Structural equation and factor analyses for several populations and longitudinal data
This dissertation considers the use of latent variable modeling in multi-population studies and longitudinal studies. Possibly correlated populations and unbalanced longitudinal data are considered. For non-normal samples, practical statistical procedures are developed using the existing computer packages designed for normally distributed observations and independent populations or occasions. Model formulations and parameterizations are found, so that the results from the statistical analysis make sense, and so that the analysis produces correct inferences for parameters and model fit. The dissertation consists of three papers;In the first paper, a general latent variable model with mean and covariance structures is considered for multi-population studies. A model formulation that allows meaningful interpretation is suggested. The parameters are estimated by the maximum normal likelihood estimation method. The asymptotic properties of the estimates are derived under assumptions covering most types of non-normal data. It is shown that the limiting distribution of the estimators for the important parameters is common for normal and non-normal data, and for independent and correlated populations. A simulation study is also presented;In the second paper, the analysis using the model with augmented-moment structure is discussed. A certain part of the limiting covariance matrix of the proposed estimator is common under four different sets of assumptions. Thus, the correct standard errors can be computed under an incorrect but simpler set of assumptions. A simulation study compares the finite-sample and asymptotic standard errors;The third paper proposes a new method for analyzing unbalanced longitudinal data using factor analysis. Difficulties and disadvantages of the full-likelihood method and time series modeling approach are explained. The proposed method uses a reduced form of the likelihood, does not assume restrictive time series structure, and can be readily implemented. The new method is shown to produce valid and useful asymptotic results for models with non-normal factors and errors and without any specified correlation structure over time. The efficiency loss of the method relative to the full-likelihood method, when the latter can be carried out, is shown to be negligible.