ram_s: RAM Sigma/S

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

Description

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

Usage

ram_s(A, sigma2, F, I, SigmaMatrix = TRUE)

Arguments

A	Asymmetric paths, such as regression coefficients and factor loadings.
sigma2	Vector of variances (σ^2).
F	Filter matrix used to select the observed variables.
I	Identity matrix.
SigmaMatrix	Logical. If TRUE, returns the model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)). If FALSE, returns the \mathbf{S} matrix.

Details

Derives the model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) or the \mathbf{S} matrix from the \mathbf{A} matrix and sigma squared (σ^2) vector (variances). Note that the first element in the matrix should be an exogenous variable.

Value

Returns the model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) or the \mathbf{S} matrix derived from the \mathbf{A} matrix and σ^2 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: 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(), 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
)
sigma2 <- c(15^2, 15^2, 15^2)
F <- I <- diag(3)
# Returns the model-implied variance-covariance matrix
ram_s(A = A, sigma2 = sigma2, F = F, I = I, SigmaMatrix = TRUE)
# Returns the model-implied S matrix
ram_s(A = A, sigma2 = sigma2, F = F, I = I, SigmaMatrix = FALSE)

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