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Generalized Linear Model (GLM)
Unlike the least-square fitting, generalized linear models use maximum likelihood estimation.  The methods for solving generalized linear model can be classified into three categories according to the error distribution: normal linear model, Poisson regression, and binomial regression.
Normal Linear Model:

A generalized linear model with Normal (Gaussian) errors is used to solve the model equation of the form

,

where are the exploring variables.   The link functions are:

identity link:

log link:

This model uses the maximum likelihood method to solve for the parameters.

Poisson Regression:

A generalized linear model with Poisson errors is used to solve the model equation of the form

,

where are the exploring variables.   The link functions are:

identity link:

log link:

When offset is involved, the model equation would be:

This model uses the maximum likelihood method to solve for the parameters. 

Binomial Regression:

A generalized linear model with Binomial errors is used to solve the model equation of the form

,

where are the exploring variables.   The link functions are:

logit link:

probit link:

This model uses the maximum likelihood method to solve for the parameters.  The odds=log(p/(1-p)) and the odds ratios (OR=exp()) will also be reported on your data sheet.

 

   
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