In a new volume in the CAS Monograph series, “Practical Mixed Models for Actuaries,” Professor Ernesto Schirmacher, FSA, PhD, of Bentley University proposes ideas on bridging credibility theory and mixed models to enhance actuarial practice with deeper statistical foundations. Mixed models, sometimes known as hierarchical models, offer advantages over generalized linear models (GLMs) by accounting for group-level variability and correlation within clustered data. This leads to more accurate and generalizable inferences.
Kenneth Hsu, FCAS, a member of the Monograph Editorial Board, discusses the development process, the importance of interdisciplinary connections, and the collaborative effort that helped bring this monograph to life with the author.
Kenneth: What motivated you to write this monograph?
Ernesto: The motivation dates back to when I was first learning about GLMs. Steve Mildenhall’s paper on minimum bias procedures (PCAS 1999 vol. 86) demonstrated a connection between those methods and GLMs. Still, these ideas weren’t fully placed in a broader statistical framework. Years later, I encountered another paper by Frees, Young, and Luo (Insur. Math. Econ. 1999) that connected credibility models to linear mixed models. That was a lightbulb moment. Actuaries and statisticians have often worked in parallel but siloed within their own disciplines. I wanted to bridge the gap and make the connections more accessible and practical for actuaries.
Kenneth: What is the main takeaway you hope readers gain?
Ernesto: I hope readers walk away with a clearer understanding of how credibility theory and mixed models are related. Even for those already applying credibility methods in practice, seeing how they connect to mixed models opens up new opportunities. That deeper insight can enhance both the theoretical grounding and the practical outcomes of their work.
Kenneth: What would you like readers to know outside of the paper to get the most value from the monograph?
Ernesto: A strong grasp of GLMs will help, but I recognize many actuaries have only encountered them through exam preparation. That kind of exposure tends to compartmentalize understanding. Real-life applications are different. The examples in the monograph are designed to encourage hands-on learning, and I hope even readers with modest technical backgrounds can follow the progression from the simpler to more advanced concepts.
Kenneth: What were the biggest challenges you faced while writing the monograph?
Ernesto: The hardest part was deciding what to include. I wanted to share all the code and computations so readers could replicate every result, but that would have made the monograph long and tedious. Striking a balance between transparency and readability was a real challenge. And it takes a few rounds of back-and-forth between multiple peer reviews to strike the right balance. Readers will be the ultimate judges.
Kenneth: What surprised you most during the process?
Ernesto: How far software has come. I tested examples using different tools — R, SAS, and others — and usually got consistent results. But in some edge cases, tools behaved differently. For instance, R flagged convergence issues while SAS didn’t, yet after rescaling the data, both produced the same outputs. I’ve always been skeptical about whether these tools handle edge cases properly, so this kind of validation was both worrying and reassuring.
Kenneth: What advice do you have for those interested in contributing to CAS research?
Ernesto: Don’t hesitate. Start writing down your ideas; it’ll help you think more clearly and contribute meaningfully. People often ask, “Do I know enough?” The truth is you probably do. There’s always someone behind you who could benefit from what you’ve learned and published. And while your ideas may not feel revolutionary to you, they could be very impactful to someone else.
Kenneth: What’s the biggest value-add to the actuarial research community?
Ernesto: I think it helps make the connection between actuarial methods and broader statistical frameworks feel more natural. It shows that by repurposing ideas across disciplines, we can innovate and expand our toolkit. Hopefully, this inspires more actuaries to explore beyond traditional boundaries.
Kenneth: How was your experience working with CAS volunteers and the Monograph Editorial Board?
Ernesto: Truly outstanding! From the beginning, I was paired with [you], who provided steady support and invaluable feedback. The reviewers were also fantastic, and their input helped shape the monograph into something much more complete. I’m deeply grateful to all of them and encourage readers to thank them if you see them at an event.
Kenneth: Finally, tell us something personal. Any interests or hobbies you’d like to share?
Ernesto: I have some quirky hobbies. I love learning new programming languages. Lisp, for example, is my favorite. Python gets a lot of praise, but Lispers had many of those features ages ago! I also admire the elegance of mathematical typesetting and aspire to be a capable technician. I cook, though my culinary skill is quite limited. I also enjoy home projects, but I’m not allowed to go into Home Depot unsupervised!
