IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
A normal-error linear model is fitted to 12 observations with 3 parameters. Its residual sum of squares is 45. A competing GLM comparison uses the scaled deviance. What is the estimate of the scale parameter σ² commonly used when comparing nested models with unknown scale?
The scale parameter is estimated as the deviance divided by the residual degrees of freedom, 12 minus 3 equals 9. This gives 45/9 = 5.00. Dividing by n would give the biased maximum likelihood estimate instead.
- A45/12 = 3.75
- B45/9 = 5.00Correct
- C45/3 = 15.0
- D45/11 = 4.09
- 45/15 = 3.00
Explanation
The unbiased estimate is deviance divided by residual degrees of freedom: n − p = 12 − 3 = 9. So 45/9 = 5. Dividing by n gives the maximum likelihood estimate, which is biased and not the one used for F comparisons.
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