Raw Data Maximum Likelihood Estimation for Common Principal Component Models: A State Space Approach

The specifications of state space model for some principal component-related models are described, including the independent-group common principal component (CPC) model, the dependent-group CPC model, and principal component-based multivariate analysis of variance. Some derivations are provided to show the equivalence of the state space approach and the existing Wishart-likelihood approach. For each model, a numeric example is used to illustrate the state space approach. In addition, a simulation study is conducted to evaluate the standard error estimates under the normality and nonnormality conditions. In order to cope with the nonnormality conditions, the robust standard errors are also computed. Finally, other possible applications of the state space approach are discussed at the end.