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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

Two nested Poisson GLMs for claim counts are fitted to the same data. Model A (5 parameters) has deviance 312.4. Model B (8 parameters) adds three rating factors and has deviance 298.1. The 5% critical value of chi-squared with 3 degrees of freedom is 7.81, and with 8 degrees of freedom is 15.51. Which conclusion is correct?

The extra factors significantly improve the fit. The deviance difference is 312.4 minus 298.1, equal to 14.3, compared with chi-squared on 3 degrees of freedom. Since 14.3 exceeds the critical value 7.81, Model B is preferred at the 5% level.

  1. ADeviance difference 14.3 exceeds 7.81, so the extra factors significantly improve the fitCorrect
  2. BDeviance difference 14.3 exceeds 7.81, so Model A should be retained
  3. CDeviance difference 14.3 is below 15.51, so the extra factors are not significant
  4. DDeviance difference 610.5 is the test statistic, so Model B is rejected
  5. Deviance difference 14.3 should be compared with chi-squared on 5 degrees of freedom, giving no significant improvement

Explanation

The difference in deviance is 312.4 - 298.1 = 14.3, referred to chi-squared with 8 - 5 = 3 degrees of freedom. Since 14.3 > 7.81, the added factors are significant, so Model B is preferred. Using 8 degrees of freedom is the wrong degrees of freedom.

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