General vs Generalized Linear Models

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Ninja say what!?!
#1
While defending my thesis yesterday, this difference was pointed out. Surprised that there was actually a difference I wasn't aware of, I've looked it up and understand it better now....but this does make me curious.

How many of you happen to know the difference right now without having to look it up? I'm just wondering if my case is unusual or if this is more prevalent than I thought.
 
#2
While defending my thesis yesterday, this difference was pointed out. Surprised that there was actually a difference I wasn't aware of, I've looked it up and understand it better now....but this does make me curious.

How many of you happen to know the difference right now without having to look it up? I'm just wondering if my case is unusual or if this is more prevalent than I thought.
Yeah, I've run into this problem as well, bummer that it was during your defense! Everything turn out oke?

In a sentence, the general linear model is just the standard linear model form as we all know it Y=AX+E (Where X is the design matrix and A a matrix of parameters ) used in many procedures: ANOVA, ANCOVA ect and fit with OLS (with all normal assumptions). But in generalized linear modeling, the key difference is a relaxation of the OLS; i.e. the errors do not need to follow a normal distribution, but may follow any error model of your choice.

I totally agree with you that the names are not very useful. Lets think of some better names and start a trend, by stubbornly refusing to use the old names:yup:
 

Link

Ninja say what!?!
#3
LOL. Thanks for the thoughts. It wasn't a big problem though since the professors are nice. It turned out rather well though.
 

Dason

Ambassador to the humans
#4
I totally agree with you that the names are not very useful. Lets think of some better names and start a trend, by stubbornly refusing to use the old names:yup:
It'll never work... once things get set it's terribly hard to change.

I did know the difference by the way but I wouldn't have been able to tell you the difference a year and a half ago...
 
#5
Someone asked me once if I knew how to use generalized linear models. I said yes. They then explained their data to me and that their dependent variable was binary. I spend the following couple of days figuring it out : )

SPSS helps, I think.

Congrats.
 
#7
I would have called them linear models and generalised linear models. I've never heard them called general linear models before, but, now I know!
 
#9
Why does the Generalized linear model not have an error term? That is, the function is written as [math]n=X\beta[/math] opposed to [math]n=X\beta+\epsilon[/math]. The most common example I see is the logistic regression example, which makes sense; however, I would like to understand it in a more generalized sense. Does it have something to do with the variance function?
 

Dason

Ambassador to the humans
#10
You don't typically see [math]n[/math] on the left hand side of that equation. It's typically [math]\mu[/math] that gets put there. In a generalized linear model you're modeling the conditional mean of the response given the covariates (the X matrix). Since we can specify a number of different distributions for the conditional distribution it doesn't necessarily make sense to think of it in terms of "mean + error" and instead just think of it as a random response where we know something about the mean.
 

hlsmith

Omega Contributor
#11
Yeah I know the difference, but like Dason, there was a time when I would have figured they were the same thing. Statistics seems saturated in confusing terms, since so many fields depend on them. I actually took a generalized course before graduating (in a stats department, not my own), so I lucked out there. I always think of it as a fewer assumptions approach.


Recently, I have been hearing more and more about how you ideally want to make the fewest assumptions you can about your data, which can help with avoiding model miss-specification. This seems to push one more towards non-parametric approaches (e.g., non-parametric bootstrapping, etc.).
 

hlsmith

Omega Contributor
#13
Well, I haven't given this tremendous thought, but the ability to use say sandwich estimators. It was my feeling that once you 'give-up' and use such approaches you are departing from general regression and making I guess different assumptions (perhaps not as stringent).