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IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models

A Bernoulli GLM with logit link and only an intercept is fitted to 40 policies, of which 10 lapsed (y = 1). What is the maximum likelihood estimate of the intercept beta0?

The estimate is minus log 3. The maximum likelihood estimate of the lapse probability is 10/40 = 0.25, so the odds are 1/3, and the logit intercept is log(1/3), which equals minus log 3.

  1. Alog(3)
  2. B-log(3)Correct
  3. Clog(0.25)/2
  4. D0.25
  5. -log(4)

Explanation

The MLE of p is the sample proportion, 10/40 = 0.25. The logit is log(p/(1-p)) = log(0.25/0.75) = log(1/3) = -log 3. The option 0.25 is the probability, not the logit, and -log 4 uses 1/4 as the odds.

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