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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

A Poisson GLM with log link is fitted to claim counts. The null model has deviance 180.4 on 99 degrees of freedom. After adding 3 rating factor parameters, the deviance is 162.1 on 96 degrees of freedom. Using the chi-square test at 5% (critical value for 3 df is 7.815), which conclusion is correct?

The deviance falls by 18.3 for 3 extra parameters. This exceeds the chi-square 5% critical value of 7.815, so the simpler model is rejected and the added rating factors are retained as significant.

  1. ADifference in deviance is 18.3 on 3 df; reject the null and keep the added parametersCorrect
  2. BDifference in deviance is 18.3 on 96 df; do not reject the null
  3. CDifference in deviance is 18.3 on 3 df; do not reject the null
  4. DDifference in deviance is 342.5 on 3 df; reject the null
  5. Difference in deviance is 9.15 on 3 df; do not reject the null

Explanation

The change in deviance is 180.4 - 162.1 = 18.3, with degrees of freedom change 99 - 96 = 3. Since 18.3 exceeds 7.815, we reject the simpler model and keep the extra parameters. Option 2 uses the wrong df, and option 3 misreads the comparison with the critical value.

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