An Aggregate IRT Procedure for Exploratory Factor Analysis.

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.