By David R. Clark. Generalized Linear Models (GLM) are a standard tool for insurance classification ratemaking. This paper provides an intuitive way of understanding the GLM in terms of weighted averages. More on eforum.casact.org

Generalized linear models are generalizations of linear models. In stats, generalized means that it includes the main idea as a case, but includes many other cases. For instance, the Weibull Distribution is a generalized exponential distribution because it includes the exponential distribution as a special case (k=1). When the errors are assumed to be Normal, then GLMs are exactly the same as linear models. The great thing about GLMs is that they can include many other types of regression, such as logistic regression or poisson regression, by changing the link function and the distribution of the errors. As a final note, I very rarely hear the term "general" linear regression. Its usually just called linear regression. I can't think of a situation where you would need to specify that it's general. More on reddit.com

First, you need to know about generalized linear models. You use these instead of linear models when the target variable is not a linear function of the predictors, such as when the target is binary (yes or no), count of occurrences in a fixed period of time, etc. As a simple example, suppose I was trying to model whether or not someone's next phone purchase would be an iPhone. I would count yes's as 1 and no's as 0 and for each case my model would fit the likelihood of that person's purchasing an iPhone. This is not linear. First of all, the output is bounded between 0 and 1. Second of all, the slope is not constant. If a predictor was number of previous iPhone purchases, the difference in likelihood of purchasing between 1 previous purchases and 2 would be huge while the difference between 7 and 8 would be quite small (nearly 100% to nearly 100%). Using a GLM, you get a number as a linear function of the predictors, then you transform it to be between 0 and 1. This is what the link function does. Read the wikipedia on GLM's: http://en.wikipedia.org/wiki/Generalized_linear_model . There is a table in the middle which tells you which link function to use for the different shapes of the target variable. Next, you need to learn about mixed effects - fixed effects and random effects. Fixed effects coefficients are treated as though their coefficients are non-random. Random effects are treated as though their coefficients are random. Suppose I was modeling the number of fouls called in a basketball game based on the teams involved, referees, etc. I would probably specify the categorical variable of which referee is reffing each game as a random effect. We assume the propensity of the refs to call fouls is randomly distributed among the refs (usually for random effects, you assume a normal distribution). The random effects model will result in a more conservative estimate for the effect of each ref because it assumes extreme propensities to call fouls are unlikely. We would use fixed effects if we were looking at a few specific refs. If a ref was accused of cheating (calling lots of fouls to increase the point totals of games), we would not assume his propensity to call fouls came from the same distribution as the other refs, so we would use a fixed effect. This variable would be whether he was the ref or not and we would drop the random effects categorical variable. In this case, the model would assume his propensity to call fouls was whatever best fit the data. In general, you use fixed effects when the different classes of a categorical variable were chosen manually and their coefficients are of interest to you and you use random effects when you have lots or all classes of a categorical variable and you don't care about each class's specific coefficient. A mixed effects model has fixed and random effects. One final example, I want to model the likelihood of a person being cured of a disease based on the doctor and treatment method to find which treatment method is best. This is a GLMM. It is generalized because I'm predicting a probability. It is mixed because it has fixed and random effects. The fixed effect is which treatment - I have selected which treatments are of interest to me and I want to see which does best. The doctor variable is a random effect - there are a lot of doctors, some are better than others, I don't care how good each doctor is (in this case), I just want it to be accounted for in the model. More on reddit.com

It's like guess and check... using computers. More on reddit.com