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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

Two nested Poisson GLMs are fitted by maximum likelihood to the same data. Model A has 4 parameters and log-likelihood -520.0. Model B has 7 parameters and log-likelihood -514.0. Which statement is correct?

The likelihood ratio statistic is twice the log-likelihood gain, 12.0, on 3 degrees of freedom. Since this exceeds 7.815, the extra three parameters significantly improve fit, so Model B is preferred.

  1. AThe likelihood ratio statistic is 12.0 on 3 df and exceeds the 5% critical value 7.815, so B is preferredCorrect
  2. BThe likelihood ratio statistic is 6.0 on 3 df and is below 7.815, so A is preferred
  3. CThe likelihood ratio statistic is 12.0 on 7 df and is below 14.07, so A is preferred
  4. DThe likelihood ratio statistic is 6.0 on 3 df and exceeds 7.815, so B is preferred
  5. The likelihood ratio statistic is 12.0 on 4 df and is below 9.488, so A is preferred

Explanation

The statistic is 2(-514 - (-520)) = 12.0, with df 7 - 4 = 3. As 12.0 > 7.815, the larger model is significantly better. The other options use a missing factor of 2 or the wrong df.

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