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Structural equation modeling (SEM) has been deemed as a proper method when variables contain measurement errors. In contrast, path analysis with composite scores is preferred for prediction and diagnosis of individuals. While path analysis with composite scores has been criticized for yielding biased parameter estimates, recent literature pointed out that the population values of parameters in a latent-variable model depend on artificially assigned scales. Consequently, bias in parameter estimates is not a well-grounded concept for models involving latent constructs. This article compares path analysis with composite scores against SEM with respect to effect size and statistical power in testing the significance of the path coefficients, via the z- or t-statistics. The data come from many sources with various models that are substantively determined. Results show that SEM is not as powerful as path analysis even with equally weighted composites. However, path analysis with Bartlett-factor scores and the partial least-squares approach to SEM perform the best with respect to effect size and power. [ABSTRACT FROM AUTHOR]

This is a follow-up reply to "Structural parameters under partial least squares and covariance-based structural equation modeling: A comment on Yuan and Deng (2021)" by Schuberth et al. (2023). In this reply, explanations are provided on why the messages in the comment article are mostly from a lack of a coherent understanding of the results in Yuan and Deng (2021, YD21). Implications of the results in YD21 are explicated to facilitate proper comparison between covariance-based structural equation modeling (SEM) and partial least-squares SEM. The meaning of bias and mean-squared errors for parameter estimates is also elaborated for models involving latent variables that have no predefined scales. [ABSTRACT FROM AUTHOR]

Partial-least-squares approach to structural equation modeling (PLS-SEM) uses proxies of latent variables to conduct regression analysis, which directly addresses the needs of prediction and classification. Regression analysis using factor-scores has the same capacity but different factor scores have been noted with different properties. This article shows that different combinations of Bartlett- and regression-factor-scores are statistically equivalent in regression analysis for the purpose of prediction and parameter testing, and PLS-SEM mode B is equivalent to regression analysis using factor-scores when the model is correctly specified. Because proxies under PLS-SEM mode B enjoy the property of maximum reliability as that of factor-scores and PLS-SEM mode A enjoy numerical stability, a structure-based transformation from mode A to mode B is proposed. This transformation is expected to perform well for PLS-SEM in practice as long as the model has a relatively good fit to the data. Following the equivalence between factor-score regression and mode B of PLS-SEM, this article further proposes to use the maximum reliability coefficient as a formal measure for the goodness of PLS-SEM mode B and another consistent reliability coefficient for the goodness of mode A. The equivalence between PLS-SEM and the method of factor-score regression is examined via the analysis of a real dataset. A robust transformation technique is also introduced and illustrated for conducting empirical data analysis. [ABSTRACT FROM AUTHOR]

Survey data in social, behavioral, and health sciences often contain many variables (p). Structural equation modeling (SEM) is commonly used to analyze such data. With a sufficient number of participants (N), SEM enables researchers to easily set up and reliably test hypothetical relationships among theoretical constructs as well as those between the constructs and their observed indicators. However, SEM analyses with small N or large p have been shown to be problematic. This article reviews issues and solutions for SEM with small N , especially when p is large. The topics addressed include methods for parameter estimation, test statistics for overall model evaluation, and reliable standard errors for evaluating the significance of parameter estimates. Previous recommendations on required sample size N are also examined together with more recent developments. In particular, the requirement for N with conventional methods can be a lot more than expected, whereas new advances and developments can reduce the requirement for N substantially. The issues and developments for SEM with many variables described in this article not only let applied researchers be aware of the cutting edge methodology for SEM with big data as characterized by a large p but also highlight the challenges that methodologists need to face in further investigation. [ABSTRACT FROM AUTHOR]

Multigroup structural equation modeling (SEM) plays a key role in studying measurement invariance and in group comparison. However, existing methods for multigroup SEM assume that different samples are independent. This article develops a method for multigroup SEM with correlated samples. Parallel to that for independent samples, the focus here is on the cross-group stability of the within-group structure and parameters. In particular, the method does not require the specification of any between-group relationship. Rescaled and adjusted statistics as well as sandwich-type covariance matrices make the developed method work for possibly nonnormal variables with finite 4th-order moments. The method is applied to a longitudinal data set on the development of entrepreneurial teams across 4 phases. Detailed analysis is provided regarding the stability of the effect of psychological compatibility on team performance, as it is mediated by fairness perception and team cohesion. [ABSTRACT FROM PUBLISHER]