How do you interpret and report SEM results in a clear and concise way?

To interpret and report SEM (Structural Equation Modeling) results, focus on key findings: summarize the model fit indices (e.g., RMSEA, CFI, TLI) to assess overall model adequacy. Highlight significant paths, coefficients (regression weights), and their p-values to describe relationships between variables. Discuss the direction and strength of these relationships, noting any unexpected findings. Conclude with the model's implications for your research questions, emphasizing how the results support or challenge existing theories. Keep the explanation straightforward, using non-technical language for broader accessibility.

The Structural equation modeling (SEM) results are divided into two parts: The measurement model that demonstrates the relationship between response items and their underlying latent constructs and you need to assess the model for unidimensionality validity and reliability. The structural model demonstrates the inter-relationships among constructs in the study and the constructs are assembled based on the hypothesis stated in the theoretical framework, AMOS is the one of the software that provide SEM results.

From my experience, I would always recommend using SPSS AMOS software whenever you can. Mainly because it's much easier to use, especially for people without much experience and knowledge in programming language (like myself), as STATA, JASP, and R studio all require the use of programming language for the model specification. AMOS literally ask you to draw the model on white paper with circles, squares and arrows. Also, when reporting the SEM results, I usually would only include the structural model (which I think is more impactful) just to make the findings more clearly stand out. You can mention how the observed indicators reflect the latent variable in the main text.

Interpreting SEM (Structural Equation Modeling) results involves evaluating model fit indices like RMSEA (Root Mean Square Error of Approximation), CFI (Comparative Fit Index), and TLI (Tucker-Lewis Index) to assess how well the model describes the data. Values close to 0.06 for RMSEA or above 0.95 for CFI and TLI indicate a good fit. Examine path coefficients to understand the strength and direction of relationships between variables; significant coefficients (usually p < 0.05) suggest meaningful connections. Finally, review the squared multiple correlations for endogenous variables to gauge how much variance is explained by the model, providing insights into its predictive power.

Before interpreting the SEM result, check normality to make sure the result you get from your selected type of SEM estimation method is useful and informative. Then, check the global model fit, which is the fit indices. It is recommended to include GFI, NNFI or IFI, CFI, and RMSEA as the selected global fit index. Thirdly, it is also suggested that discrepancy information should be presented (which is the local fit indices, such as the variance/covariance matrix of the observed variables). Such two-step model fitness-checking can provide a more accurate understanding of the model's fitness.

Before presenting the SEM results, first we need to check the assumptions of multivariate normality, multicollinearity, sample size and positive definiteness, also we need to check the model fit indices like CFI (Comparative fit index), GFI(Goodness of fit index), TLI(Tucker-Lewis index), NFI(Normed fit index), as values above 0.90 and RMSEA with values less than 0.05, this related to construct validity, also convergent validity by checking the AVE that should be higher than 0.5 and discriminant validity, the composite reliability is also a must, then presenting the SEM by showing the path coefficients, p-value and standard error to understand the relationships between constructs

The reporting guideline recommended to follow is the 2018 APA JARS–Quant standards, which contain a series of reporting guidelines for different quantitative analyses. The link is here: https://apastyle.apa.org/jars/quantitative. There is a specific pdf guideline for SEM, which you can find in this link here. https://apastyle.apa.org/jars/quant-table-7.pdf Additionally, I found a paper by Rick H. Hoyle and Jennifer C. Isherwood in 2013 particularly useful, as the paper provided a list of questions to check whether your reporting of the SEM is good enough. The DOI of that paper is here: https://doi.org/10.1037%2Farc0000004

Reporting SEM (Structural Equation Modeling) results should succinctly cover key aspects: Start with a description of the model's theoretical basis and its specification. Present the fit indices (e.g., RMSEA, CFI, TLI) to demonstrate the model's overall fit to the data, highlighting values that indicate a good fit. Summarize the path coefficients, including estimates, standard errors, and significance levels, to detail the strength and direction of relationships between variables. Include a discussion on the variance explained (R2) for dependent variables. Conclude with a brief interpretation of how the findings align with research hypotheses or questions, focusing on the model's contribution to your field.

To visualize SEM (Structural Equation Modeling) results effectively, consider using software like JMP. It allows for the creation of path diagrams that display the relationships between variables, including latent and observed variables. In JMP, you can illustrate the model structure, showing direct and indirect paths, with arrows indicating the direction of relationships and the strength of these relationships often represented by the thickness of the arrows or annotated with standardized path coefficients. Highlight significant relationships in different colors or with special markers. Such visualizations make it easier to communicate complex SEM findings to a broader audience, understanding and interpretation of the model's implications.

Validating SEM (Structural Equation Modeling) results involves several steps. First, assess model fit using indices like RMSEA, CFI, and TLI; good fit values indicate the model adequately represents the data. Second, check the reliability and validity of the constructs through Cronbach’s alpha for reliability, and confirmatory factor analysis (CFA) for construct validity. Third, use cross-validation or a holdout sample to test the model's predictive accuracy on different data sets. Finally, compare your model with alternative models to ensure it is the most parsimonious explanation of the relationships between variables. These steps help confirm the robustness and generalizability of SEM findings.

SEM can be understood but only for those who are willing to spend sufficient hands on exercise with a data at hand. Many today resort to SMART PLS and feel that SEM is rather superfluous but that is not really the case. Enjoy SEM.