David W. Gerbing

Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach

In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis

A Monte Carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions, improper solutions and the distribution of goodness-of-fit indices in maximum likelihood confirmatory factor analysis. Nonconvergent and improper solutions occurred more frequently for smaller sample sizes and for models with fewer indicators of each factor. Effects of practical significance due to sample size, the number of indicators per factor and the number of factors were found for GFI, AGFI, and RMR, whereas no practical effects were found for the probability values associated with the chi-square likelihood ratio test.

Some Methods for Respecifying Measurement Models to Obtain Unidimensional Construct Measurement

Lack of unidimensionality in structural equation models most often represents misspecification. The authors review the necessary conditions for unidimensional measurement of constructs. Two methods...

On the Meaning of Within-Factor Correlated Measurement Errors

The meaning of correlated measurement errors is discussed within a hierarchical framework of error terms provided by true score, first-order factor, and second-order factor models: random error, indicator specific error, and group specific error, respectively. Group specific error can be represented either as extraneous first-order factors or as unwanted components of first-order factors that define a second-order factor. The uncritical use of correlated measurement errors without theoretical justification is shown to lead merely to more acceptable fit while obfuscating a more meaningful theoretical structure.

Toward a Conceptualization of Impulsivity: Components across the Behavioral and Self-Report Domains

The components underlying items from a comprehensive but diverse domain of impulsivity measures were investigated. The disparity of items within this domain attests to the lack of a coherent framework from which to conceptualize impulsivity. The self-report measures included in this study were the 16PF Impulsivity scale, the GZTS Restraint, Thoughtfulness and General Activity scales, the PRF Impulsivity scale, the EASI-III Impulsivity scale, the BIS-8 and BIS-10, the I-5 and I-7, the SSS, and selected MMPI items. Behavioral measures included in this study were the MFFT, Simple Reaction Time, Time Estimation, and Time Production. From a restricted factor analysis (without correlated measurement errors) of the responses of 379 subjects to the 373 self-report items and of 228 subjects (or more) to each of the behavioral measures, 15 distinct impulsivity components were identified, with moderate to low and some negative correlations. From the analysis of the corresponding scales, a second-order model revealed three broad impulsivity factors: Spontaneous, Not Persistent, and Carefree. Implications of these results were discussed for establishing a coherent conceptualization and measurement strategy of impulsivity based, for example, on this derived second-order structure.

The Effects of Sampling Error and Model Characteristics on Parameter Estimation for Maximum Likelihood Confirmatory Factor Analysis

Monte Carlo methods were used to systematically study the effects of sampling error and model characteristics upon parameter estimates and their associated standard errors in maximum likelihood confirmatory factor analysis. Sample sizes were varied from 50 to 300 for models defined by different numbers of indicators per factor, numbers of factors, correlations between factors, and indicator reliabilities. The measurement and structural parameter estimates were generally unbiased except for the structural parameters relating factors defined by only two indicators. Sampling variability can be quite large, though, particularly as sample size becomes smaller, there are fewer indicators per factor and the reliabilities are lower. However, the estimated standard errors were adjusted accordingly.

Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternate respecifications

A Monte Carlo approach was employed to investigate the interpretability of improper solutions caused by sampling error in maximum likelihood confirmatory factor analysis. Four models were studied with two sample sizes. Of the overall goodness-of-fit indices provided by the LISREL VI program significant differences between improper and proper solutions were found only for the root mean square residual. As expected, indicators of the factor on which the negative uniqueness estimate occurred had biased loadings, and the correlations of its factor with other factors were also biased. In contrast, the loadings of indicators on other factors and those factor intercorrelations did not have any bias of practical significance. For initial solutions with one negative uniqueness estimate, three respecifications were studied: Fix the uniqueness at .00, fix it at .20, or constrain the domain of the solution to be proper. For alternate, respecified solutions that were converged and proper, the constrained solutions and uniqueness fixed at .00 solutions were equivalent. The mean goodness-of-fit and pattern coefficient values for the original improper solutions were not meaningfully different from those obtained under the constrained and uniqueness fixed at .00 respecifications.

A Large-scale Second-order Structural Equation Model of the Influence of Management Participation on Organizational Planning Benefits

This study analyzes the relationship between management participation in strategy formation and organizational planning benefits with the construction and subsequent empirical validation of a large-scale structural equation model with 57 items. This model simultaneously considered first-order and second-order measurement models as well as the structural model. Methodological emphasis was placed on developing expanded conceptualizations of these strategy constructs by modeling them as second-order factors and expressing their defining constituent domains of content as first-order factors. Results indicate a strong causal linkage between management participation and two classes of strategic benefits, suggesting that management participation enhances the effectiveness of the strategy process.

The 16PF Related to the Five-Factor Model of Personality: Multiple-Indicator Measurement versus the A Priori Scales

This article examines the Sixteen Personality Factor Inventory (16PF; Cattell, Eber, & Tatsuoka, 1970) in terms of recent methodological and substantive developments: restricted (confirmatory) factor analysis and the five-factor model of personality as operationalized by the NEO-PI (NEO Personality Inventory). A multiple-indicator measurement model of the 16PF was constructed and analyzed with a restricted factor analysis and then cross-validated with a confirmatory analysis on a new sample. The relations of the a priori 16PF scales and the derived scales with the NEO-PI were investigated with comparative canonical correlation analyses. Both the a priori and derived 16PF scales demonstrated strong relationships to the NEO-PI scales, with the canonical correlations for the a priori scales slightly larger. These findings lead to the conclusion that the original 16PF remains robust in the context of these more recent developments.

The surprising viability of a simple alternate estimation procedure for construction of large‐scale structural equation measurement models

As part of developing a comprehensive strategy for structural equation model building and assessment, a large‐scale Monte Carlo study of 7,200 covariance matrices sampled from 36 population models was conducted. This study compared maximum likelihood with the much simpler centroid method for the confirmatory factor analysis of multiple‐indicator measurement models. Surprisingly, the contribution of maximum likelihood to model analysis is limited to formal evaluation of the model. No statistically discernible differences were obtained for the bias, standard errors, or mean squared error (MSE) of the estimated factor correlations, and empirically obtained maximum likelihood standard errors for the pattern coefficients were only slightly smaller than their centroid counterparts. Further supporting the recommendations of Anderson and Gerbing (1982), the considerably faster centroid method may have a useful role in the analysis of these models, particularly for the analysis of large models with 50 or more inpu...