Full-Information Item Bi-Factor Analysis
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1990
- Accession Number
- ADA229346
Entities
People
- Donald R. Hedeker
- R. D. Bock
- Robert D. Gibbons