Combining Linear and Non Linear Modeling Techniques

Combining Linear and Non-linear Modeling

TechniquesEMB America + Salford SystemsGetting the best of Two Worlds

Who is EMB?

Insurance industry predictive modeling applications

EMBLEM- our GLM tool

How we have used CART with EMBLEM

Case studies

Other areas of expected synergies

Outline

Global network of p&c insurance consultants servicing clients throughout the world

(insert globe)

EMB Worldwide

Predictive Modeling Ratemaking & Profitability Analysis Underwriting & Credit Scoring Enterprise Risk Management, Pro Forma, Business

Planning Retention & Conversion Modeling New Program Development Competitive Analysis Reinsurance Program Analysis Reserve Analysis & Opinion Letters Software Development & Software Support Expert Witness Testimony Regulatory Support & Law Analysis

Consulting Services Offered

EMB’s suite of software products cover all aspects of personal and commercial lines of insurance◦ EMBLEM◦ Rate Assessor◦ Classifier ◦ Igloo Professional◦ ExtrEMB◦ ResQ Professional ◦ PrisEMB◦ RePro

State-of-the-Art Software

We use EMBLEM, a GLM tool, for our predictive modeling needs

Why?

EMBLEM

Primary application:◦ Estimating the cost of the product they sell (insurance) two steps:

Reserving= estimating the cost of outstanding insurance claims Pricing= estimating the cost of future insurance coverage

Secondary applications◦ Retention Modeling= probability that a policyholder will renew

◦ Conversion Modeling= probability that a prospective policyholder will purchase a policy

◦ Price Optimization

◦ Claim fraud detection

◦ Marketing

Predictive Modeling in the Insurance Industry

Goal is to develop a unique rate for every risk◦ Don’t think in terms of good/bad risks

◦ State Farm/Allstate vs GEICO/Progressive

◦ Quickly exhausts the data Credibility/ variability/ stability

Risks are described by the predictor variables, not the target.◦ Need to have a mapping of the predictor variable levels to a target

value- not the other way around

Other way around makes it difficult to derive impact of individual predictor variables

Important because actual data often does not describe all possible combinations of potential customers

Estimating the Cost of Insurance

Highly regulated marketplace◦ Restrictions

Predictors can and cannot use Credit scores

Rules on values for the predictors Ages 65+ relativities cannot be >110% of ages 40-60 Maximum rate change between adjacent territories

Rules on predictor order and magnitude of importance CA Sequential Analysis (driving record>annual mileage>years held license)

◦ Regulatory Approval Rates need to be supported

Black box methodologies will not be accepted

Estimating the Cost of Insurance

Response variable is continuous/discrete function

(insert graph)◦ Gamma consistent with severity modeling, or even Inverse Gaussian

(insert graph)◦ Poisson consistent with frequency modeling

No single trial/outcome◦ Trial is measured in terms of time

◦ Actual policy length varies tremendously because of changes Marital status New car moved

Estimating the Cost of Insurance

In 1996, EMB designed EMBLEM to provide access to GLM for statisticians and non-statisticians pricing personal and commercial insurance

EMBLEM revolutionized the use of GLM’s, enabling analysis that was previously either impossible or too time-consuming to be worth attempting

EMBLEM is now used by over 100 insurance companies globally:◦ 18 of the top 20 personal auto writers in the UK◦ 50 companies in the US including 8 of the top 10 personal auto writers

Fastest GLM tool with the capability to model millions of observations in seconds with a host of diagnostic tools:◦ Graphical, practical, statistical, automated.

◦ Stand-alone software package that can be integrated with a variety of external software including SAS®

◦ Microsoft® Visual Basic® for Applications provides ultimate flexibility

Solution? EMBLEM

GLM characteristics work to our advantage◦ Exponential family does an excellent job of describing

the underlying components of insurance losses

◦ Output of the model is in the form of Beta parameters which can easily be converted to rate relativities

◦ EMBLEM is not automated User has complete control over the model structure

Complete diagnostic tools to assist the modeler with decisions

EMBLEM

In terms of estimating the cost of insurance:◦ UK has embraced predictive modeling

Experienced with its techniques

Knowledgeable with the factors that tend to be predictive

◦ US is learning about predictive modeling Saturation with big players in personal lines marketplace

Companies not using predictive modeling techniques are being adversely selected against

Now expanding dimensionality of databases

Still fairly new concept in commercial lines marketplace

Big players are using techniques but historical rating structures are hindering the rapid expansion

