Simultaneous hypothesis testing of spline truncated model in nonlinear structural equation modeling (SEM)

Model of spline truncated in structural equation modeling (SEM) is a nonlinear structural model of SEM that measures a nonlinear relationship between the latent variables. This report was developed a hypothesis testing for the parameter of spline truncated model in nonlinear SEM using likelihood ratio test (LRT). To test hypothesis H₀:C′γ = τ versus H₀:C′γ ≠ τ in spline truncated model of nonlinear SEM for matrix C, vector parameter γ and a constant vector τ, is discovered that a statistical testing is in form of (Formula presented) which has a distribution F(d₁,d₂), and rejects H₀ in which W values are quite large.