Yes you can do something but I would need to know more about your DV to say exactly what. I will include an example of our recent work to give you some idea of what our group does. Best, D. Booth

Dear David Eugene Booth,

Thank you very much for the reply. In this hypothetical example of mine, my dependent variable is of binary nature, of course, but my question is a general one. What should I call such a model? Is it a glm with a AR(1) covariance structure or a simply a gls? I need to know this because I need it for reporting the outputs of the regression. Thanks in advance.

Not AR(1) because dependence isn't thru the DV, binary DV makes it a logistic regression, Looks like a repeated measure on Group All of this makes a longitudinal model using logistic regression. BTW all regression models have a cov structure. Best, D. Booth By the way we can model tons of different error distribution.

David Eugene Booth , thank you for taking your time to reply, sir. What should I call the model below then? Is it a glm with AR(1) covar structure now? Group here is the same for all observations; there is only a single time series.

model

I would call it a longitudinal generalized linear model. You might find these notes useful:

https://www4.stat.ncsu.edu/~davidian/st732/notes.html

Multivar. Long. Models:

https://www.researchgate.net/post/What_statistical_test_is_appropriate_for_pre_and_post_trails_with_1_before_treatment_value_and_4_after_treatment_values_assessed_weekly

best, D. Booth

Agreed with @ David Eugene Booth