Using factor score estimates in latent variable analysis
This dissertation consists of 2 separate papers. Both papers include topics related to using factor score estimates in latent variable analysis.;Here is an abstract for the paper entitled: Nonlinear latent covariate analysis using factor score estimate. Latent variables have an important role in assessing the effectiveness of comparative treatment outcomes in social and behavioral studies. In such studies, the latent intervention treatment effect measured through observed indicators is often marginal or ambiguous. But most studies also contain measurements related to other latent quantities that can be used as covariates in improving the sensitivity of the intervention assessment. For example, socio-economic characteristics that pre-date the intervention are usually available. Typically, the potential covariates are also latent variables measured by a large number of observed indicators. Furthermore, the covariates' relationships to the intervention-targeted response variable are often complex, and may require investigation/modeling. We propose an approach that estimates the values of latent variables and allows for an efficient and proper assessment of the intervention effect. This approach can also be useful in modeling potentially nonlinear relationships among latent variables.;Here is an abstract for the paper entitled: Improved inference procedures for true values of latent variables. The use of latent factor structure is reasonable in social, medical, business, and behavioral sciences because the theoretical constructs are often observed only indirectly through a set of observable indicators. Although estimates of standard factor scores are available, making inferences about the true value of a latent construct has not been discussed widely. In this paper, a variance estimator for the factor score estimator is derived that incorporates the additional variability due to the parameter estimation. Also, an estimated residual vector in the latent variable analysis is defined, and its properties derived. Diagnostic procedures using the factor score and residual estimates are proposed. Simulation studies and an example are given.