Polynomial factor models: non-iterative estimation via method-of-moments

We introduce a non-iterative method-of-moments estimator for non-linear latent variable (LV) models. Under the assumption of joint normality of all exogenous variables, we use the corrected moments of linear combinations of the observed indicators (proxies) to obtain consistent path coefficient and factor loading estimates. However, the estimation also works under milder assumptions. Besides providing the theoretical background, we run a Monte Carlo simulation to compare our approach to the Latent Moderated Structural Equations (LMS), a maximum likelihood estimator which serves as a benchmark. In this context, we use a single equation with two LVs, their quadratic terms and one interaction term. Moreover, we vary the sample size, the number of indicators, the factor loadings, and the correlation between the two exogenous
single LVs. The results show that our approach is promising, in particular in situation where the sample size is small and the number of indicators is large. Although we have investigated only a simple model in our study, it is straightforward to extend our approach to deal with an arbitrary number of recursive equations containing an arbitrary number of factors, interaction,
and higher-order terms.