Unique variable analysis: A network psychometrics method to detect local dependence

The local independence assumption states that variables are unrelated after conditioning on a latent variable. Common problems that arise from violations of this assumption include model misspecification, biased model parameters, and inaccurate estimates of internal structure. These problems are not limited to latent variable models but also apply to network psychometrics. This paper proposes a novel network psychometric approach to detect locally dependent pairs of variables using network modeling and a graph theory measure called weighted topological overlap (wTO). Using simulation, this approach is compared to contemporary local dependence detection methods such as exploratory structural equation modeling with standardized expected parameter change and a recently developed approach using partial correlations and a resampling procedure. Different approaches to determine local dependence using statistical significance and cut-off values are also compared. Continuous, polytomous (5-point Likert scale), and dichotomous (binary) data were generated with skew across a variety of conditions. Our results indicate that cut-off values work better than significance approaches. Overall, the network psychometrics approaches using wTO with graphical least absolute shrinkage and selector operator with extended Bayesian information criterion and wTO with Bayesian Gaussian graphical model were the best performing local dependence detection methods overall.