Ph.D. Dissertation Defense: Eugene J. Geis

Monday, August 19, 2019 10:00am - 12:00pm

GSE 347

STOCHASTIC APPROXIMATION EM FOR EXPLORATORY ITEM FACTOR ANALYSIS

Eugene is a doctoral student in the Statistics and Measurement (LCID) concentration of the Doctor of Philosophy program.

Committee: Greg Camilli (Chair), Chia-Yi Chui, Suzanne Brahmia (Univ. of Washington), Drew Gitomer

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 from one to ten dimensions of factor loadings are used to compare accuracy and gauge CPU time of the SAEM algorithm. An algorithm for retention of factors from the eigenanalysis of the augmented data matrix is formalized. Finally, three applications of the algorithm are also reported that demonstrate the effectiveness of the method for enabling substantive interpretations when this method is applied to real data.

     

Who to contact:

Matthew Winkler

matt.winkler@gse.rutgers.edu