Covariance structures under polynomial constraints: Applications to correlation and alpha-type structural models

factor analysis, structural models ABSTRACT. This paper provides methods for the estimation of covariance structure models under polynomial constraints. Estimation is based on maximum likelihood principles under constraints, and the test statistics, parameter estimates, and standard errors are based on a statistical theory that takes into account the constraints. The approach is illustrated by obtaining statistics for the squared multiple correlation, for predictors in a standardized metric, and in the analysis of longitudinal data via old and new models having constraints that cannot be obtained by standard methods. Covariance structure models have become recognized for having an im-portant role in educational and psychological research, particularly in the context of theory testing with nonexperimental data (e.g., Ben tier, 1980; Cooley, 1978; Joreskog, 1978). Their development over the past decade has covered such fundamental technical areas as alternative mathematical repre