An Aggregate IRT Procedure for Exploratory Factor Analysis. (August 2015)

• Record Type: Journal Article
• Authors: Camilli, Gregory; Fox, Jean-Paul
• Is Part Of: Journal of educational and behavioral statistics. Volume 40:Number 4(2015)
• Page Start: 377
• Page End: 401
• Publication Date: 2015-08
• Subjects: multilevel model -- IRT -- MIRT -- data aggregation -- exploratory factor analysis -- TIMSS mathematics; Educational statistics -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 370.2
• DOI: 10.3102/1076998615589185
• Languages: English
• ISSNs: 1076-9986

Abstract

An aggregation strategy is proposed to potentially address practical limitation related to computing resources for two-level multidimensional item response theory (MIRT) models with large data sets. The aggregate model is derived by integration of the normal ogive model, and an adaptation of the stochastic approximation expectation maximization algorithm is used for estimation. This methodology is used to conduct an exploratory factor analysis of the 2007 mathematics data from Trends in International Mathematics and Science Study (TIMSS) fourth grade to illustrate potential uses. A comparison to flexMIRT and two brief simulations indicate the aggregate model provides accurate estimates of Level 2 parameters despite loss of information ensuing from key assumption.