Gainesville, FL 32611
Associate Director of Research & Development of Precima, Inc.
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.
Department of Industrial and Systems Engineering at the University of Florida