Missing data is almost inevitable for various reasons in many applications. For hierarchical latent variable models, there usually exist two kinds of missing data problems. One is manifest variables with incomplete observations, the other is latent variables which cannot be observed directly. Missing data in manifest variables can be handled by different methods. For latent variables, there exist several kinds of partial least square (PLS) algorithms which have been widely used to estimate the value of latent variables. In this paper, we not only combine traditional linear regression type PLS algorithms with missing data handling methods, but also introduce quantile regression to improve the performances of PLS algorithms when the relationships among manifest and latent variables are not fixed according to the explored quantile of interest. Thus, we can get the overall view of variables’ relationships at different levels. The main challenges lie in how to introduce quantile regression in PLS algorithms correctly and how well the PLS algorithms perform when missing manifest variables occur. By simulation studies, we compare all the PLS algorithms with missing data handling methods in different settings, and finally build a business sophistication hierarchical latent variable model based on real data.

中文翻译：

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具有缺失数据的分层潜变量模型中偏最小二乘算法的比较

在许多应用程序中，由于各种原因，丢失数据几乎是不可避免的。对于分层潜变量模型，通常存在两种缺失数据的问题。一种是观察不完全的显变量，另一种是不能直接观察到的潜在变量。清单变量中缺失的数据可以通过不同的方法处理。对于潜在变量，存在多种偏最小二乘 (PLS) 算法，这些算法已被广泛用于估计潜在变量的值。在本文中，我们不仅将传统的线性回归类型的 PLS 算法与缺失数据处理方法相结合，而且还引入了分位数回归来提高 PLS 算法的性能，当显性变量和潜在变量之间的关系根据探索的兴趣分位数不固定时. 因此，我们可以在不同层次上获得变量关系的整体视图。主要挑战在于如何在 PLS 算法中正确引入分位数回归，以及在缺少清单变量时 PLS 算法的表现如何。通过仿真研究，我们将所有PLS算法与不同设置下的缺失数据处理方法进行了比较，最终构建了基于真实数据的业务成熟度层次潜变量模型。