C.3. Multivariate Classification

Question 1

3 reasons GLMs have grown in popularity

Answer 1

1. Increased computing power
2. Better data availability
3. Competitive pressure

Question 2

Benefits of multivariate methods (particularly GLMs)

Answer 2

1. Properly adjust for exposure correlations
2. Focus on signal and ignore noise
3. Provide statistical diagnostics (CIs)
4. Allow for consideration of interactions between rating variables

Question 3

Adv/disadv of minimum bias procedures

Answer 3

A: properly adjusts for exposure correlation
D: do not provide ways to test for whether variables are statistically significant, also computationally inefficient

Question 4

Sequential analysis

Answer 4

Meh

Question 5

Important steps in solving GLMs

Answer 5

Compiling dataset with enough data for modeling, selecting a link function, specifying distribution of underlying random process, and using maximum likelihood to calculate parameters of the model

Question 6

Why GLMs are usually run of frequency and severity instead of loss ratios

Answer 6

No need to on-level premiums at granular level, a priori expectations of frequency and severity but not loss ration patterns, no standard distribution for modeling loss ratios, loss ratio models become obsolete when rates are changed

Question 7

Common GLM diagnostic tests

Answer 7

Looking at CIs around estimates
Chi-square, F-tests, other tests
Running model on separate consecutive time periods of data to see if parameters are consistent over time
Building model on a subset of historical data and comparing prediction with actual
Judgmental decision

Question 8

Actuaries’ role in GLMs

Answer 8

Obtaining reliable data (GIGO)
Exploring anomalous results in GLM with additional analysis
Considering model results from statistical and business perspective
Developing appropriate methods to communicate model results based on company’s ratemaking objectives

Question 9

Common types of external data used in GLMs

Answer 9

Geo-demographic information
Weather data
Property characteristics
Information about insured individuals or businesses (i.e. credit scores)

Question 10

Data mining techniques

Answer 10

Factor analysis (reduce number or variables needed)
Cluster analysis (combine similar risks into groups)
CART (classification and regression trees): if-then rules
MARS (multivariate adaptive regression spline): turns continuous variables into categorical variables
Neural networks: training algorithms to identify patterns