Ch 18: GLM

Question 1

One-way analysis

Answer 1

• Looks at the frequency and severity of each rating factor separately.
• Ignores correlations and interaction effects between variables, as a results the model may underestimate or double count the effects of variables.

Question 2

When should an interaction term be used in the GLM?

Answer 2

• Should be used where the pattern in the response variable is better modelled by including extra parameters for each combination of two or more factors
• Interaction exists when an effact of one factor depends on the value of another factor.

Question 3

Drawbacks of simple linear regression

Answer 3

• Assumes the response variable is normally distributed, which may not be appropriate
• The normal distribution has constant variance which may not be appropriate for the variable beoing modelled (for example variance of claims increase as claim numbers increase - poisson distribution has this property)
• Normal model ‘adds’ together the effects of different explanatory variables, but is seldom what is observed in practice, effects may be multiplicative rather than additive
• More difficult to find solution where there is more thna 2 explanatory variables

Question 4

Advantages of GLM over simple regression

Answer 4

• Response can take any distribution from the exponential family
• Link function is introduced, acts to remove the assumption that affects of different variables must be added together
• Additionaly allow for an offset term

Question 5

Properties of exponential family of distributions

Answer 5

• Distribution is completely specified in terms of its mean and variance
• Variance of the response is a function of its mean

Question 6

Why tweedie distribution is nice for modelling claims experience

Answer 6

• Variance proportional to mu^p (p is additional parameter)
• If p is selected between 1 and 2, the distribution has a point mass at zero
• Distribution corresponds to the compound distribution of a Poisson claim number process and a gamma claim size distribution

Question 7

What does chi-squared test measure?

Answer 7

Measures whether the inclusion of one or more additional explanatory variables in the model improves the model fit significantly