Full information MML estimation of the bi-factor model requires only two-dimensional integrations under more general conditions than the probit-link, multivariate-normal derivation of Gibbons and Hedeker¶
Claim · All claims
Evidence · 1 study · theoreticalr3·q2
Currency · newest study 2009 · not yet checked against its sources · not reviewed by a person · overdue for a recheck since 2012: tool and model accuracy changes quickly
Subclaims¶
Reading the evidence codes
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q2 i? The junction-tree derivation reduces the bi-factor model's E-step to two-dimensional integrations over (theta_g, theta_k) for any link function, without assuming multivariate normality, requiring only conditional independence of the specific latent variables given general ability. → Rijmen 2009
Evidence¶
Rijmen 2009¶
Rijmen, F. (2009). Efficient Full Information Maximum Likelihood Estimation for Multidimensional IRT Models. ETS Research Report RR-09-03. http://www.ets.org/research/contact.html doi:10.1002/j.2333-8504.2009.tb02160.x
q2 · i? · theoretical · r3
Analytical derivation in the paper, using the graphical model framework applied to the bi-factor model. It generalizes the earlier result that full information estimation "only requires the integration over two-dimensional integrals" beyond the probit link, normal distribution, and fully independent latent variables assumed by Gibbons and Hedeker.
"It follows that an efficient full information MML estimation method, involving a sequence of two-dimensional integrations over the sets ( ),g kθ θ , can be derived under much more general conditions than the ones stated by Gibbons and Hedeker (1992)."
Discussion¶
Related Claims¶
- Full information MML estimation of a multidimensional IRT model with a second-order dimension also requires only two-dimensional integrals — related
- Computational complexity of the graph-based MML procedure scales with the number of latent variables within a conditionally independent subset, and brute-force integration scales exponentially with dimensionality — a broader claim this one bears on
- Bifactor and second-order structures within measurement occasions keep multidimensional growth IRT models computationally tractable — related
- Under ordinal (WLSMV) estimation the bifactor model is not identifiable, with the S-1 diagnostic implicating the effectiveness-specific factor — related
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
mml-bifactor-two-dimensional-integrals-general-conditions |
title |
Full information MML estimation of the bi-factor model requires only two-dimensional integrations under more general conditions than the probit-link, multivariate-normal derivation of Gibbons and Hedeker |
description |
Full information MML estimation of the bi-factor model requires only two-dimensional integrations under more general conditions than the probit-link, multivariate-normal derivation of Gibbons and Hedeker |
status |
review |
evidence_strength |
weak |
newest_evidence |
2009 |
recheck_by |
2012 |
generated |
by process:wiki-ingest on 2026-09-27 |
trust |
unverified — no one has confirmed this page's content |
sources |
1 — rijmen-2009 |
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