Full information MML estimation of a multidimensional IRT model with a second-order dimension also requires only two-dimensional integrals¶
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
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q2 i? For a multidimensional IRT model in which all dependencies between first-order dimensions are explained by a second-order dimension, the efficient EM algorithm's E-step involves a sequence of two-dimensional integrals over (zk, zg). → 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 demonstration in the section on a multidimensional model with a second-order dimension, derived from the junction tree for a four-dimensional model (Figures 5 and 6). The article notes the second-order model "is a bi-factor model with the additional restriction that the conditional item response probabilities do not directly depend on the general dimension".
"It turns out that full information maximum likelihood estimation for such a model also requires the evaluation of two-dimensional integrals only."
Discussion¶
Related Claims¶
- 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 — 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
- Multidimensional latent variable models rarely support more than about four to six latent variables, limiting fine-grained SKIVE modeling — related
Page metadata
| Field | Value |
|---|---|
type |
claim |
id |
mml-second-order-dimension-two-dimensional-integrals |
title |
Full information MML estimation of a multidimensional IRT model with a second-order dimension also requires only two-dimensional integrals |
description |
Full information MML estimation of a multidimensional IRT model with a second-order dimension also requires only two-dimensional integrals |
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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