Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM), where latent variables are approximated by weighted composites of indicators. It has no formal mechanism to incorporate errors in indicators, which in turn renders components prone to the errors as well. We propose to extend GSCA to account for errors in indicators explicitly. This extension, called GSCA_M, considers both common and unique parts of indicators, as postulated in common factor analysis, and estimates a weighted composite of (...) indicators with their unique parts removed. Adding such unique parts or uniqueness terms serves to account for measurement errors in indicators in a manner similar to common factor analysis. Simulation studies are conducted to compare parameter recovery of GSCA_M and existing methods. These methods are also applied to fit a substantively well-established model to real data. (shrink)

Extended redundancy analysis is a statistical method that relates multiple sets of predictors to response variables. In ERA, the conventional approach of model evaluation tends to overestimate the performance of a model since the performance is assessed using the same sample used for model development. To avoid the overly optimistic assessment, we introduce a new model evaluation approach for ERA, which utilizes computer-intensive resampling methods to assess how well a model performs on unseen data. Specifically, we suggest several new model (...) evaluation metrics for ERA that compute a model’s performance on out-of-sample data, i.e., data not used for model development. Although considerable work has been done in machine learning and statistics to examine the utility of cross-validation and bootstrap variants for assessing such out-of-sample predictive performance, to date, no research has been carried out in the context of ERA. We use simulated and real data examples to compare the proposed model evaluation approach with the conventional one. Results show the conventional approach always favor more complex ERA models, thereby failing to prevent the problem of overfitting in model selection. Conversely, the proposed approach can select the true ERA model among many mis-specified models. (shrink)