Soft Modelling by Latent Variables: The Non-Linear Iterative Partial Least Squares (NIPALS) Approach

The NIPALS approach is applied to the ‘soft’ type of model that has come to the fore in sociology and other social sciences in the last five or ten years, namely path models that involve latent variables which serve as proxies for blocks of directly observed variables. Such models are seen as hybrids of the ‘hard’ models of econometrics where all variables are directly observed (path models in the form of simultaneous equations systems) and the ‘soft’ models of psychology where the human mind is described in terms of latent variables and their directly observed indicators. For hybrid models that involve one or two latent variables the NIPALS approach has been developed in 38, 41 and 42. The present paper extends the NIPALS approach to path models with three or more latent variables. Each new latent variable brings a rapid increase in the pluralism of possible model designs, and new problems arise in the parameter estimation of the models. Iterative procedures are given for the point estimation of the parameters. With a view to cases when the iterative estimation does not converge, a device of range estimation is developed, where high profile versus low profile estimates give ranges for the parameter estimates.