EQS

Equations and Variances–Covariances

The LISREL and BW models involve matrix equations and require matrix algebra. This is a challenge in many educational settings and is avoided in many LISREL-type implementations by the use of simple interfaces. Unfortunately, these interfaces can obscure the actual model being run. This difficulty is avoided in EQS, where any SEM model is specified via equations involving V, F, E, and D variables, and the exact model being run is always visible. Vs represent observed data variables that are numbered as ordered in the data file: V1, V2, and so on. The rest are hypothetical generating variables—latent factors (Fs), residuals in equations for Vs (Es), and residuals in equations for Fs, namely, Ds (for disturbance). If a model has three Fs, typically these are numbered F1, F2, and F3. The number in an E or D corresponds to its V or F. In EQS, the dependent variable in any equation—the left side of an equation—can only be a V or F variable. Illustrative equations are V3 = *F1 + E3 and F5 = *F1 + *F2 + *V6 + D5, where the “*” are unknown parameters. Notice that in the F5 equation, predictors F1 and F2 are latent factors, while V6 is an observed variable—such mixed predictors are simple in EQS but difficult in LISREL-type models. According to the BW model, the parameters of any SEM are the coefficients in its equations (the “*” in the examples) and the variances and covariances of independent variables, which are variables that never are dependent variables in any equation. Structured means models, such as growth curve models, also have the means of independent variables as parameters. The remaining discussion focuses on models without mean parameters.

Model and Output Files

Equations and variance/covariance specifications can be typed into a model file text file (called an eqs file) and then submitted to EQS for immediate processing. The output will be a text file (called an out file) with optimal parameter estimates as well as many types of statistics and indices indicating the adequacy of the model. Examples of output include case numbers that contribute to multivariate normality and a test on multivariate normality, information on the identification status of the parameters, standard errors of parameter estimates, model fit indices such as the comparative fit index and root-mean-square error of approximation, and standard and robust chi-square statistics for evaluating the model’s ability to explain the observed sample variances and covariances.

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