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Research

I see myself as a theoretician whose primary aim is to strengthen and further develop the fields of psychometrics, educational measurement, and quantitative methodology in the social sciences by grounding them on a rigorous mathematical-statistical foundation. My research program branches into two interconnected strands: the study of Monte Carlo simulation in quantitative methodology and the use of copula theory to understand multivariate distributional structures. Both areas are unified by a central concern with high-dimensional, non-Gaussian structures, which I believe lie at the core of many unresolved questions in our field.  

I study the mathematical properties of the data-generating algorithms that we regularly use in published research to investigate multivariate non-normality. These algorithms form the backbone of countless Monte Carlo studies, yet their underlying systems of equations often conceal delicate properties with profound consequences for applied conclusions. A central focus of mine is polynomial transformations of random variables for moment-matching. For a random variable with finite moments, one can construct:  

and then solve for coefficients so that achieves a targeted set of moments. The moment equations take the form:  

which rapidly grow complex, giving rise to highly coupled nonlinear systems. In the multivariate case, with variables  ,  one can consider: 

and must contend not only with marginal moments, but also with their correlation structure. This is usually captured through the intermediate correlation matrix.  The intermediate correlation matrix, denoted as , represents the target correlation structure of the transformed marginals prior to discretization or other nonlinear modifications. Formally, for ,

so that

The challenge is to derive or approximate given a desired correlation structure among the observed variables after transformation. 

A second strand of my work uses copula theory to study the structure of multivariate non-normality. By Sklar’s theorem, any joint distribution with marginals    admits the representation:

where is a copula function. This decomposition provides a powerful framework for connecting data-generating algorithms across domains and for clarifying how dependence structures influence psychometric analysis. My interest lies especially in contrasting elliptical versus non-elliptical copulas, since their different tail behaviors and symmetry properties bear directly on how latent continua are discretized into ordinal or categorical data.  

Alongside these technical lines, I also explore the meta-science of simulation: why certain design choices are made, which models are privileged, and what kinds of conclusions researchers seek to draw. Simulation research, viewed in this way, becomes not only a computational exercise but also a lens onto the epistemic culture of quantitative methodology itself.  

Although psychometrics is primarily an applied, empirical science, I proudly position myself  on the theoretical side of it. It is unusual in our field to encounter someone whose research agenda is driven less by direct applications than by the mathematical-statistical structures that underlie them. Yet I believe such work is essential: the rigor of theory not only safeguards the conclusions of practice but also reveals deeper unifying principles across the diverse analytic methods we use. It is within this rare space, where computational experimentation and statistical theory converge, that I situate my contribution to the science of educational measurement.  
 

For more information on my research programme .

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.