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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

For a fitted binomial GLM with grouped data, the residual deviance is 24.0 on 10 degrees of freedom. Which interpretation is most appropriate?

With grouped binomial data, the residual deviance is approximately chi-squared on the residual degrees of freedom if the model is adequate. A value of 24.0 exceeds the 5% point of 18.31 for 10 df, indicating lack of fit or overdispersion.

  1. AThe model fits well because the deviance exceeds the degrees of freedom
  2. BThe deviance is above the 5% chi-squared(10) point of 18.31, suggesting lack of fit or overdispersionCorrect
  3. CThe deviance is below the chi-squared(10) point, so the model is adequate
  4. DThe deviance must be compared with chi-squared on 24 degrees of freedom
  5. A deviance can only be assessed for ungrouped binary data

Explanation

For grouped binomial data the residual deviance is approximately chi-squared with the residual df if the model is adequate. 24.0 exceeds 18.31, so there is evidence of lack of fit or overdispersion. The other options misuse the comparison.

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