Confirmatory item factor analysis (IFA) has seen increasing use in the social, behavioral, and health sciences. IFA allows a researcher to specify models that hypothesize the factor structure of a battery of test items, e.g., standardized educational assessments, personality inventories, and patient reported quality of life measures. However, the maximum marginal likelihood (MML) approach to parameter estimation in IFA presents difficult numerical integration problems that challenge existing approaches of estimation. The project will study a new parameter estimation algorithm for confirmatory IFA that combines the Metropolis-Hastings sampler and the Robbins-Monro stochastic approximation algorithm. The new algorithm is called the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm. The project will further integrate existing research on algorithms for multidimensional IFA, extend MH-RM to ordinal and nominal item types, explore the merits of different implementations of MH-RM, and examine methods of convergence acceleration. The project will evaluate the performance of the new algorithm by means of simulations and comparisons with current "gold standard" algorithms using real and simulated item response data. The project also will investigate the possibility of taking advantage of inherent features of MH-RM in modern parallel processing computing environments.
The MH-RM algorithm has the potential of becoming the first general and self-adaptive algorithm for arbitrarily high-dimensional IFA. It naturally integrates existing research on IFA and furthers the understanding of the relationship between latent trait models and incomplete data estimation. The project will develop a viable method for evaluating the factor structure of test items, solve problems with current estimation algorithms, and enhance the development of modern test theory. The project is likely to have an impact on any field that uses IFA as a data analytic tool. As a result, the project will aid in enhancing the quality of tests and the research that uses those tests in the educational, psychological, and health outcomes related fields. As a Doctoral Dissertation Research Improvement award, this award also will provide support to enable a promising student to establish a strong independent research career.
