Full-Information Item Bi-Factor Analysis
Rept. for 31 Jul 1989-31 Jul 1990
ILLINOIS STATE PSYCHIATRIC INST CHICAGO BIOMETRIC LAB
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A plausible s-factor solution for many types of psychological and educational tests is one in which there is one general factor and s-1 group or method related factors. The bi-factor solution results from the constraint that each item has a non-zero loading on the primary dimension alpha j 1 and at most one of the s-1 group factors. This structure has been termed the bi-factor solution by Holzinger Swineford but it also appears in the work of Tucker and Joreskog. All attempts at estimating the parameters of this model have been restricted to continuously measured variables it has not been previously considered in the context of item-response theory IRT. It is conceivable, however, that the bi-factor structure might arise in IRT related problems. The purpose of this paper is to derive a bi-factor item-response model for binary response data, and to develop a corresponding method of parameter estimation. This restriction leads to a major simplification of the likelihood equations that 1 permits the statistical evaluation of problems of unlimited dimensionality 2 permits conditional dependence among discrete and previously identified subsets of items, and 3 in some cases provides more parsimonious factor solutions than an unrestricted full-information item factor analysis might provide e.g. Bock and Aitkin, 1981. Keywords Factor analysis, Psychometrics, Biometry.
- Statistics and Probability