rammutheta: Reticular Action Model - Model-Implied Mean Vector...

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

Description

Derives the model-implied mean vector \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right) using the Reticular Action Model (RAM) notation.

Usage

rammutheta(M, A, filter)

Arguments

M	m x 1 numeric vector \mathbf{M}_{m \times 1}. Mean structure. Vector of means and intercepts.
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 model-implied mean vector \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right) as a function of Reticular Action Model (RAM) matrices is given by

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

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,

• \mathbf{M}_{m \times 1} represents the mean structure, that is, a vector of means and intercepts,

• 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 model-implied mean vector \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right) derived from the \mathbf{A}, \mathbf{F}, \mathbf{I}, matrices and \mathbf{M} 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: ramM(), ramSigmatheta(), ramsigma2()

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