The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman’s eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use fit indexes as BIC and EBIC and the less used and studied approach called very simple structure (VSS). In the present paper a new approach to estimate the number of dimensions will be introduced and compared via simulation to the traditional techniques pointed above. The approach proposed in the current paper is called exploratory graph analysis (EGA), since it is based on the graphical lasso with the regularization parameter specified using EBIC. The number of dimensions is verified using the walktrap, a random walk algorithm used to identify communities in networks. In total, 32,000 data sets were simulated to fit known factor structures, with the data sets varying across different criteria: number of factors (2 and 4), number of items (5 and 10), sample size (100, 500, 1000 and 5000) and correlation between factors (orthogonal, .20, .50 and .70), resulting in 64 different conditions. For each condition, 500 data sets were simulated using lavaan. The result shows that the EGA performs comparable to parallel analysis, EBIC, eBIC and to Kaiser-Guttman rule in a number of situations, especially when the number of factors was two. However, EGA was the only technique able to correctly estimate the number of dimensions in the four-factor structure when the correlation between factors were .7, showing an accuracy of 100% for a sample size of 5,000 observations. Finally, the EGA was used to estimate the number of factors in a real dataset, in order to compare its performance with the other six techniques tested in the simulation study.

Exploratory graph analysis (EGA) is a new technique that was recently proposed within the framework of network psychometrics to estimate the number of factors underlying multivariate data. Unlike other methods, EGA produces a visual guide-network plot-that not only indicates the number of dimensions to retain, but also which items cluster together and their level of association. Although previous studies have found EGA to be superior to traditional methods, they are limited in the conditions considered. These issues are addressed through an extensive simulation study that incorporates a wide range of plausible structures that may be found in practice, including continuous and dichotomous data, and unidimensional and multidimensional structures. Additionally, two new EGA techniques are presented: one that extends EGA to also deal with unidimensional structures, and the other based on the triangulated maximally filtered graph approach (EGAtmfg). Both EGA techniques are compared with 5 widely used factor analytic techniques. Overall, EGA and EGAtmfg are found to perform as well as the most accurate traditional method, parallel analysis, and to produce the best large-sample properties of all the methods evaluated. To facilitate the use and application of EGA, we present a straightforward R tutorial on how to apply and interpret EGA, using scores from a well-known psychological instrument: the Marlowe-Crowne Social Desirability Scale. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Exploratory Graph Analysis (EGA) has emerged as a popular approach for estimating the dimensionality of multivariate data using psychometric networks. Sampling variability, however, has made reproducibility and generalizability a key issue in network psychometrics. To address this issue, we have developed a novel bootstrap approach called Bootstrap Exploratory Graph Analysis (bootEGA). bootEGA generates a sampling distribution of EGA results where several statistics can be computed. Descriptive statistics (median, standard error, and dimension frequency) provide researchers with a general sense of the stability of their empirical EGA dimensions. Structural consistency estimates how often dimensions are replicated exactly across the bootstrap replicates. Item stability statistics provide information about whether dimensions are unstable due to misallocation (e.g., item placed in the wrong dimension), multidimensionality (e.g., item belonging to more than one dimension), and item redundancy (e.g., similar semantic content). Using a Monte Carlo simulation, we determine guidelines for acceptable item stability. After, we provide an empirical example that demonstrates how bootEGA can be used to identify structural consistency issues (including a fully reproducible R tutorial). In sum, we demonstrate that bootEGA is a robust approach for identifying the stability and robustness of dimensionality in multivariate data.

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 cutoff 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 cutoff 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.