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以下文字引自Reckase的Multidimensional Item Response Theory (pp. 70-71)，有心的同学不妨找他提到的以下文献学习一下：
Bock RD, Aitkin M (1981) Marginal maximum likelihood estimation of item parameters: Applications
of an EM algorithm. Psychometrika 46:443–459
Bock RD, Gibbons R, Muraki E (1988) Full information item factor analysis. Applied Psychological
Measurement 12:261–280
McDonald RP (1967) Nonlinear factor analysis. Psychometric Monograph 15
Samejima F (1974) Normal ogive model on the continuous response level in the multidimensional
space. Psychometrika 39:111–121
总之，Reckase第一段话的大意是：the statistical procedures are virtually identical。
3.3.3 Comparison of the Factor Analytic and MIRT Approaches
Factor analysis and MIRT have virtually identical statistical formulations when
they are applied to matrices of item responses. This can be noted from a comparison
of the models presented by Bock and Aitken (1981), Samejima (1974),
and McDonald (1967). In fact, the software for the full information factor analysis
methodology presented by Bock et al. (1988) can be used for either factor analysis
or MIRT.
If the statistical procedures are virtually identical, what is the difference in the
two types of methodology? First, factor analysis is thought of as a data reduction
technique. The goal is usually to find the smallest number of factors that
reproduces the observed correlation matrix. MIRT is a technique for modeling
the interaction between persons and test items. Reckase and Hirsch (1991) have
shown that using too few dimensions might degrade the modeling of the item/person interactions, but using too many dimensions does not cause serious problems. Thus,
MIRT may be a better analysis tool when it is not thought of as a data reduction technique.
It is a method for modeling the meaningful contributors to the interactions of
people with test items.
Second, factor analysis typically ignores the characteristics of the input variables
while MIRT focuses on them. Analyzing the correlation matrix implies that differences
in means and variances of variables is of little or no consequence. On the
one hand, newer versions of factor analysis, such as structural equation modeling,
do consider means, variances, and covariances, but not for the purpose of getting a
better understanding of the input variables. MIRT, on the other hand, focuses on the
differences in means and variances of the item scores because they are directly related
to important characteristics of test items such as difficulty and discrimination.
These item characteristics are actively used in MIRT applications.
Finally, MIRT analyses actively work to find solutions that use the same latent
space across tests and samples. The goal is to keep a common coordinate system
for all analyses so that the items will have parameter estimates on common metrics.
Having item parameters on a common metric support their storage in an item bank
for use in test forms construction and computerized adaptive testing. Factor analysis
procedures have developed some procedures for putting the solutions into common
coordinate systems, but those methods are not widely used. Instead, factor analysis
methods now emphasize confirmatory methods and structural equation modeling.
The methods developed for factor analysis like Procrustes rotations are now being
used to place MIRT solutions onto common scales. Such methods are an extension
of unidimensional IRT methods for test equating and linking of calibrations. Developing
methods for linking calibrations from different tests and examinee samples is
a major part of the research on MIRT. These methods will be described in detail in
Chap. 9 of this book.
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