  Joint maximum likelihood (JML) estimation is one of the earliest approaches
to fitting item response theory (IRT) models. This procedure treats both the
item and person parameters as unknown but fixed model parameters and estimates
them simultaneously by solving an optimization problem. However, the JML
estimator is known to be asymptotically inconsistent for many IRT models, when
the sample size goes to infinity and the number of items keeps fixed.
Consequently, in the psychometrics literature, this estimator is less preferred
to the marginal maximum likelihood (MML) estimator. In this paper, we
re-investigate the JML estimator for high-dimensional exploratory item factor
analysis, from both statistical and computational perspectives. In particular,
we establish a notion of statistical consistency for a constrained JML
estimator, under an asymptotic setting that both the numbers of items and
people grow to infinity and that many responses may be missing. A parallel
computing algorithm is proposed for this estimator that can scale to very large
datasets. Via simulation studies, we show that when the dimensionality is high,
the proposed estimator yields similar or even better results than those from
the MML estimator, but can be obtained computationally much more efficiently.
An illustrative real data example is provided based on the revised version of
Eysenck's Personality Questionaire (EPQ-R).
