Factor Retention in Ordinal Data Under Local Item Dependence: A Monte Carlo Comparison of Correlation Estimators and Retention Methods.

Abstract

Local item dependence (LID) is a persistent threat to dimensionality assessment in ordinal data, yet its effects on factor retention methods remain incompletely understood. Five factor retention methods (minimum average partial [MAP], parallel analysis [PA], Exploratory Graph Analysis [EGA]-Walk, EGA-Leiden, EGA-TMFG) combined with six correlation matrix estimators (Pearson, polychoric, and four fuzzy-based variants) were evaluated in a Monte Carlo simulation spanning 900 conditions and 450,000 datasets. First, pairwise and testlet LID structures produced asymmetric effects on factor retention: pair-LID induced systematic overfactoring in GLASSO-based EGA methods and PA, while testlet-LID produced near-ceiling MAP accuracy (.99) through mechanical error compensation rather than correct structural identification. Second, correlation matrix choice had negligible influence on retention performance. All four fuzzy variants were statistically indistinguishable from Pearson across all conditions, while polychoric showed a condition-dependent profile, with modest advantages under local independence but poorer performance under severe testlet-LID. Third, threshold distribution shape exerted no meaningful influence on retention outcomes, either as a main effect or in interaction with LID condition. EGA-TMFG showed the strongest resilience and is recommended when local dependence is plausible. LID structure and factor loading strength were the primary determinants of retention accuracy; correlation matrix preprocessing provided no practical corrective benefit.