Estimation of truncated spline in nonlinear structural equation modeling using weighted least squares method

Abstract

Structural equation modeling (SEM) consists of two parts, the measurement model and the structural model. In this paper, we develop a SEM model that the measurement model is linear and the structural model is nonlinear. Structural model explain about relationship between latent variables. Truncated spline is used for modeling the nonlinear relationship between the latent variables. Trought weighted least squares (WLS) method, It is found that estimation of parameter truncated spline in nonlinear SEM for two exogen and an endogen latent variables is resulted by optimizing min γ {Σ - 1 2 ( ω η - Γ ξ κ γ ) 2 } and it gave an estimator γ ^ = ( Γ ′ ξ k Σ - 1 Γ ξ k ) - 1 Γ ′ ξ k Σ - 1 ω η The estimator influenced by the location and some knot points κ 1 and κ 2.