A Two-Tier Full-Information Item Factor Analysis Model with Applications

Motivated by Gibbons et al.'s (Appl. Psychol. Meas. 31:4-19, 2007) full-information maximum marginal likelihood item bifactor analysis for polytomous data, and Rijmen, Vansteelandt, and De Boeck's (Psychometrika 73:167-182, 2008) work on constructing computationally efficient estimation algorithms for latent variable models, a two-tier item factor analysis model is developed in this research. The modeling framework subsumes standard multidimensional IRT models, bifactor IRT models, and testlet response theory models as special cases. Features of the model lead to a reduction in the dimensionality of the latent variable space, and consequently significant computational savings. An EM algorithm for full-information maximum marginal likelihood estimation is developed. Simulations and real data demonstrations confirm the accuracy and efficiency of the proposed methods. Three real data sets from a large-scale educational assessment, a longitudinal public health survey, and a scale development study measuring patient reported quality of life outcomes are analyzed as illustrations of the model's broad range of applicability.