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GLM models allow us to build a linear relationship between the response and predictors, even though their underlying relationship is not linear. This is made possible by using a link function, which links the response variable to a linear model.

The link function provides the relationship between the linear predictor and the mean of the distribution function. There are many commonly used link functions, and their choice is informed by several considerations.

The Gamma Regression tool relates a gamma-distributed, strictly positive variable of interest (target variable) to one or more variables (predictor variables) that are expected to have an influence on the target variable.

The link function connects the random and systematic (non-random) components of a GLM: the random component specifies a probability distribution for XY while the systematic component relates a parameter ? to predictors (inputs) X. The link function ?links? these components 1.

The commonly used links for the Gamma family are. Inverse: ? = 1/µ Log: ? = logµ Identity: ? = µ The inverse is the canonical link. The log link is constraint-free. The deviance of a fitted Gamma model is given by.

Link Function To define a regression model using the GEE methodology, one needs to define the following: The distribution of the dependent variable (which must be a member of the exponential family) The link function. The independent variables. The covariance structure of the repeated measurements.

In the case of Poisson regression, the typical link function is the log link function. This is because the parameter for Poisson regression must be positive (explained later). The last component is the probability distribution which generates the observed variable y.