Covariance structure analysis: statistical practice, theory, and directions

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.