Derives the mean structure vector \(\mathbf{M}\) using the Reticular Action Model (RAM) notation.
ramM(mu, A, filter)
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Returns the mean structure vector \(\mathbf{M}\) derived from the \(\mathbf{A}\), \(\mathbf{F}\), \( \mathbf{I}\), matrices and \( \boldsymbol{\mu} \left( \boldsymbol{\theta} \right)\) vector.
The mean structure vector \(\mathbf{M}\) as a function of Reticular Action Model (RAM) matrices is given by
$$ \mathbf{M} = \left( \mathbf{I} - \mathbf{A} \right)^{-1} \mathbf{F}^{T} \boldsymbol{\mu} \left( \boldsymbol{\theta} \right) $$
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,
\(\boldsymbol{\mu} \left( \boldsymbol{\theta} \right)\) 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 \(k + q\) .
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:
ramSigmatheta(),
rammutheta(),
ramsigma2()