ram: RAM

In jeksterslabds/jeksterslabRds: Jekster's Lab Data Science and Statistics

Description

Model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) using the Reticular Action Model notation.

Usage

ram(A, S, F, I)

Arguments

A	Asymmetric paths, such as regression coefficients and factor loadings.
S	Symmetric matrix representing variances and covariances.
F	Filter matrix used to select the observed variables.
I	Identity matrix.

Details

\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right) = \mathbf{F} ≤ft( \mathbf{I} - \mathbf{A} \right)^{-1} \mathbf{S} ≤ft[ ≤ft( \mathbf{I} - \mathbf{A} \right)^{-1} \right]^{T} \mathbf{F}^{T}

Value

Returns the model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) derived from the \mathbf{A}, \mathbf{S}, \mathbf{F}, and \mathbf{I} 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: eqs_mu(), eqs(), lisrel_fa(), lisrel_obs_xy(), lisrel_obs_yx(), lisrel_obs_yy(), lisrel_obs(), lisrel_xx(), lisrel_xy(), lisrel_yx(), lisrel_yy(), lisrel(), ram_mu(), ram_m(), ram_s(), sem_fa(), sem_lat(), sem_obs()

Examples

A <- matrix(
  data = c(
    0, 0.26^(1 / 2), 0,
    0, 0, 0.26^(1 / 2),
    0, 0, 0
  ),
  ncol = 3
)
S <- F <- I <- diag(3)
S[1, 1] <- 225
S[2, 2] <- 166.5
S[3, 3] <- 166.5
ram(A = A, S = S, F = F, I = I)

jeksterslabds/jeksterslabRds documentation built on July 16, 2020, 3:41 p.m.