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GLM


General Notes
 
GLM, or General Linear Models, can be thought of as an extension of Linear Regression and ANOVA methods.  Experiments based on DOE can use GLM methods for their analysis.
 
A model based on GLM has three main aspects
  1. an assumption about the distribution of the response variable (and residuals),
  2. a Link function, and
  3. the model equation giving the form and relationship of the model's explanatory variables.
 
GLM algorithms may use methods based on Least Squares, Maximum Likelihood, or other approaches. 
  • In ANOVA it is common to find an algorithm based on Least Squares, and it is often helpful if sample sizes are equal among treatments (or designed for a particular situation). 
  • In GLM it is common to find Maximum Likelihood methods being employed. 

It is still helpful if sample sizes are equal, or are designed to meet the specific needs of an experiment, but GLM algorithms can account somewhat for imbalance in the data (sometimes resulting in more uncertainty in the form of higher standard errors for model coefficients and wider confidence intervals/bands).

See also Generalized Linear Models (GLZ). 

 

Assumptions
 
The assumptions for GLM models are often the same as for linear regression.  However, they are influenced by the distribution of the response variable (and residuals), among other things.
 


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