Omega: Matrix of symmetric paths (double-headed arrows)...

In jeksterslab/ram: Reticular Action Model (RAM) Notation

Description

Derives the matrix of symmetric paths (double-headed arrows) \boldsymbol{Ω} using the Reticular Action Model (RAM) notation.

Usage

Omega(A, Sigmatheta)

Arguments

A	t x t numeric matrix \mathbf{A}_{t \times t}. Asymmetric paths (single-headed arrows), such as regression coefficients and factor loadings.
Sigmatheta	t x t numeric matrix \boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right). Model-implied variance-covariance matrix.

Details

The matrix of symmetric paths (double-headed arrows) \boldsymbol{Ω} as a function of Reticular Action Model (RAM) matrices is given by

\boldsymbol{Ω} = ≤ft( \mathbf{I} - \mathbf{A} \right) \boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right) ≤ft( \mathbf{I} - \mathbf{A} \right)^{\mathsf{T}}

where

• \mathbf{A}_{t \times t} represents asymmetric paths (single-headed arrows), such as regression coefficients and factor loadings,

• \boldsymbol{Σ}_{t \times t} represents the model-implied variance-covariance matrix,

• \mathbf{I}_{t \times t} represents an identity matrix,

• j number of observed variables,

• k number of latent variables, and

• t number of observed and latent variables, that is j + k .

Value

Returns the matrix of symmetric paths (double-headed arrows) \boldsymbol{Ω} derived from the A and Sigmatheta matrices.

Author(s)

Ivan Jacob Agaloos Pesigan

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: Sigmatheta(), mutheta(), m()

jeksterslab/ram documentation built on Jan. 8, 2021, 12:45 a.m.