4  Gamma Regression

When to Use and Not Use Gamma Regression

Gamma regression is a type of generalized linear model that is appropriately used under the following conditions:

• The outcome variable is continuous and non-negative as shown in Figure 4.1. Examples include insurance claim amounts, pollutant concentrations, and operational spending. Note that this outcome should not be a count variable.
• Outcomes are statistically independent from one to the next.
• The distribution of the outcome is right-skewed. This means that as the mean of the outcome increases, the variance also increases at a faster rate.
• We intend to use the logarithm of the mean of the outcome as a link function, which ensures that our predictions are always positive.

However, Gamma regression should not be used in the following scenarios:

• The outcome variable includes zeros or negative values.
• The outcome variable is of the count type. In this case, check the Classical Poisson, Negative Binomial, Zero-Inflated Poisson or Generalized Poisson regressions.
• The variance of the outcome increases at a constant rate relative to the corresponding mean.

mindmap
  root((Regression 
  Analysis)
    Continuous <br/>Outcome Y
      {{Unbounded <br/>Outcome Y}}
        )Chapter 3: <br/>Ordinary <br/>Least Squares <br/>Regression(
          (Normal <br/>Outcome Y)
      {{Nonnegative <br/>Outcome Y}}
        )Chapter 4: <br/>Gamma Regression(
          (Gamma <br/>Outcome Y)
    Discrete <br/>Outcome Y

Figure 4.1: Regression analysis mind map depicting all modelling techniques explored so far in this book. Depending on the type of outcome \(Y\), these techniques are split into two large zones: discrete and continuous.