Reticular Action Model - The \(\mathbf{S}\) Matrix from \(\sigma^2\)

Derives the \(\mathbf{S}\) matrix using the Reticular Action Model (RAM) notation from variable variances \(\sigma^2\). The off-diagonal elements of the \(\mathbf{S}\) matrix are assumed to be zeroes.

ramsigma2(sigma2, A, start = TRUE)

Arguments

sigma2	Numeric vector. Vector of variances \(\sigma^2\).
A	m x m numeric matrix \(\mathbf{A}_{m \times m}\). Asymmetric paths (single-headed arrows), such as regression coefficients and factor loadings.
start	Logical. If TRUE, an exogenous variable is positioned as the first element in the matrices. If FALSE, an exogenous variable is positioned as the last element in the matrices.

Value

Returns the \(\mathbf{S}\) matrix.

Details

The \(\mathbf{S}\) matrix is derived using the \(\mathbf{A}\) matrix and sigma squared \(\left( \sigma^2 \right)\) vector (variances). Note that the first or last (see start argument) element in the A and S matrices should be an exogenous variable.

References

McArdle, J. J. (2013). The development of the RAM rules for latent variable structural equation modeling. In A. Maydeu-Olivares & J. J. McArdle (Eds.), Contemporary Psychometrics: A festschrift for Roderick P. McDonald (pp. 225--273). Lawrence Erlbaum Associates.

McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the Reticular Action Model for moment structures. British Journal of Mathematical and Statistical Psychology, 37 (2), 234--251.

See also

Other SEM notation functions: ramM(), ramSigmatheta(), rammutheta()