# Longitudinal analysis

#### noetsi

##### Fortran must die
I am reading a book on medical analysis using SAS. These questions relate to longitudinal analysis. During a signficant section of the book they use Generalized Linear Models to measure impact on the DV by IV - for longitudinal data. I don't understand how you can use GLM (or regression generally other than specialized forms that adress autoregressive error such as ARDL models) for that. Can you?

An example is when you have a group score before and after some treatment. A related question is, is there a regression equivalent of repeated measure designs in ANOVA? Regression usually assumes independence, but since ANOVA uses specialized t test which do not assume indepence I assume regression can as well.

But I don't know any regression equivalent of repeated measure designs.

#### Miner

##### TS Contributor
One of my MBB instructors in Six Sigma (a long time Kodak statistician) told us that you could analyze anything with regression that you could with ANOVA plus a lot more that you cannot do in ANOVA. I have been able to duplicate any ANOVA that I have done using regression, so it typically boils down to preference and which has the better output from the software. For Repeated Measures studies, I have to use GLM (which uses regression behind the curtain) as Minitab does not have an RM-ANOVA.

#### noetsi

##### Fortran must die
Since ANOVA and Regression are both the same method done in different ways (largely for historical reasons as they were developed in different fields) I am sure you can in theory do anything in one you can in the other. I was just not sure how. It appears that one way, which I found out after I asked this, is linear mixed effects models a form of GLM I think.

#### Dason

##### Ambassador to the humans
is linear mixed effects models a form of GLM I think.
No. GLMs don't contain random effects so linear mixed models aren't a special case of GLMs.

#### noetsi

##### Fortran must die
That's interesting dason. I had never seen random effects used in GLM, but I assumed it was something I had not run into. Since ANOVA is (I think) a form of GLM and ANOVA has random effects in some versions, how does that work?

#### Jake

##### Cookie Scientist
Basically we have LM (the classical linear model). And then we have two models that both generalize LM but do so in different ways: GLM (generalized linear model) generalizes LM by allowing non-normal responses, and LMM (linear mixed models) generalizes LM by allowing both fixed and random effects, which is one way to relax some of the independence assumptions in LM. Both of these (GLM and LMM) are subsumed under the family of models known as GLMM (generalized linear mixed models), which can have fixed and random effects and also non-normal responses.

#### GretaGarbo

##### Human
That's interesting dason. I had never seen random effects used in GLM, but I assumed it was something I had not run into. Since ANOVA is (I think) a form of GLM and ANOVA has random effects in some versions, how does that work?
Hmm! Although I agreed with Dason above, I guess that we have to agree that Noetsi is right about this one.

Since, in the old fashioned anova, there was a model with random effects, and that was a part of the general linear model, and thus also a part of a generalized linear model - a GLM, then GLM has random effects.

But maybe that is "old school". And now days GLM:s are only thought of as model with fixed effects. And if there are any random effects it would be called a "generalized linear mixed model". (In the old books it was called a "fixed effect model", "a random effect model" and "a mixed model" if it had both fixed and random effects.)

So maybe the nomenclature changes.

#### noetsi

##### Fortran must die
Nomeclature (and the lack of standardization in it between authors) is to me one of the frustrating elements of statistics. It is difficult enought without different authors using different terms for the same thing or the same term for different things.