IAI Actuarial Core Principles · Actuarial Statistics · Generalised linear models
A Poisson GLM with log link for claim frequency, fitted by a Mumbai insurer, gives a coefficient of 0.20 for vehicles in the 'urban' zone relative to the 'rural' base level, with other factors unchanged. Using e^0.20 = 1.221, what is the estimated percentage increase in expected claim frequency for urban relative to rural?
The estimated increase is 22.1%. In a log-link model the coefficient is on the log scale, so the urban relativity is e^0.20 = 1.221 times the rural frequency. This is a 22.1% rise, not the 20% obtained by reading the coefficient directly.
- A20.0%
- B2.0%
- C22.1%Correct
- D12.2%
- 122.1%
Explanation
With a log link the relativity is exp(0.20) = 1.221, so frequency is 22.1% higher. Reading the coefficient directly as 20% ignores the exponential, which is the main error.
Did you get it right without looking?
One question tells you little. A timed set on Generalised linear models shows your real accuracy, how long you take and where you lose marks.
More Generalised linear models questions
- Y is distributed as an exponential family member with b(θ) = −ln(−θ) for θ < 0 and φ = 1/ν for a constant ν > 0. Using E(Y) = b'(θ) and Var(…
- Two nested Poisson GLMs for claim counts are fitted to the same data. Model A (5 parameters) has deviance 312.4. Model B (8 parameters) adds…
- A Poisson GLM with log link is fitted to claim counts. The null model has deviance 180.4 on 99 degrees of freedom. After adding 3 rating fac…
- A Poisson GLM with log link has fitted coefficient 0.18 for a binary factor (1 = urban, 0 = rural), other covariates equal. By what percenta…
- A logistic GLM models the probability that a policy lapses. The fitted linear predictor for a particular policyholder is -1.5. What is the e…
- 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 e…