ramM: Reticular Action Model - Mean Structure Vector \mathbf{M}

In jeksterslabds/jeksterslabRsem: Jekster's Lab Structural Equation Modeling Utilities

Description

Derives the mean structure vector \mathbf{M} using the Reticular Action Model (RAM) notation.

Usage

ramM(mu, A, filter)

Arguments

mu	k x 1 numeric vector \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right)_{k \times 1} . Model-implied meam vector.
A	m x m numeric matrix \mathbf{A}_{m \times m}. Asymmetric paths (single-headed arrows), such as regression coefficients and factor loadings.
filter	k x m numeric matrix \mathbf{F}_{k \times m}. Filter matrix used to select variables.

Details

The mean structure vector \mathbf{M} as a function of Reticular Action Model (RAM) matrices is given by

\mathbf{M} = ≤ft( \mathbf{I} - \mathbf{A} \right)^{-1} \mathbf{F}^{T} \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right)

where

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

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

• \mathbf{F}_{k \times m} represents the filter matrix used to select the observed variables,

• \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right) is the k \times 1 model-implied mean vector

• k number of observed variables,

• q number of latent variables, and

• m number of observed and latent variables, that is k + q .

Value

Returns the mean structure vector \mathbf{M} derived from the \mathbf{A}, \mathbf{F}, \mathbf{I}, matrices and \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right) vector.

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: ramSigmatheta(), rammutheta(), ramsigma2()

jeksterslabds/jeksterslabRsem documentation built on July 28, 2020, 5:24 a.m.