GLM

Question 1

Model Specifications

Answer 1

Target Variable
Predictors
Link Function
Error Distribution
Weights

Question 2

Why log continuous variables when using log link?

Answer 2

Otherwise positive coefficients will result in exponential effect on target

Question 3

When to use weights

Answer 3

If rows in dataset represents an average for multiple data points

Question 4

When to use offsets

Answer 4

1. Variable modeled elsewhere (territory model, deductible, limits)
2. Want to change only some variables in rating plan
3. Target variable varies directly with exposure (e.g. modeling claim counts)

Question 5

Correlated Vars (How Identify and Adjust)

Answer 5

Identify with two-way correlation table

Can adjust with principal component analysis

Question 6

Multicollinearity

Answer 6

When 2 or more predictors strongly predictive or a third

Two-way tables may not show

Identify with Variance Inflation Factor

Question 7

Aliasing

Answer 7

Perfect correlation
Must remove one

Question 8

Effects of highly correlated variables

Answer 8

Unstable Model (large std errs)
Unreasonable coefficients
Model may not converge

Question 9

GLM Limitations

Answer 9

Assign full credibility to data
Alt: GLMMs or Elastic Net GLMs

Assume randomness of outcomes uncorrelated
(Untrue if multiple years of data or cat risk)

Question 10

Freq/Sev Models vs PP

Answer 10

More stable

PP can overfit if variable only affects one or other

Tweedie dist assumes freq/sev move in same direction

Question 11

Target Variable Considerations

Answer 11

Split coverages, perils
Capping
Remove CATs and model separately
Trend/Develop
On-Level Premium

Question 12

Predictor Selection Criteria

Answer 12

Significance
Cost of collecting
IT constraints
Regulatory requirements

Question 13

Partial Residual Plots

Answer 13

Detect non-linearity

Question 14

Correcting Non-Linearity

Answer 14

1. Binning
2. Polynomial terms
3. Piecewise
4. Splines

Question 15

Loglikelihood

Answer 15

How well model explains data

Con: Requires identical dataset

Question 16

Deviance

Answer 16

How far model is from saturated model

Want unscaled to compare different models

Cons:
-Need to assume same error dist. in models
-Always decreases when add more params so overfits

Question 17

F-Test

Answer 17

Only for nested models

Question 18

AIC and BIC

Answer 18

Can compare any models

BIC over-penalizes large datasets

Question 19

Working Residual Plots

Answer 19

vs Linear Predictor (look for systemic over/under prediction)

vs One Predictor (look for non-linearity)

vs Weight (look for homoscedasticity)

Question 20

3 Ways to Assess Model Stability

Answer 20

1. Cook’s Distance (influential records)
2. Cross-Validation (consistent param estimates - not good for insurance when more manual intervention needed)
3. Bootstrapping (consistent param estimates)

Question 21

Quantile Plot

Answer 21

How well model differentiates between best and worst risks

Quintiles by prediction. Then plot actual vs predicted

Want:
Actual close to predicted
Actual increasing monotonically
Large lift from actual endpoints

Question 22

Double Lift Chart

Answer 22

Compares two models directly

Quintiles by A/B. Then plot actual, A, B

Want model that’s closer to actual

Harder to interpret since compares where models disagree most

Question 23

Loss Ratio Chart

Answer 23

Whether model better at segmenting than current

Sort by Predicted LR. Plot actual LR

Want more spread

Only tells if good at segmenting not predicting

Question 24

Gini Index and Lorenz Curve

Answer 24

Plot cuml % of EE vs cuml % of Loss

Lorenze curve formed by points

Gini Index = 2 * area between curve and y=x

Question 25

ROC Curve

Answer 25

Used for logistic models 1-Specificity vs Sensitivity AUROC higher better (no predictive power is y=x or .5)

Question 26

Specificity

Answer 26

True Neg/Total Negative

Question 27

Sensitivity

Answer 27

True Pos/Total Positive

Question 28

Why shouldn't model ILFs or Deds

Answer 28

Policy Options chosen by insured May give counterintuitive results Never charge more for less coverage Correlation with results but not causation

Question 29

Ensembling

Answer 29

Averaging models together Improves performance when errors uncorrelated

Question 30

GLM Shortcomings

Answer 30

1. Predictions must be based on linear function of predictors 2. Instability if data thin or highly correlated vars 3. Full credibility for each predictor coefficient 4. Assumes randomness uncorrelated 5. Dispersion param must be constant

Question 31

GLMM

Answer 31

Allows credibility in coeff estimates Fixed and random effects

Question 32

DGLMs

Answer 32

Allows different dispersion parameters

Question 33

GAMs

Answer 33

Allows non-linearity without manual intervention

Question 34

MARS Models

Answer 34

Allows non-linearity without manual intervention

Question 35

Elastic Net GLMs

Answer 35

Allows credibility in coeff estimates Automatic variable selection

Question 36

Why center continuous variables

Answer 36

Intercept more intuitive since meaningful base case Makes signs of coefficients more intuitive

Question 37

Working Residual Advantages

Answer 37

Retain properties after binning (no pattern and homoscedastic)