GLM

Question 1

What is the target variable?

Answer 1

Denoted y, the predicted variable of the GLM. In property casualty, the target variable is typically Claim count, claim severity, Pure premium, or loss ratio.

GLM pg2

Question 2

What two components are assumed to drive the outcome of the target variable in a GLM?

Answer 2

1. The systematic component
2. The random component

GLM pg 2

Question 3

What does the systematic component refer to in the GLM

Answer 3

The systematic component refers to that portion of the variation in the outcomes that is related to the values of the predictors.

GLM pg2

Question 4

What is the random component of a target variable?

Answer 4

The random component is the portion of the outcome driven by causes other than the predictors in our model.

Includes pure randomness and that which may be predictable with additional variables that are not in our model.

GLM pg3

Question 5

In a GLM, what family of distributions is the target variable y assumed to follow?

Answer 5

The distribution is assumed to be a member of the exponential family of distributions

GLM pg3

Question 6

What distributions are included in the exponential family of distributions?

Answer 6

Normal
Poisson
Gamma
Inverse Gaussian
Negative Binomial
Binomial
Tweedie

GLM pg7

Question 7

How can the randomness of the outcome of any particular risk (denoted y_i) be formally expressed?

Answer 7

y_i~Exponential(mu_i, pi)

Exponential is a placeholder for any member of the exponential family

mu_i is the mean of the distribution (record specific)
pi is the dispersion parameter, and is related to the variance (but is not the variance)

GLM pg3

Question 8

What are some advantages that multiplicative models have over other rating structures?

Answer 8

• They are simple and practical to implement
• Having additive terms in a model can result in negative premiums
• A multiplicative model has more intuitive appeal

GLM pg5

Question 9

What is the definition of the standard error of each coefficient in the GLM?

Answer 9

The standard error is the standard deviation of the random process from which the coefficient is estimated

GLM pg8

Question 10

How are p-values and confidence intervals related?

Answer 10

The confidence interval is the range of values that would not be rejected at the chosen p-value.

GLM pg9-10

Question 11

What is the p-value of an estimate?

Answer 11

The p-value is an estimate of the probability of a value of that magnitude or higher arising by pure chance.

GLM pg9

Question 12

What are two types of predictor variables?

Answer 12

1. Continuous variable - a numeric variable that represents a measurement on a continuous scale, e.g. age, amount of insurance
2. Categorical variable - a variable that takes on one of two or more possible values, assigning a category

GLM pg 10