sem_fa: Structural Equations with Latent Variables (Factor Analysis).

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

Description

Model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) for factor analysis.

Usage

sem_fa(L, TH, PH)

Arguments

L	\boldsymbol{Λ}_{q \times n} matrix of factor loadings (\boldsymbol{λ}). q is the number of indicators and n is the number of latent factor variables.
TH	\boldsymbol{Θ}_{q \times q} matrix of residual variances and covariances.
PH	\boldsymbol{Φ}_{n \times n} variance-covariance matrix of \boldsymbol{ξ}.

Details

\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right) = \boldsymbol{Λ} \boldsymbol{Φ} \boldsymbol{Λ}^{T} + \boldsymbol{Θ}

Note that this notation treats all latent variables as exogenous variables \boldsymbol{ξ}.

Value

Returns the model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) derived from the \boldsymbol{Λ}, \boldsymbol{Θ}, and \boldsymbol{Φ} matrices.

Author(s)

Ivan Jacob Agaloos Pesigan

References

Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.

Jöreskog, K. G., & Sörbom, D. (1996). Lisrel 8: User's reference guide (2nd ed.). Scientific Software.

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(), ram(), sem_lat(), sem_obs()

Examples

L <- matrix(
  data = 0,
  nrow = 9,
  ncol = 3
)
L[1:3, 1] <- 0.76
L[4:6, 2] <- 0.76
L[7:9, 3] <- 0.76
PH <- matrix(
  data = c(
    1, 0.50, 0.25,
    0.50, 1, 0.50,
    0.25, 0.50, 1
  ),
  ncol = 3
)
TH <- diag(
  x = 0.76,
  nrow = 9,
  ncol = 9
)
sem_fa(L = L, TH = TH, PH = PH)

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