In addition to the well known estimation and confirmation approach for path models, LISREL by Jöreskog and Sörbom (1987) the partial least squares (PLS) algorithm by Wold (1973) has gained popularity as an instrument of analysis and forecasting in sociometrics and econometrics during recent years. The PLS approach to path models is data oriented and mostly descriptive or explorative, the model being defined purely by an algorithm.
The traditional PLS model involves observable, manifest variables (MV)
and
latent, i.e.,
not directly observable variables
(LV)
. The
latter are assumed to be certain constructs composed from those
MVs. Furthermore, the LVs are assumed to be connected with each
other by the linear inner or structural model:
What is called the outer or measurement model describes the assumed linear relations between the MVs and the LVs:
Finally new weights
are
estimated by OLS regression between the MVs and the approxies. The
scores of the LVs being approximately known after stopping the
iteration process, we can easily estimate the parameter matrices
and
by OLS, using model equations (11.1) and (11.2) respectively.
More details about PLS are given by Lohmöller (1984) who is the author of the PLS computer programme LVPLS.
In Section 11.2 of this paper a PLS-like approach to a class of dynamic models with latent variables will be suggested. The way to use these models for prediction will be shown, and a measure for goodness of fit will be deduced. Then, a computer programme for dynamic partial least squares modelling will be presented. The final section will show a small five-block model with an first order autoregressive distributed lag relation between the LVs.