effects models. Overdispersion can be handled for so-called marginal models. Many authors outside of SAS would use "GLM" for a generalized linear model. Hence, the confusion. Generalized linear mixed models (fixed and random effects), or GLMMs, can be fitted using GLIMMIX. Exponential family of distributions and fixed and random effects.

[TadaoSHIBAYAMA]

Helped so much.  Many thanks to PaigeMiller (2014.10.13), and also to lvm (2014.10.13), for the comments extremely valuable.

The word “distribution” is very expressive surely.

To avoid unnecessary proliferation of nomenclature, acronym GdLM proposed for GLIM in SAS purposely in this question may be read, case to case,

Gd_distribution, or Gd(distribution), or furthermore, Gd(link-function&distribution), etc., linear model, or linear mixed model, etc.

Any linear model is built of the linear component, direct or anyway-linked,

fixed or random factor effect, fluctuation, and the probabilistic distribution behind a random or fluctuation element. 

These components are classified to fixed and random groups to be basis of the analysis. 

Among various linear models, the Goodnight’s old classical GLM seems to be the unique prototype of models.

I like to stick it to understand it enough.  Tadao SHIBAYAMA (2014.10.15).

[lvm]

Anyone who is confused by acronyms for "linear models" should read Stroup's excellent Global Forum paper.

http://support.sas.com/resources/papers/proceedings11/349-2011.pdf

[TadaoSHIBAYAMA]

Really, it is a glamourous, illuminating and readable paper (Strout).

http://support.sas.com/resources/papers/proceedings11/349-2011.pdf

Thanks sincerely to lvm (2014.10.13-15), and to PaigeMiller (2014.10.10-15).

The volume of the proceedings, contains another informative paper (Littell). 

http://support.sas.com/resources/papers/proceedings11/325-2011.pdf

Many thanks again. With all the informations upto here

I should like to begin another discussion in this community. 

“The acronym GLIM, how read it correctly” 

Viewers could please follow and give any possible advices kindly.

A last message of mine around (2014.10.18) is deleted now.

That is correctly included in this message. Tadao SHIBAYAMA (2014.12.06)