Blind-spot maps: auditing what a structural equation model’s design could not have detected
Abstract
A structural equation model can fit its data even when the design had little chance of detecting substantively relevant alternatives. A blind-spot map enumerates single-parameter alternatives to a fitted model, applies each at a standardized magnitude that holds implied variances fixed, and reports the probability that a stated decision rule would flag the model if the alternative were true, beside the probability that the same rule flags a correctly specified model. Analytic detection from the noncentral chi-square is paired with a simulated path that measures each rule’s finite-sample size, and equivalence that follows from a saturated latent structure is certified by proof instead of by a numerical threshold. In ten published designs with N from 20 to 2,566, 2,035 alternatives are detectable, and all 177 admissible directed-path and latent-covariance alternatives are certified equivalent, so the fits test only the measurement structure. Median detection under the likelihood-ratio test rises from .071 at N = 20 to .996 at N = 2,566, and the largest design still has three blind spots, residual correlations of 0.3 detected at most 9.6 percent of the time against a size of 5.8 percent. The RMSEA > .06 rule flags 457 alternatives below .50 that the likelihood-ratio test detects above .80, and its measured size reaches .434 at N = 20. A declared block of correlated residuals among reverse-keyed items is detected with probability .998 where no single pair exceeds .520. Independent R and Julia packages generate reproducible artifacts.
Related
- Adaptive Probe Design for Auditing AI Agents
- Detectability without Interference: Efficient Canary Design for Privacy Auditing in One Run
- Wrong Operator or Blind Design? A Post-Training Diagnostic for Physics-Informed Coefficient Learning
- Dynamic Structural Equation Modeling in Blimp
- Measurement Error and Nonlinear Confounding: Structural Equation Modeling Versus Double Machine Learning
BibTeX
@misc{deja2026blindspot,
title = {{Blind-spot maps: auditing what a structural equation model’s design could not have detected}},
author = {Marek Deja},
howpublished = {PsyArXiv},
year = {2026},
month = oct,
doi = {10.31234/osf.io/367dn_v1},
url = {https://osf.io/preprints/psyarxiv/367dn_v1/},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Blind-spot maps: auditing what a structural equation model’s design could not have detected
AU - Marek Deja
PY - 2026
DA - 2026/10/22
PB - PsyArXiv
DO - 10.31234/osf.io/367dn_v1
UR - https://osf.io/preprints/psyarxiv/367dn_v1/
AB - A structural equation model can fit its data even when the design had little chance of detecting substantively relevant alternatives. A blind-spot map enumerates single-parameter alternatives to a fitted model, applies each at a standardized magnitude that holds implied variances fixed, and reports the probability that a stated decision rule would flag the model if the alternative were true, beside the probability that the same rule flags a correctly specified model. Analytic detection from the noncentral chi-square is paired with a simulated path that measures each rule’s finite-sample size, and equivalence that follows from a saturated latent structure is certified by proof instead of by a numerical threshold. In ten published designs with N from 20 to 2,566, 2,035 alternatives are detectable, and all 177 admissible directed-path and latent-covariance alternatives are certified equivalent, so the fits test only the measurement structure. Median detection under the likelihood-ratio test rises from .071 at N = 20 to .996 at N = 2,566, and the largest design still has three blind spots, residual correlations of 0.3 detected at most 9.6 percent of the time against a size of 5.8 percent. The RMSEA > .06 rule flags 457 alternatives below .50 that the likelihood-ratio test detects above .80, and its measured size reaches .434 at N = 20. A declared block of correlated residuals among reverse-keyed items is detected with probability .998 where no single pair exceeds .520. Independent R and Julia packages generate reproducible artifacts.
ER -