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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

Which statement about the components of a GLM is correct?

The linear predictor is linear in the parameters, and the link function connects it to the expected value of the response, g(μ)=η. The link is not a transformation of the observations, and the response need not be normal.

  1. AThe linear predictor must be linear in the covariates' parameters, and the link function relates it to the mean of the responseCorrect
  2. BThe response must be normally distributed with constant variance
  3. CThe link function transforms the response observations before fitting
  4. DThe linear predictor must be linear in the covariates themselves, so x² terms are not allowed
  5. The link function must always be the identity for the exponential family

Explanation

A GLM requires linearity in parameters, so terms like x² are allowed. The link g relates the mean μ to η, g(μ)=η; it does not transform the observations. The response comes from an exponential family, not necessarily normal.

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