David A. Kenny
November 7, 1994

Miscellaneous Variables
Composite Cause (an index)
A composite cause refers to an index of a weighted sum of variables. Consider a set of k exogenous variables (usually single-indicator variables) are combined to form an index. A latent variable C is created which has no indicators or disturbance. One of the k paths leading into C is fixed to one. All of the remaining paths are free. The correlations or covariances between the k variables are still estimated. An example of a composite cause is socio-economic class whose indicator causes might be education, income, and occupational status.

When there is a single endogenous variable and no other exogenous variables, the standardized paths leading into C are beta weights divided by the multiple correlation and the path from C to the endogenous variable is the multiple correlation. In general, the standardized paths leading into C are proportional to canonical coefficients.

To evaluate the utility of C to represent the paths from the k variables, drop C from the model and have each variable cause the appropriate endogenous variables. Compare the fit of this model to the one with C. The chi square difference will have k(p - 1) degrees of freedom where p is the number of endogenous variables.

Second-Order Factor
A second-order latent variable is a latent variable whose indicators are themselves latent variables. Such a latent variable would then have no measured indicators. It would have a disturbance if it were caused. Rules of identification still hold. The scale of the second-order factor must be fixed (either by standardizing the variable if it is exogenous or by forcing one its loadings to one) and there must be a sufficient number of indicators. An example of a second-order factor might be political orientation whose indicators might be the factors attitude toward social issues, attitude the economy, and attitudes toward defense.

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