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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

A Poisson GLM with log link has a coefficient estimate of 0.30 for a vehicle-type indicator with standard error 0.12. Which statement is correct for a Wald test at 5% (critical value 1.96) and the multiplicative effect on the mean?

The Wald statistic is 0.30/0.12 = 2.5, above 1.96, so the effect is significant. Under a log link the mean is multiplied by exp(0.30), approximately 1.35.

  1. Az = 2.5, significant; the mean is multiplied by about 1.35Correct
  2. Bz = 2.5, significant; the mean is increased by 0.30
  3. Cz = 0.4, not significant; the mean is multiplied by 1.35
  4. Dz = 2.5, significant; the mean is multiplied by 0.74
  5. z = 0.36, not significant; the mean is multiplied by 1.30

Explanation

z = 0.30/0.12 = 2.5 > 1.96, so significant. With a log link the multiplicative effect is exp(0.30) = 1.35. Option 2 ignores the log link and option 4 uses exp(-0.30).

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