IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
A logistic GLM models the probability that a policy lapses. The fitted linear predictor for a particular policyholder is -1.5. What is the estimated lapse probability, given e^1.5 = 4.482?
The estimated lapse probability is 0.182. With a logit link, p equals 1 divided by 1 plus e^1.5, which is 1/5.482. The figure 0.223 is the odds e^-1.5, not the probability, and 0.818 is the probability of not lapsing.
- A0.182Correct
- B0.223
- C0.818
- D0.250
- 0.150
Explanation
With a logit link, p = 1/(1+e^1.5) = 1/5.482 = 0.182. The value 0.223 is e^-1.5, which is the odds, not the probability.
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