By Natasha K. Bowen and Shenyang Guo
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Additional resources for Structural Equation Modeling
Instead of 81 pieces of information in a 9 by 9 covariance matrix, there are p (p +1)/2, or 9(10)/2 = 45, unique pieces of information, where p is the number of observed variables. 1 illustrates a covariance matrix of three variables (p = 3). The variances of the three variables are along the diagonal and are nonredundant pieces of information. The three covariances above and below the diagonal are redundant—only one set should be counted. 1. In any measurement model, the parameters to be estimated include elements of the Λ, Φ and Θδ matrices (the factor loadings of observed indicators on one or more factors, the variances and covariances of the latent factors, and the error variances of the observed indicators, respectively).
Decide How to Handle Missing Data Before deciding how to handle missing values, researchers should be aware of the extent to which their datasets have missing values and understand the mechanisms of missingness. The extent to which data are missing from variables to be analyzed can be examined by obtaining univariate descriptive data in any general statistical analysis program. Output includes the number and percentage of missing values. Users can obtain information on the extent to which individual cases are missing values on variables to be used by conducting a count of the missing value code across analysis variables, and then obtaining descriptives on the newly created count variable.
As stated earlier, matrices are also the basis of the fundamental SEM method of evaluating the quality of a model—comparing the original input matrix to the model-implied matrix of covariances. More about each of these roles of matrices in SEM is presented below. A full explanation of matrix algebra is beyond the scope of this book. Bollen (1989) provides a useful summary for interested readers. Long (1983) discusses matrix algebra as it applies to CFA. In addition to being used by SEM programs to estimate models, matrices are useful tools that researchers use to specify models in great detail.
Structural Equation Modeling by Natasha K. Bowen and Shenyang Guo