Ph.D. Dissertation Defense: Eugene J. Geis

Monday, July 16, 2018 1:00pm - 3:00pm

GSE 211

Dissertation Defense

The Stochastic Approximation Expectation Maximization Algorithm For Fast, High-Dimension, Large-Scale Factor Analysis With Applications To Item Response Theory On Dichotomous and Polythomous Data

Eugene is a doctoral student in the Learning, Cognition, Instruction and Development concentration of the Doctor of Philosophy program

Committee: Greg Camilli (chair), Chia-Yi Chiu, Drew Gitomer, Suzanne Brahmia

ABSTRACT

The stochastic approximation EM algorithm (SAEM) is described for the estimation of item and person parameters given test data coded as ordinal variables. The method hinges upon eigenanalysis of missing variables sampled as augmented data; the augmented data approach was introduced by Albert's seminal work applying Gibbs sampling to Item Response Theory in 1992. Similar to maximum likelihood factor analysis, the factor structure depends only on sufficient statistics, which are computed from the missing variables. A second feature of the SAEM algorithm is the use of the Robbins-Monro procedure for establishing convergence. Contrary to Expectation-Maximization methods where costly integrals must be calculated, this method is well-suited for highly multidimensional data. Multiple calculations of errors applied within this framework of Markov Chain Monte Carlo will be presented to constrain uncertainty of parameter estimates. A minimal implementation of this algorithm requires less than 100 lines of code with no derivatives or matrix inversions, and is programmed entirely in R. Simulation conditions are proposed to compare accuracy and CPU time of the SAEM algorithm and the Metropolis-Hastings Robbins-Monro algorithm as implemented in the computer program flexMIRT. Two applications are also to be reported that demonstrate the effectiveness of the method for enabling substantive interpretations when applied to real data.

     

Who to contact:

Ericka Diaz

ericka.diaz@gse.rutgers.edu