Tools for model specification in the latent variable framework (add-on to the lava package). The package contains three main functionalites: Wald tests/F-tests with improved control of the type 1 error in small samples, adjustment for multiple comparisons when searching for local dependencies, and adjustment for multiple comparisons when doing inference for multiple latent variable models.
The latent variable models (lvm) considered in this package can be written as a measurement model: $$Y_i = \nu + \eta_i \Lambda + X_i K + \epsilon_i$$ and a structural model: $$\eta_i = \alpha + \eta_i B + X_i \Gamma + \zeta_i$$ where \(\Psi\) is the variance covariance matrix of the residuals \(\zeta\) and \(\Sigma\) is the variance covariance matrix of the residuals \(\epsilon\).
The corresponding conditional mean is: $$ \mu_i(\theta) = E[Y_i|X_i] = \nu + (\alpha + X_i \Gamma) (1-B)^{-1} \Lambda + X_i K $$ $$ \Omega(\theta) = Var[Y_i|X_i] = \Lambda^{t} (1-B)^{-t} \Psi (1-B)^{-1} \Lambda + \Sigma $$
Therefore:
\(\nu\), \(K\), \(\alpha\), \(\Gamma\) are pure mean parameters.
\(\Psi\), \(\Sigma\) pure variance parameters.
\(\Lambda\), \(B\) are both mean and variance parameters.