Why are "Linear" Models so Important? I am an MBA student that is taking courses in statistics. Yesterday, I attended a statistics seminar in which some graduate students presented their research on some psychology experiments (e.g. response of mice to some stimulus).
The students presented some theory behind the models they used - in particular, they showed us about "General Linear Models" (GLM). I think I was able to follow the general ideas that were discussed. It seems to me that GLM's model some function of the mean instead of directly modelling the mean - this gives GLM's the advantage of being more flexible and versatile in modelling more complicated datasets.

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*The one thing that I couldn't understand however, is that why is the "Linear" part of GLM's so important? Why can't you just use/call it "General Models"?


*When I tried to raise this point in the question and answer period, someone told me that the "Linear" aspect of GLM's allow for "ease in estimation" (i.e. easier "number crunching") compared to "Non-Linear" models and that the "Linear" aspect also allows for easier interpretation of the model compared to "Non-Linear" Models.
I am also not sure what exactly is a "Non-Linear" Model. I would have thought that a Logistic Regression is a "Non-Linear" Model because the output looks non-linear and it can model non-linear relationships, but it was explained to me that any model that can be written "linearly" like "x1b1 + x2b2 + ..." is called a "Linear Model". Therefore, is something like a Deep Neural Network a "Non-Linear Model"?
I couldn't really understand why this is true - can someone please help me with this?

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*GLMs are linear in parameters, that's why “linear”. See also Distinction between linear and nonlinear model and Why is polynomial regression considered a special case of multiple linear regression? for more explanations.

*Why would GLMs be “general models” any more than any other models? You also got the name wrong, it stands for the generalized linear models, because it is a generalization of linear regression. General linear model in fact stands for something else.

*They are important because they are simple, yet versatile. They are easy to interpret, yet very flexible, and often work remarkably well for many problems.

