Abstract

Generalized structured component analysis (GSCA) is used for specifying and testing the relationships between observed variables and components. GSCA can perform model selection by comparing theoretically established models. In practice, however, theories may not always completely and unambiguously specify the relationships between variables in the model. In such situations, a specification search strategy allows for exploring potential relationships between variables in a data-driven manner. A specification search based on prediction of unseen observations is attractive as it does not require the provision of theoretically plausible models. To date, GSCA has not been equipped with such a specification search strategy. Addressing this limitation, we propose a prediction-oriented specification search algorithm for GSCA, which reveals the best combination of predictors that minimizes each target variable’s prediction error. We conduct a simulation study to examine the new algorithm’s performance and apply it to real data to further investigate and demonstrate its practical usefulness.

摘要

广义结构化成分分析 (GSCA) 用于指定和测试观察到的变量和成分之间的关​​系。GSCA 可以通过比较理论建立的模型来进行模型选择。然而，在实践中，理论可能并不总是完全明确地指定模型中变量之间的关系。在这种情况下，规范搜索策略允许以数据驱动的方式探索变量之间的潜在关系。基于对看不见的观察结果的预测的规范搜索很有吸引力，因为它不需要提供理论上合理的模型。迄今为止，GSCA 还没有配备这样的规范搜索策略。针对这一限制，我们提出了一种面向预测的 GSCA 规范搜索算法，它揭示了最小化每个目标变量的预测误差的预测变量的最佳组合。我们进行了一项模拟研究，以检查新算法的性能并将其应用于实际数据，以进一步研究和证明其实际用途。