Previous research evaluating the performance of Horn's parallel analysis (PA) factor retention method with ordinal variables has produced unexpected findings. Specifically, PA with Pearson correlations has performed as well as or better than PA with the more theoretically appropriate polychoric correlations. Seeking to clarify these findings, the current study employed a more comprehensive simulation study that included the systematic manipulation of 7 factors related to the data (sample size, factor loading, number of variables per factor, number of factors, factor correlation, number of response categories, and skewness) as well as 3 factors related to the PA method (type of correlation matrix, extraction method, and eigenvalue percentile). The results from the simulation study show that PA with either Pearson or polychoric correlations is particularly sensitive to the sample size, factor loadings, number of variables per factor, and factor correlations. However, whereas PA with polychorics is relatively robust to the skewness of the ordinal variables, PA with Pearson correlations frequently retains difficulty factors and is generally inaccurate with large levels of skewness. In light of these findings, we recommend the use of PA with polychoric correlations for the dimensionality assessment of ordinal-level data.

An early step in the process of construct validation consists of establishing the fit of an unrestricted "exploratory" factorial model for a prespecified number of common factors. For this initial unrestricted model, researchers have often recommended and used fit indices to estimate the number of factors to retain. Despite the logical appeal of this approach, little is known about the actual accuracy of fit indices in the estimation of data dimensionality. The present study aimed to reduce this gap by systematically evaluating the performance of 4 commonly used fit indices-the comparative fit index (CFI), the Tucker-Lewis index (TLI), the root mean square error of approximation (RMSEA), and the standardized root mean square residual (SRMR)-in the estimation of the number of factors with categorical variables, and comparing it with what is arguably the current golden rule, Horn's (1965) parallel analysis. The results indicate that the CFI and TLI provide nearly identical estimations and are the most accurate fit indices, followed at a step below by the RMSEA, and then by the SRMR, which gives notably poor dimensionality estimates. Difficulties in establishing optimal cutoff values for the fit indices and the general superiority of parallel analysis, however, suggest that applied researchers are better served by complementing their theoretical considerations regarding dimensionality with the estimates provided by the latter method.

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.

We systematically examined the factor structure and criterion validity across the full scale and 10 short forms of the Center for Epidemiological Studies Depression Scale (CES-D) with Chinese youth. Participants were 5,434 Chinese adolescents in Grades 7 to 12 who completed the full CES-D; 612 of them further completed a structured diagnostic interview with the major depressive disorder (MDD) module of the Kiddie Schedule for Affective Disorder and Schizophrenia for School-age Children. Using a split-sample approach, a series of 4-, 3-, 2-, and 1-factor models were tested using exploratory structural equation modeling and cross-validated using confirmatory factor analysis; the dimensionality was also evaluated by parallel analysis in conjunction with the scree test and aided by factor mixture analysis. The results indicated that a single-factor model of depression with a wording method factor fitted the data well, and was the optimal structure underlying the scores of the full and shortened CES-D. Additionally, receiver operating characteristic curve analyses for MDD case detection showed that the CES-D full-scale scores accurately detected MDD youth (area under the curve [AUC] = .84). Furthermore, the short-form scores produced comparable AUCs with the full scale (.82 to .85), as well as similar levels of sensitivity and specificity when using optimal cutoffs. These findings suggest that depression among Chinese adolescents can be adequately measured and screened for by a single-factor structure underlying the CES-D scores, and that the short forms provide a viable alternative to the full instrument. (PsycINFO Database Record

Despite strong evidence supporting the use of Velicer’s minimum average partial (MAP) method to establish the dimensionality of continuous variables, little is known about its performance with categorical data. Seeking to fill this void, the current study takes an in-depth look at the performance of the MAP procedure in the presence of ordinal-level measurement. Using Monte Carlo methods, seven factors related to the data (sample size, factor loading, number of variables per factor, number of factors, factor correlation, number of response categories, and skewness) as well as two factors related to the MAP method (type of correlation matrix and power) were systematically manipulated. The results indicate that using polychoric correlations and the squared partial correlations leads to considerably more accurate estimations than using Pearson correlations and/or raising the partial correlations to the fourth power. Additionally, the MAP method is shown to be a biased estimator of dimensionality in two conditions: (a) for low factor loadings (.40) and (b) for medium factor loadings (.55) and a small number of variables per factor (≤ 6). The applicability of this method with categorical variables is discussed in the context of these findings.