Current Status in Insurance Marketplace

Result?◦ UK is expanding into secondary applications

Retention modeling

Conversion modeling

Price optimization

Claim fraud detection

◦ Because Predictive Modeling has been around for some time in the UK, the datasets are getting larger in terms of the number of predictors to evaluate

◦ Experienced US companies are beginning to evaluate the secondary applications

◦ Marketing is used in a manner similar to other industries

Current Status in Insurance Marketplace

How does CART fit into this?◦ As we transition into the secondary applications we move from

modeling a continuous function to a binary function

Tree-based techniques can add value to the analysis

Retention and Conversion modeling◦ Accept/ Reject target variable

◦ Desirable smooth surface

◦ Price optimization integrates these with premium models

Marketing and Fraud detection ◦ Classic tree applications

CART

Using CART and EMBLEM◦ Goal is to play off of the strengths of each tool

CART strengths◦ Automatic separation of relevant from irrelevant predictors

◦ Easily rank-orders variable importance

◦ Automatic interaction detection (requires additional work)

◦ Captures multiple structures within a dataset rather than a single dominant structure

◦ Can handle missing values and is impervious to outliers

CART and EMBLEM

EMBLEM Strengths

◦ User has control over the model structure

◦ Ease of communication/conceptualization- effects of each explanatory variable is transparent

◦ Provides predicted response values for new data points

CART and EMBLEM

CART◦ Factor selection

◦ Interaction detection

◦ Model validation

EMBLEM◦ Model structure

◦ Incorporating time/seasonality trend effects

◦ Implementation of results

CART and EMBLEM

Both CART and EMBLEM are excellent tools both of which produce consistent results in similar situations

◦ This is not an exercise of seeing which is better

The purpose of this discussion is to show how efficiencies can be gained in the modeling process

◦ As datasets get larger in terms of the number of predictors time becomes a crucial element

Speakers Note

Retention modeling assignment

◦ 97,227 observations

Each observation represents one trial/outcome

Split 50/50 between training/test datasets

◦ 11 predictors

Grand total number of levels:147

Case Study #1- US Dataset

Modeling Process◦ Started with Forward Entry Regression

Automated process Used Chi-Squared statistic for testing significance Took about 30 minutes to run

◦ Significant factors (8)

Rating Area Vehicle Category Age NCD Driver Restriction Vehicle Age Change Over Last Year’s Premium Market Competitiveness

Case Study # 1

Build a model with no factors and add based on prespecified criteria regarding improvement in model fit:

(insert table)

Add the factor that performed the best on the Chi Square test. (Policyholder Age)

Iterate process with the new base model until no further factors indicated removal

Forward Entry Regression

Compared results with CART/ TreeNet

◦ Significant factors were essentially the same

◦ Model predictiveness was the same (ROC=0.7)

Interactions

◦ No significant interactions were found by EMBLEM or CART

Test Dataset

◦ ROC=0.7

Case Study #1

Retention modeling assignment

◦ 198,386 observations

Each observation represented one trial/outcome

Split 50/50 between training/test datasets

◦ 135 predictors

Grand total number of levels: approx 3,752

Case Study #2- UK Dataset

Forward Entry Regression◦ Found 57 predictors to be significant

◦ Took a weekend to run

Comparison to CART/ TreeNet◦ Found 24 significant predictors

◦ Top 15 based on variable importance were also found by EMBLEM

◦ Correlations with the rest of the predictors

Through the modeling process we reduced the number of predictors to 26

Case Study #2

Interactions

◦ We relied on indications from CART/ TreeNet

◦ 6 interactions were identified and included in the model

EMBLEM Results

◦ Training ROC= .862

◦ Test ROC= .85

Case Study #2

Variable importance

Segmentation

Super-Profiling

Other Expected Synergies

CART excels at identifying different segments in data

CART may also help determine where to segment data

Segmentation is a useful alternative to fitting many interactions

◦ Example: In a automobile insurance renewal problem, a CART analysis showed several occurrences of a split between those policyholders with just one years duration and those with a greater duration

This suggests segmenting the data into two parts:◦ Policies renewing with one year duration

◦ Policies renewing with more than one year

Segmentation

After a GLM model is constructed use CART to model the residuals to see if any patterns exists

◦ If a pattern is discovered, go back to the model structure and incorporate the findings

◦ Test to see if model structure was inadvertently over-simplified

Super-Profiling