Reporting Structural Equation Modeling and Confirmatory Factor Analysis Results: A Review

(2006) - James B. Schreiber, Amaury Nora, Frances K. Stage, Elizabeth A. Barlow, Jamie King

Journal: The Journal of Educational Research
Link:: https://www.tandfonline.com/doi/full/10.3200/JOER.99.6.323-338
DOI:: 10.3200/JOER.99.6.323-338
Links::
Tags:: #paper #Methods #StructuralEquationModel
Cite Key:: [@schreiberReportingStructuralEquation2006]

Abstract

The authors provide a basic set of guidelines and recommendations for information that should be included in any manuscript that has confirmatory factor analysis or structural equation modeling as the primary statistical analysis technique. The authors provide an introduction to both techniques, along with sample analyses, recommendations for reporting, evaluation of articles in The Journal of Educational Research using these techniques, and concluding remarks.

Notes

“many instances, researchers are interested in variables that cannot be directly observed, such as achievement, intelligence, or beliefs.” (Schreiber et al., 2006, p. 323)

“Factor analysis (exploratory and confirmatory) and structural equation modeling (SEM) are statistical techniques that one can use to reduce the number of observed variables into a smaller number of latent variables by examining the covariation among the observed variables.” (Schreiber et al., 2006, p. 323)

“Unobserved variables are termed latent factors, factors, or constructs and are depicted graphically with circles or ovals (Figure 1). Common factor is another term used because the effects of unobserved variables are shared in common with one or more observed variables” (Schreiber et al., 2006, p. 323)

“CFA is a confirmatory technique—it is theory driven. Therefore, the planning of the analysis is driven by the theoretical relationships among the observed and unobserved variables. When a CFA is conducted, the researcher uses a hypothesized model to estimate a population covariance matrix that is compared with the observed covariance matrix.” (Schreiber et al., 2006, p. 323)

“The latent variables are deep processing (Deep) and knowledge is isolated facts (Isolated).” (Schreiber et al., 2006, p. 323)

“SEM has been described as a combination of exploratory factor analysis and multiple regression (Ullman, 2001).” (Schreiber et al., 2006, p. 324)

“SEM, in comparison with CFA, extends the possibility of relationships among the latent variables and encompasses two components: (a) a measurement model (essentially the CFA) and (b) a structural model (Figure 3).” (Schreiber et al., 2006, p. 325)

“two other terms are associated with SEM: exogenous, similar to independent variables and endogenous, similar to dependent or outcome variables. Exogenous and endogenous variables can be observed or unobserved, depending on the model being tested.” (Schreiber et al., 2006, p. 325)

“A major component of a CFA is the test of the reliability of the observed variables.” (Schreiber et al., 2006, p. 325)

“n sum, SEM allows researchers to test theoretical propositions regarding how constructs are theoretically linked and the directionality of significant relationships.” (Schreiber et al., 2006, p. 326)

“Although the strength of path analysis lies in its ability to decompose the relationships among variables and to test the credibility of a theoretical perspective (or model), the use of such a statistical technique is predicated on a set of assumptions that are highly restrictive in nature (Pedhazur, 1982). Three of those postulations include the assumption that variables used in testing a causal model through path analysis should be measured without error, the assumption that error terms (or residuals) are not intercorrelated, and the supposition that the variables in the model flow are unidirectional (does not incorporate feedback loops among variables).” (Schreiber et al., 2006, p. 326)

“Almost all of the variables of interest in education research are not directly observable.” (Schreiber et al., 2006, p. 326)

“Another drawback of path analysis is that it does not permit the possibility of a degree of interrelationship among the residuals associated with variables used in the path model.” (Schreiber et al., 2006, p. 326)

“or one sample analysis, there is no exact rule for the number of participants needed; but 10 per estimated parameter appears to be the general consensus” (Schreiber et al., 2006, p. 326)

“The core of the postanalysis should be an examination of the coefficients of hypothesized relationships and should indicate whether the hypothesized model was a good fit to the observed data” (Schreiber et al., 2006, p. 327)

“Research questions dictated the use of structural modeling. Assessing whether the research questions lent themselves to CFA and SEM was the first step in reviewing the articles because of the confirmatory nature of both methods.” (Schreiber et al., 2006, p. 333)

“Sufficient theoretical justification provided. The studies revealed a trend that the theoretical discussion focused much more on the formation of constructs than on the configuration of the confirmatory or structural model” (Schreiber et al., 2006, p. 334)

“Tables and figures—appropriate and sufficient. The inclusion of a graphic figure of at least one model in the articles presented was evident.” (Schreiber et al., 2006, p. 334)

“mplications in line with findings. Discussions centered on practice and policy were driven by the findings derived from the data analysis; however, at times we had difficulty assessing the appropriateness of those implications adequately without access to a full set of results.” (Schreiber et al., 2006, p. 334)

“Sample size. Two issues that we found with sample size are (a) actual size of the sample and (b) missing data.” (Schreiber et al., 2006, p. 334)

“Basic assumptions. Essentially, authors provided no discussion concerning normality, outliers, linearity, or multicollinearity in the articles.” (Schreiber et al., 2006, p. 335)

“Assessment of fit. Hong (1998) described the structure and goodness of fit of the initial measurement model, provided a description of, and theoretical justification for, changes in parameter constraints and presented the results of the final model.” (Schreiber et al., 2006, p. 335)