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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

In IRLS for a Poisson GLM with log link, the working weight for an observation is W = (d(mu)/d(eta))^2 / Var(Y). What is W for an observation with fitted mean mu = 5?

The working weight is 5. With the log link, the derivative of mu with respect to eta equals mu, so W = mu squared divided by the Poisson variance mu, which equals mu, namely 5.

  1. A1/5
  2. B25
  3. C1
  4. D5Correct
  5. sqrt(5)

Explanation

With the log link, mu = exp(eta), so d(mu)/d(eta) = mu = 5. Var(Y) = mu = 5 for the Poisson. So W = 25/5 = 5. The value 1/5 comes from using the derivative of eta on mu rather than of mu on eta.

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