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Introduction to Structural Equations with Latent Variables

Estimation Methods

The CALIS procedure provides three methods of estimation specified by the METHOD= option:

ULS unweighted least squares
GLS generalized least squares
ML maximum likelihood for multivariate normal distributions

Each estimation method is based on finding parameter estimates that minimize a badness-of-fit function that measures the difference between the observed sample covariance matrix and the predicted covariance matrix given the model and the parameter estimates. See the section "Estimation Methods" in Chapter 19, "The CALIS Procedure," for formulas, or refer to Loehlin (1987, pp. 54 -62) and Bollen (1989, pp. 104 -123) for further discussion.

The default is METHOD=ML, which is the preferred method for most applications with respect to statistical considerations. The option METHOD=GLS usually produces very similar results to METHOD=ML. Both methods are suitable regardless of the scaling of the covariance matrix. The ULS method is appropriate for a covariance matrix only if the variables are measured on comparable scales; otherwise, METHOD=ULS should be applied to the correlation matrix. PROC CALIS cannot compute standard errors or test statistics with the ULS method.

You should not specify METHOD=ML or METHOD=GLS if the observed or predicted covariance matrix is singular -you should either remove variables involved in the linear dependencies or specify METHOD=ULS.

PROC CALIS should not be used if your data are extremely nonnormal data, especially if they have high kurtosis. You should remove outliers and try to transform variables that are skewed or heavy-tailed. This applies to all three estimation methods, since all the estimation methods depend on the sample covariance matrix, and the sample covariance matrix is a poor estimator for distributions with high kurtosis (Bollen 1989, pp. 415 -418; Huber 1981; Hampel et. al 1986). PROC CALIS displays estimates of univariate and multivariate kurtosis (Bollen 1989, pp. 418 -425) if you specify the KURTOSIS option in the PROC CALIS statement.

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