Workshop on the Foundations:
Regression with Actuarial Applications

VIII Simposio Internacional de Actuaria

About the Workshop

Modern machine learning tools are founded on classical regression principles. Participants in this course will receive an exposure, both theoretical and practical, to regression tools. This course will provide participants with a springboard to further their studies to gain a deep understanding of machine learning approaches.

The format of the course will consist of alternating between presentations of the underlying principles and practical applications. In a typical block, the instructor will spend 45 minutes reviewing the insurance motivation and key mathematical underpinnings. This will be followed by a 45 minute block of time in which participants will actively explore a selected case study. Thus, it is anticipated that participants will bring a laptop with the statistical package R installed to the workshop. (Sharing a laptop with a colleague is also a great way to learn.)

Target Audience: Practicing actuaries, students, and educators interested in exposure to the foundations of insurance analytics.

Keywords and Phrases: Insurance analytics, ratemaking, statistical distributions, estimation and model selection, regression analysis.

Workshop Preparation. To prepare for the workshop, many participants will wish to review R code available at the website:

Online Tutorial on Regression Modeling with Actuarial and Financial Applications.

This site employs interactive “Datacamp” style exercises.

See also below for additional suggestions on things you can do to prepare yourself for the workshop.

Schedule

\[ {\small \begin{array}{l | l} \hline \text{9:00-9:20 am} &\text{Welcome, Introduction to the workshop,} \\ &~~~~\text{ How it will work, What you can get out of it.} \\ \hline \text{9:20-10:00 am} &\text{Topic 1. Introduction to Analytics} \\ \text{10:00-10:30 am} &\text{Participants will explore features that influence} \\ &~~~~\text{prices of term life policies} \\ \text{10:30-11:00 am} &\text{Coffee Break} \\\hline \text{11:00-11:45 am} &\text{Topic 2. Regression and Linear Models} \\ &~~~~\text{ with an Emphasis on Prediction} \\ \text{11:45-12:30} &\text{Participants will explore health data} \\ \text{12:30-2:00 pm} &\text{Lunch} \\\hline \text{2:00-2:45 pm} &\text{Topic 3. Logistic Regression and Generalized Linear Models} \\ \text{2:45-3:30 pm} &\text{Participants will explore health expenditure data} \\ \text{3:30-3:50 pm} &\text{Break} \\\hline \text{3:50-4:20 pm} &\text{Topic 4. Predictive Modeling: Frequency-Severity Models} \\ \text{4:20-4:50 pm} &\text{Participants will explore automobile data for pricing purposes} \\ \text{4:50-5:00 pm} &\text{Wrap-Up} \\\hline \end{array} } \]

Summaries of the theory and the cases are drawn from three sources written by the instructor:

• Regression Modeling with Actuarial and Financial Applications, Cambridge University Press (2010).
• Predictive Modeling Applications in Actuarial Science, Volume 1, Cambridge University Press (2014).
• Loss Data Analytics, Edition Two (2024).

Participants need not purchase these books for the workshop. The sources are provided for your information.

A group of volunteers is working to make available a Spanish translation of the first book that will be free and available online. See our current progress at

Modelado de Regresión con Aplicaciones Actuariales y Financieras.

About the Instructor

Learn About the Instructor

Edward (Jed) Frees is a Fellow of the American Statistical Association and a former Fellow of the Society of Actuaries. He served as founding chairperson of the Society of Actuaries’ Education and Research Section as well as a member of the Board of Directors of the Society of Actuaries; he has also served as a Trustee of the Actuarial Foundation. Professor Frees served as an actuarial representative to the Social Security Advisory Board’s Technical Panel on Methods and Assumptions. Professor Frees was the Editor and is currently on Honorary Advisory Boards for the North American Actuarial Journal and the Annals of Actuarial Science. He is also an Associate Editor for Insurance: Mathematics and Economics.

Professor Frees is an emeritus professor at the University of Wisconsin-Madison and was a professor of actuarial studies with the Australian National University. He is

• the editor of the Spanish version of the open actuarial textbook, Loss Data Analytics, is
• working with a group to provide a (free) Spanish translation of his regression modeling book, and is
• currently wrapping up his latest book, entitled Constructing Insurable Risk Portfolios.

You can contact Jed at jfrees@bus.wisc.edu. See the Frees Research Website for more information about his background.

Additional Resources

Here are additional resources you can use to prepare yourself for the course.

Packages

Learn About the Packages

Here is a list of the R packages that will be used in the course. It will save you a bit of time if you install them on your machine in advance of the course.

• abind
• cluster
• doBy
• dplyr
• faraway
• Hmisc
• knitr
• kableExtra
• MASS
• psych
• stargazer
• statmod
• tweedie

Data Sets

Learn About the Data Sets

Here is a list of the datasets that will be used in the course. It will save you a bit of time if you download them to your machine in advance of the course. All datasets are in “.csv” (comma separated value) format, a type of text file.

