lavaSearch2 {lavaSearch2}

Tools for Model Specification in the Latent Variable Framework

Description

The package contains three main functionalities:

• compare2, summary2: Wald tests/robust Wald tests/F-tests/robust F-tests with improved control of the type 1 error in small samples.

• glht2: adjustment for multiple comparisons when doing inference for multiple latent variable models.

• modelsearch2: searching for local dependencies with adjustment for multiple comparisons.

It contains other useful functions such as:

• calibrateType1: simulation study of the type 1 error of Wald tests.

• createContrast: user-friendly function generating a contrast matrix.

• getVarCov2: reconstruct the conditional variance covariance matrix.

• iidJack: extract the jackknife iid decomposition.

Details

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 \Sigma is the variance covariance matrix of the residuals \epsilon,
and \Psi is the variance covariance matrix of the residuals \zeta.

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

The package aims to provides tool for testing linear hypotheses on the model coefficients \nu, \Lambda, K, \Sigma, \alpha, B, \Gamma, \Psi. Searching for local dependency enable to test whether the proposed model is too simplistic and if so to identify which additional coefficients should be added to the model.

Limitations

'lavaSearch2' has been design for Gaussian latent variable models. This means that it may not work / give valid results:

• in presence of censored or binary outcomes.

• with stratified models (i.e. object of class multigroup).