Solved – the difference between ANOVA, Linear Regression, GLM, and GLMM

One of the difficult aspects of statistics that I have found is the nomenclature and terminology being used.

I would like to know what the difference between the following 'techniques' are and examples of when they are most applicable.

Analysis of Variance (ANOVA) Linear Regression Generalized Linear Model (GLM) Generalized Linear Mixed Model (GLMM) 

As an aside, is the term 'linear' referring to the coefficients and not the fact that there can be quadratic or cubic factor effects?


Y = B0 + B1*X1 + B2*X1^2 = B0 + B1*X1 + B2*X2 (where X2 = X1^2) 

As @Tim said in a comment, this is a really broad question. However, it's possible to give a sort of summary, I think:

ANOVA and linear regression are equivalent. The term ANOVA is usually used when the independent variables are categorical. They model a continuous dependent variable (DV) as a linear combination of one or more independent variables (IV). They assume various things, including that the data are independent and that the errors are normally distributed.

Generalized linear models relax the assumption about the dependent variables.

Generalized linear mixed models relax the assumption about independence.

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