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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

A pricing team fits a Poisson log-link GLM for frequency with model A having deviance 1,250 on 980 degrees of freedom. Adding a vehicle-age factor with 3 extra parameters gives model B with deviance 1,236. At the 5% level (chi-square with 3 df critical value 7.81), which conclusion is correct?

The factor significantly improves the fit. The deviance falls by 14 (1,250 minus 1,236), which is compared with a chi-square with 3 degrees of freedom; since 14 exceeds the 5% critical value of 7.81, the added factor is significant.

  1. ADeviance drop is 14, exceeding 7.81, so the factor significantly improves the fitCorrect
  2. BDeviance drop is 14, below 7.81, so the factor is not significant
  3. CDeviance drop is 14, but compare with chi-square on 980 df so no conclusion
  4. DDeviance drop is 14/3 = 4.67, below 7.81, so not significant
  5. Deviance drop is 1,236 so it is highly significant

Explanation

The difference in deviance is 1,250 - 1,236 = 14, compared with chi-square with 3 df because three parameters were added. 14 > 7.81 so the factor is significant. Dividing by 3 is a wrong adjustment for a chi-square comparison.

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