A2. GLM

Question 1

Advantage of using log link function for rate making

Answer 1

1. Simple and practical to implement
2. Guarantee positive premiums
3. impact of risk characteristics is more intuitive

Question 2

2 uses of offset terms

Answer 2

1. incorporate pre-determined values for certain variables
2. when target variable varies directly on a particular measure

Question 3

2 solutions to deal with correlation

Answer 3

1. remove all except one (but could lose unique info)
2. Dimensionality reduction technique like PCA/Factor analysis (but takes additional time)

Question 4

Problem with correlations among variables

Answer 4

could produce unstable model with erratic coefficients that have high standard error

Question 5

2 uses of weight assigned to each observation

Answer 5

1. when an observation can obtain grouped information
2. when different observations represent different time periods

Question 6

define multicollinearity

Answer 6

nearly perfect linear dependency

Question 7

how to detect multicollinearity

Answer 7

use VIF (variance inflation factor) to detect
VIF >=10 considers high

Question 8

define aliasing

Answer 8

perfect linear dependency
GLM will not converge

Question 9

2 GLM limitations

Answer 9

1. GLMs give full credibility, even to low volume of data or high volatility
2. GLMs assume that randomness of outcomes are uncorrelated (renewal of the same policy, weather events)

Question 9

4 Advantages of modeling frequency/severity over pure premium

Answer 9

1. gains more insights and intuition about impact of each predictor variable.
2. each of frequency and severity separately is more stable
3. pure premium modeling can lead to overfit if a predictor variable only impact frequency or severity but not both.
4. Tweedie distribution for pure premium model assumes both frequency and severity move in the same direction (which may not be true)

Question 10

2 disadvantage of modeling frequency/severity over pure premium

Answer 10

1. require more data
2. take more time to build 2 models

Question 11

4 ways to transform variables in GLM

Answer 11

1. binning the variable (increase df, more things to estimate which may lead to overfit, may result in inconsistent or impractical pattern, variation within bins is ignored)
2. Add polynomial terms (loss of interpretability without a graph, higher order polynomials can behave erratically at edges of the data)
3. Add piecewise linear function (adding hinge function max (0, Xj-C) at each breaking point C, Breaking point C must be manually chosen)
4. Natural Cubic Splines (combines piecewise function and polynomials, results in continuous curve but fits edges of the data better, but need graph to interpret model)

Question 12

Why is model selection different from model refinement

Answer 12

1. some model may be proprietary
2. decision on final model may be a business decision not a technical one

Question 13

3 methods to test model stability

Answer 13

1. Cook’s distance for individual record (high cook’s distance should be given additional scrutiny to whether include or not)
2. Cross-validation comparing in-sample parameter estimates
3. Bootstrapping to compare mean and variance

Question 14

4 Lift based measures

Answer 14

1. simple quintile plot
2. double lift chart
3. loss ratio charts
4. Gini index

Question 15

Describe double lift charts

Answer 15

Calculate sort ratio (sort ratio = model 1 predicted loss cost / model 2 predicted loss cost)
Sort and bucket
Calculate average predicted loss cost for each model in each quantile and average actual loss cost. divide each by the overall average loss cost and plot.
Winning model: one that best matched the actual in each quantile

Question 15

describe simple quintile plot

Answer 15

Sort data based on predicted loss costs
Then bucket into quantiles with equal exposures
Calculate average predicted loss cost & average actual loss cost for each bucket and graph
Winning model: Predictive accuracy, look at the difference between actual and predicted. Monotonicity, the actual pure premium should increase.
Vertical distance of actual loss cost between 1st and last quantile should be large

Question 16

Describe loss ratio charts

Answer 16

Sort based on predicted LRs
Bucket into quantiles with equal exposures
Calculate the actual LRs for each quantile & plot
The greater vertical distance between the lowest and highest LR, the greater the model at identifying further segmentation opportunities not present in the current rating plan.
LR is monotonically increasing for each quantile
This is the most easy one to understand

Question 17

Describe Gini index

Answer 17

ability to identify the best and worst risk
Sort holdout dataset based on the predicted loss cost.
Plot x as cumulative percent of exposures. y as the cumulative percent of actual loss
The curve formed is the Lorenz Curve.
Compare it with the line of equality
The area between the Lorenz Curve and Line of equality is called the Gini Index
The higher Gini Index, the better

Question 18

Sensitivity formula

Answer 18

true positive/total event occurrences

Question 19

Specificity formula

Answer 19

true negatives/total event non-occurrences

Question 20

Partial Residual formula

Answer 20

ri = (yi - mui)* g’(mui) + BetajXij

Question 21

Scaled Deviance formula

Answer 21

2*(loglikelihood from saturated model - Loglikelihood from the model)

Question 22

Unscaled Deviance formula

Answer 22

Dispersion parameter x scaled deviance

Question 23

F statistics

Answer 23

[Unscaled deviance(small) - Unscaled deviance(big)]/ [# of parameters added) x dispersion parameter,big]

Question 24

degree of freedom of F statistics

Answer 24

df of the numerator: # of parameters added
df of the denominator: # of observations - # of parameters in the big model

Question 25

working residual formula

Answer 25

wri = (yi-mui) * g’(mui)

Question 26

how does binning working residual work

Answer 26

Binning to reduce cluster in scatterplot
working weights = wwi = wi// ( V(mui) [g’(mui)^2]
Binning working residuals: weighted average of working residual based on working weights

Question 27

Model building process

Answer 27

1. set goals & objectives (such as purpose, time frame, resources)
2. communicate with key stakeholders to identify the requirements and concerns
3. Collect and process the data
4. Exploratory data analysis
5. Specify the form of the model
6. Evaluate the model output
7. validate the model by testing it using a holdout dataset and pick optimal model
8. translate the model results into a product
9. maintain and rebuild

Question 28

Merging policy and claim data considerationa

Answer 28

1. matching claims to specific policy
2. check for timing difference, when each data is updated
3. is there an unique key to merge
4. level of aggregation, time dimension (PY vs. CY)
5. fields not needed or missing

Question 29

things to check when cleaning the data

Answer 29

1. remove duplicates
2. check categorical fields against documentation
3. Reasonability of numerical fields
4. How to handle errors or missing variables
5. convert continuous variable into categorical?