CFA is a data analysis method based on statistical models, used to test whether the observed data matches the set theoretical model. It is used to evaluate and validate the factor structure, i.e. the relationship between observed variables and potential factors. CFA can help researchers validate and revise measurement tools to further understand the workings of potential concepts.

    Data description:

    Background description:

    Confirmatory Factor Analysis (CFA) is a statistical method used to test and verify whether the constructed structure is consistent with the hypotheses proposed by researchers. It is commonly used to determine the relationship between latent variables and observable variables, as well as the measurement error between these variables. Confirmatory factor analysis (CFA) is an application of structural equation modeling (SEM) to evaluate and validate the relationships between potential variables and measurement errors proposed by researchers.

    By analyzing the relationship between observed variables and potential variables, CFA can help researchers gain a deeper understanding of phenomena, events, concepts, or constructs, and validate their theoretical hypotheses. In this example, the CFA analysis results indicate that the discriminant validity between factor 1 and factor 2 is high, and the AVE and CR values of each factor are good. At the same time, the fitting indicators of the model indicate that the fitting degree of the model is good and meets the general fitting standards.

    The analysis results are as follows:

    Aggregation validity and discriminant validity: Based on factor 1, the average variance extraction (AVE) value is 0.366, less than 0.5, and the combined reliability CR value is 0.439, less than 0.7, indicating poor extraction of measurement indicators within the factor. Based on factor 2, the average variance extraction (AVE) value is 0.001, less than 0.5, and the combined reliability CR value is 0.179, less than 0.7, indicating poor extraction of measurement indicators within the factor.

1. Average Variance Extracted (AVE): Measures the explanatory power of potential variables on their measurement indicators. The AVE value is between 0 and 1, and the closer it is to 1, the better the explanatory power of the potential variable on its measurement indicator. In this example, the AVE value of factor 1 is 0.439, and the AVE value of factor 2 is 0.179
2. Composite Reliability（Composite Reliability, CR）Measure the internal consistency of potential variables, that is, the correlation between various observation indicators in the potential variables. The CR value is between 0 and 1, and the closer it is to 1, the better the internal consistency of the potential variable. In this example, the CR value of factor 1 is 0.439，The CR value of factor 2 is 0.179.
3. Differentiation validity: Used to evaluate the degree of differentiation between different latent variables, i.e. the correlation between different latent variables. The lower the numerical value, the lower the correlation between different potential variables, and it has good discriminant validity. In this example, the discriminant validity between factor 1 and factor 2 is 0.605
4. Model Fit Index: Used to evaluate the degree of fit and performance of the model. Common indicators include:
   • df (degree of freedom): The degree of freedom of the model, which represents the number of model parameters minus the number of constraint conditions
   • chi2 (chi squared value): Used to verify the fit between the observed data and the model. A lower value indicates a better fit
   • p-value: The result of the chi square test, used to determine whether the observed data conforms to the model's assumptions. A p-value greater than 0.05 indicates a good fit
   • CFI (Comparative Fit Index): Compare the degree of fit between models and independent models. The closer the value is to 1, the better the fit
   • GFI (Generalized Fit Index), AGFI (Adjusted Generalized Fit Index), NFI (Normative Fit Index), TLI (Relative Fit Index): Used to evaluate the degree of fit of the model. The closer the value is to 1, the better the fit
   • RMSEA (Root Mean Square Error Approximation Index): Used to measure the ratio between model fit and sample size, with lower values indicating

         Reference:

         [1]Brown, T. A. (2015). Confirmatory factor analysis for applied research. Guilford Publications.

         [2]Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L. (2019). Multivariate data analysis. Pearson.

         [3]Byrne, B. M. (2016). Structural equation modeling with AMOS: Basic concepts, applications, and programming (3rd ed.). Routledge.

         [4]Kline, R. B. (2015). Principles and Practice of Structural Equation Modeling (4th ed.). Guilford Publications.

         [5]Arbuckle, J. L. (2016). Amos (Version 24.0) [Computer Program]. IBM SPSS.：

     
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