Full-information item bifactor analysis of graded response data

Robert D. Gibbons*, R. Darrell Bock, Donald Hedeker, David J. Weiss, Eisuke Segawa, Dulal K. Bhaumik, David J. Kupfer, Ellen Frank, Victoria J. Grochocinski, Angela Stover

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

228 Scopus citations


A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the group factors. The authors develop estimation procedures for fitting the graded response model when the data follow the bifactor structure. Using maximum marginal likelihood estimation of item parameters, the bifactor restriction leads to a major simplification of the likelihood equations and (a) permits analysis of models with large numbers of group factors, (b) permits conditional dependence within identified subsets of items, and (c) provides more parsimonious factor solutions than an unrestricted full-information item factor analysis in some cases. Analysis of data obtained from 586 chronically mentally ill patients revealed a clear bifactor structure.

Original languageEnglish (US)
Pages (from-to)4-19
Number of pages16
JournalApplied Psychological Measurement
Issue number1
StatePublished - Jan 2007
Externally publishedYes


  • Bi-factor model
  • EM algorithm
  • Factor analysis
  • Item analysis
  • Maximum marginal likelihood
  • Ordinal data

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)


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