Dr. Lanshan Han Presents on the Estimation of Linear Mixed Models under Joint Inequality Constraints

Dr. Lanshan Han presented on the Estimation of Linear Mixed Models under Joint Inequality Constraints on Friday, Sept. 14, 2018.

Title: Estimation of Linear Mixed Models under Joint Inequality Constraints

Abstract: Linear mixed models (LMMs), which allow both fixed and random effects, are a classical extension of linear models. They are particularly applicable when there are certain hierarchical structures and hence are widely adopted in many areas. On the other hand, in many business applications, we often need to make sure the estimated coefficients to make business senses, which can be represented by constraints involving both fixed and random effect coefficients. Traditional computational tools to estimate linear mixed models do not allow us to impose constraints, especially inequality constraints on the estimated coefficients. In this talk, we present two approaches to explicitly include inequality constraints in the estimation of the LMMs. The first approach is an optimization based approach, which applies the (alternating direction method of multipliers) ADMM algorithm on the joint log-likelihood function. The second approach is a Markov Chain Monte Carlos (MCMC) simulation approach. These approaches have been applied to real-world data, and have shown superior results compared to a previously used heuristic.

Bio: Dr. Han is Associate Director of Research and Development at Precima, Inc., a subsidiary of Alliance Data System (NYSE: ADS). Before joining Precima in Aug. 2014, he was an optimization specialist in Nielsen Marketing Analytics (NYSE: NLSN) from 2011-2014. Previously, he also held a visiting assistant professor position in the Department of Industrial and Enterprise Systems Engineering at University of Illinois at Urbana Champaign and a research associate position Lyles School of Civil Engineering at Purdue University. Dr. Han received his Ph.D. in Decision Sciences and Engineering Systems with a minor in Applied Mathematics from Rensselaer Polytechnic Institute in 2007. Currently, Dr. Han is leading the development of the Precima modeling engine, which is a comprehensive computation tool box powering Precima’s analytics solutions. Dr. Han’s research interests include big data analytics in retail sector, game theory with applications in marketing and transportation systems, and non-smooth dynamical systems. Dr. Han’s studies have been published in journals such as Mathematical Programming, SIAM Journal on Numerical Analysis and Transportation Research Part B.