An Alternative Approach for Nonlinear Latent Variable Models

Abstract

In the last decades there has been an increasing interest in nonlinear latent variable models. Since the seminal paper of Kenny and Judd, several methods have been proposed for dealing with these kinds of models. This article introduces an alternative approach. The methodology involves fitting some third-order moments in addition to the means and covariances. This article discusses how the model equations can be formulated and how several standard tests, like the model fit and Lagrange multiplier tests, can be performed. The new method compares favorably with the maximum likelihood method in several studies and can provide evidence of interaction that earlier approaches might ignore.

Notes

¹The proposed method is implemented in an experimental version of EQS (Bentler, 2000–2008) and will be generally available in EQS 7.

²A sample third-order moment can be computed as averages of triple products of deviation scores s _ijk = N ⁻¹Σ ^N ₁ (z_it – _i )(z_jt – _j )(z_kt – _k ), where indexes i, j, and k can be the same or different. In EQS, such a moment is designated as (V_i ,V_j ,V_k ).

^aThe corresponding estimate is outside the 95% confidence interval.

^aThe corresponding estimate is outside the 90% confidence interval, inside the 95% confidence interval.

^bThe corresponding estimate is outside the 95% confidence interval.