COVARIANCE STRUCTURE ANALYSIS: Statistical Practice, Theory, and Directions

Abstract

Although covariance structure analysis is used increasingly to analyze nonexperimental data, important statistical requirements for its proper use are frequently ignored. Valid conclusions about the adequacy of a model as an acceptable representation of data, which are based on goodness-of-fit test statistics and standard errors of parameter estimates, rely on the model estimation procedure being appropriate for the data. Using analogies to linear regression and anova, this review examines conditions under which conclusions drawn from various estimation methods will be correct and the consequences of ignoring these conditions. A distinction is made between estimation methods that are either correctly or incorrectly specified for the distribution of data being analyzed, and it is shown that valid conclusions are possible even under misspecification. A brief example illustrates the ideas. Internet access is given to a computer code for several methods that are not available in programs such as EQS or LISREL.

Using Monte Carlo Normal Distributions to Evaluate Structural Models With Nonnormal Data

“…Bentler & Dudgeon, 1996). The asymptotic distribution of T M L without a normality assumption was obtained by Satorra and Bentler (1988) as…”

Relative contributions of parent substance use and childhood maltreatment to chronic homelessness, depression, and substance abuse problems among homeless women: mediating roles of self-esteem and abuse in adulthood

“…The S-B χ 2 was used because the data were multivariately kurtose (Bentler & Dudgeon, 1996). The RCFI ranges from 0 to 1 and reflects the improvement in fit of a hypothesized model over a model of complete independence or uncorrelatedness among the measured variables, and also adjusts for sample size (Bentler & Dudgeon, 1996).…”

Predicting protected sexual behaviour using the Information-Motivation-Behaviour skills model among adolescent substance abusers in court-ordered treatment

“…All analyses were performed using the EQS structural equation modeling (SEM) programme (Bentler, 2002). SEM compares a proposed hypothetical model explicating relationships in the data with a set of actual data.…”

“…The closeness of the variance-covariance matrix implied by the hypothetical model to the empirical variance-covariance matrix is evaluated through various goodness of fit indices. The comparative fit index (CFI) and Robust CFI (RCFI), chi-square values (both Maximum Likelihood (ML χ 2 ) and the adjusted Satorra-Bentler robust χ 2 (S-B χ 2 ), and the Root Mean Square Errors of Approximation (RMSEAs) were used as indicators of fit (Bentler, 2002;Bentler & Dudgeon, 1996;Hu & Bentler, 1999). The CFI and RCFI indicate the proportion of improvement in the overall fit of the hypothesized model relative to a null model in which all covariances between variables are zero.…”