• AutoClaims.csv (also called ‘Auto_claims.csv’ in the online tutorial)
• Galton.csv (also called ‘galton_height.csv’ in the online tutorial)
• HealthExpend.csv (also called ‘HealthMeps.csv’ in the online tutorial)
• MassBodilyInjury.csv (also called ‘MassBI.csv’ in the online tutorial)
• OutlierExample.csv (also called ‘Outlier.csv’ in the online tutorial)
• Refrigerator.csv (also called ‘Refrig.csv’ in the online tutorial)
• RiskSurvey.csv (also called ‘Risk_survey.csv’ in the online tutorial)
• TermLife.csv (also called ‘term_life.csv’ in the online tutorial)
• WiscHospCosts.csv (also called ‘WiscHcosts.csv’ in the online tutorial)
• WiscLottery.csv (also called ‘Wisc_lottery.csv’ in the online tutorial)

These datasets were developed over several years and so sometimes variables are in upper case and sometimes in lower case. (Datacamp wants lower case variables.) Hence, there are different versions of a single dataset, usually the same data with different variable names.

You may download these datasets from the Frees Regression Book Data Site. Here, you will also find additional documentation regarding variable definitions.

In addition, for the linear model section, I will illustrate techniques using two health data sets that you can retrieve using the following R code:

Retrieve the BMI Health Data Sets

#  MEPS data
#  read file MEPSpanel13.csv
#  sample of 750 observations from panel 13
 bmi <- read.table(file="http://instruction.bus.wisc.edu/jfrees/jfreesbooks/Regression%20Modeling/KyotoSageDataCode/MEPSpanel13.csv", header = TRUE, sep = ",")
#  sample of 750 observations from panel 14
bmi.14 <- read.table(file = "http://instruction.bus.wisc.edu/jfrees/jfreesbooks/Regression%20Modeling/KyotoSageDataCode/MEPSpanel14.csv", header = TRUE, sep = ",")

Slides / Overheads

Learn About the Slides / Overheads

Here is a list of the slides/overheads that will be used in the course. Most participants will not need them but I have found that some like to have them. So, you will find them listed below.

• Presentation Slides: Chapter 2 of Loss Data Analytics, Second Edition
• Presentation Slides: Chapters 2-6 of Regression Modeling with Actuarial and Financial Applications
• Presentation Slides: Chapters 11 and 13 of Regression Modeling with Actuarial and Financial Applications
• Presentation Slides: for Predictive Modeling: Frequency-Severity Models

R Code

Given a lot of time, the best way to learn the R code is to go to the original sources and work carefully through the motivation and the execution. However, in this workshop, you will not have a lot of time. So, here is a sequence of R markdown (.Rmd) files that contain the code.

I will demonstrate how to use these .Rmd files if you haven’t seen them before. Essentially, you will load each file into R studio and then you can execute each block of code by hitting a green arrow in the upper right of the code.

A Set of Useful R Markdown Files

Data are available using the following. The .Rmd file is simply text. After you download, you may do a “File, Save as” to select where to save the download. Then, open the saved version in R Studio.

• Preliminary Code
• Topic 1. Introduction to Analytics
• Topic 2. Regression and Linear Models
• BMI Linear Models
• Topic 3. Logistic Regression and GLM
• Massachuesetts Auto
• Topic 4. Predictive Modeling: Frequency-Severity Models

In the Preliminary Code file, you will find the packages as well as a small function that I wrote to present tables nicely. This is not really necessary (you can just print a table or matrix to the screen). However, to replicate the code provided, you can run the following code to implement the TableGen1() function.

Detailed Schedule

Table 1: Detailed Schedule

Time	Topic	Activity
9:00-9:20 am	Welcome	Introduction to the workshop, how it will work, what you can get out of it
9:20-10:00 am	Topic 1. Introduction to Analytics	Instructor presentation of Chapter 2 of Loss Data Analytics, Second Edition
		Instructor provides an overview of code from the Online Tutorial on Regression Modeling with Actuarial and Financial Applications
10:00-10:30 am	Explore features that influence prices of term life policies	Start with the Chapter 2 code from LDA. Then, participants can review term life data and code from the Chapter 3, Regression Modeling with Actuarial and Financial Applications.
		If there is sufficient time, participants can review code from Chapter 3 of the Online Tutorial
10:30-11:00 am	Coffee Break
11:00-11:45 am	Topic 2. Regression and Linear Models with an emphasis on Prediction	Instructor overview of Chapters 2-6 of Regression Modeling with Actuarial and Financial Applications
11:45-12:30	Explore health expenditures data	Start by reviewing the lecture BMI Modeling Code. Then, learn about the expenditures data in Regression Modeling with Actuarial and Financial Applications, Exercise 1.1. If there is sufficient time, participants can review the code in Chapter 5 of the Online Tutorial.
12:30-2:00 pm	Lunch
2:00-2:45 pm	Topic 3. Logistic Regression and Generalized Linear Models	Chapters 11 and 13 of Regression Modeling with Actuarial and Financial Applications
2:45-3:30 pm	Explore health expenditures data	Review the code in Regression Modeling with Actuarial and Financial Applications, Example 11.1, Section 11.4, and Section 13.4. Also see Exercise 12.5 (no code available).
3:30-3:50 pm	Break
4:50-4:20 pm	Topic 4. Predictive Modeling: Frequency-Severity Models	Instructor presentation of Chapter 6 of Predictive Modeling Applications in Actuarial Science, Volume 1.
4:20-4:50 pm	Explore automobile data for pricing purposes	Start by reviewing the lecture study based on the Massachusetts Automobile Claims. If there is sufficient time, participants can review the Chapter 6 Code and Data for Predictive Modeling Applications in Actuarial Science.
4:50-5:00 pm	Wrap-Up