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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

A GLM with 3 parameters is fitted to 20 observations and has deviance 30.0. Adding 2 further parameters reduces the deviance to 21.0. Assuming a Poisson response (scale parameter 1), which conclusion is correct at the 5% level? (Chi-squared 5% critical value with 2 df is 5.99.)

The drop in deviance of 9.0 is compared with a chi-squared distribution on 2 degrees of freedom, the number of added parameters. Since 9.0 exceeds 5.99, the extra parameters significantly improve the fit and should be retained.

  1. AThe change of 9.0 exceeds 5.99, so the extra parameters significantly improve the fitCorrect
  2. BThe change of 9.0 exceeds 5.99, so the extra parameters should be dropped
  3. CThe change of 9.0 is below 5.99, so the extra parameters are not needed
  4. DThe change of 9.0 should be compared with chi-squared on 5 df
  5. The change of 9.0 should be compared with chi-squared on 17 df

Explanation

The deviance difference 30 − 21 = 9 is compared with chi-squared with 2 df (number of added parameters). 9.0 > 5.99, so reject the simpler model and keep the extra parameters. Using 5 or 17 df uses the wrong degrees of freedom.

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