Oscar L. Olvera Astivia

Research

I consider myself a theoretician with the goal of advancing the fields of psychometrics, educational measurement and quantitative methodology in the social sciences from a theoretical-mathematical perspective. As such, I tend to divide my programme of research into two “aspects” that I believe are crucial to this mission.

The first “aspect” informs the theory and practice of Monte Carlo simulations within education, psychology and the quantitative social sciences in general.  I am interested in the mathematical properties of the data-generating algorithms used in this type of simulations as well as how these (mostly unacknowledged) properties can influence the conclusions we obtain from them. More specifically, I work with multivariate, non-Gaussian structures and how their mathematical properties may interact with Monte Carlo simulation designs resulting in the change and sometimes even reversal of published conclusions and recommendations. This “aspect” of my research also extends to the new field of “meta-science” where I try to understand why we do the type of Monte Carlo research that we do. Why do we select certain conditions? What kind of conclusions do we wish to obtain? What types of models are being investigated? The understanding of simulation research offers a unique window to understanding the research culture of quantitative methodology.

The second “aspect” is more playful and attempts to formally document the mathematical or statistical assumptions needed behind popular “rules-of-thumb” and data-analytic “heuristics” that are ubiquitous in our research areas. These “rules-of-thumb” were created many, many years ago and few remember why they were proposed in the first place. They jump from textbook to textbook, classroom to classroom and, over time, have become the “de-facto” standard in our teaching and use of methodology. By revisiting them through the careful of lenses of mathematical analysis, I hope to uncover the assumptions that must be satisfied for said heuristics to be true and, much more importantly, the conditions under which they fail. The need for a proper statistical education to serve empirical research has codified a variety of approaches over time that, in the words of Russell Crowe playing Dr. John Nash in A Beautiful Mind: “need revision”. 

For more information on my research programme please visit my personal website.

Areas of interest

• Simulation of multivariate, non-Gaussian structures. 
• Copula distribution theory in psychometrics.
• Power polynomial transformations of random variables. 
• Theory and applications of Monte Carlo simulations in the social sciences. 
• Simulation of structured, random correlation matrices.