I need to use a model for my Master's thesis. Looking beyond multiple linear regression, I have found extensions like the general linear model, and the generalized linear model. What is the difference between those?
For what I understood from Wikipedia:
- A multiple linear regression is a linear model, with 1 output and multiple inputs
- A general linear model is a system of multiple linear models, i.e. a (usually matrix) model with multiple outputs
- A generalized linear model (GLM) is an extension of the usual linear model, both simple (one input) and multiple (multiple inputs), where we expect the residuals to follow a distribution not normal, but of any function in the exponential family.
Therefore, there can be models that are only GLM (one output, non normal error), only general (multiple output, normal error), or both (multiple output, non normal error). Moreover, all of the above may have one single input (simple regression), or multiple ones (multivariate/multiple inputs).
Is this right?