sem_lat: Structural Equations with Latent Variables
In jeksterslabds/jeksterslabRds: Jekster's Lab Data Science and Statistics

Description Usage Arguments Details Author(s) See Also

Model-implied variance-covariance matrix (\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right)) for structural equations with latent variables.

1	sem_lat(L, TH, BE, I, PS)

`L`	\boldsymbol{Λ}_{p \times m} matrix of factor loadings (\boldsymbol{λ}). p is the number of indicators and m is the number of latent factor variables.
`TH`	\boldsymbol{Θ}_{p \times p} matrix of residual variances and covariances.
`BE`	\mathbf{B}_{m \times m} coefficient matrix.
`I`	\mathbf{I}_{m \times m} identity matrix.
`PS`	\boldsymbol{Ψ}_{m \times m} variance-covariance matrix of exogenous variables as well as variance-covariance of endogenous variables.

\boldsymbol{Σ} ≤ft( \boldsymbol{θ} \right) = \boldsymbol{Λ} ≤ft( \mathrm{I} - \mathrm{B} \right)^{-1} \boldsymbol{Ψ} ≤ft[ ≤ft( \mathrm{I} - \mathrm{B} \right)^{-1} \right]^{T} \boldsymbol{Λ}^{T} + \boldsymbol{Θ}

Note that this notation, known as the "All-y" notation, treats all variables as endogenous variables. As such, all latent variables are contained in \boldsymbol{η} and all observed variables are contained in \mathbf{y}. It is important to take note that \boldsymbol{Ψ} contains both exogenous variances and covariances as well as latent residual variances and covariances. Note that \boldsymbol{Ψ} matrix combines \boldsymbol{Ψ} and \boldsymbol{Φ} from the original LISREL notation for structural equations with latent variables. As such, it contains the variance-covariance of exogenous variables, and residual variance-covariance of endogenous variables. Note that \mathbf{B} matrix combines \mathbf{B} and \boldsymbol{Γ} from the original LISREL notation for structural equations with latent variables. As such, it contains all coefficients.

Ivan Jacob Agaloos Pesigan

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_fa(), sem_obs()