m: Mean Structure Vector \mathbf{m}
In jeksterslab/ram: Reticular Action Model (RAM) Notation

Description Usage Arguments Details Value Author(s) References See Also

View source: R/m.R

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

1	m(mutheta, A, filter = NULL)

`mutheta`	`t x 1` numeric vector \boldsymbol{μ} ≤ft( \boldsymbol{θ} \right)_{t \times 1} . Model-implied mean vector.
`A`	`t x t` numeric matrix \mathbf{A}_{t \times t}. Asymmetric paths (single-headed arrows), such as regression coefficients and factor loadings.
`filter`	`j x t` numeric matrix \mathbf{F}_{j \times t}. Filter matrix used to select variables. If `filter = NULL`, the filter matrix \mathbf{F} is assumed to be a t \times t identity matrix.

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

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

where

\mathbf{A}_{t \times t} represents asymmetric paths (single-headed arrows), such as regression coefficients and factor loadings,
\mathbf{F}_{j \times t} represents the filter matrix used to select the observed variables,
\mathbf{I}_{t \times t} represents an identity matrix,
\boldsymbol{μ} ≤ft( \boldsymbol{θ} \right) is the t \times 1 model-implied mean vector
j number of observed variables,
k number of latent variables, and
t number of observed and latent variables, that is j + k .

Returns the mean structure vector \mathbf{m} derived from the mutheta, A, and filter matrices.

Ivan Jacob Agaloos Pesigan

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.

Other SEM notation functions: Omega(), Sigmatheta(), mutheta()

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