Huang Po-Hsien
Department of Psychology, National Cheng Kung University.
Multivariate Behav Res. 2022 Mar-May;57(2-3):279-297. doi: 10.1080/00273171.2020.1820309. Epub 2020 Sep 29.
Statistical modeling with sparsity has become an active research topic in the fields of statistics and machine learning. Because the true sparsity pattern of a model is generally unknown aforehand, it is often explored by a sparse estimation procedure, like least absolute shrinkage and selection operator (lasso). In this study, a penalized least squares (PLS) method for structural equation modeling (SEM) with ordinal data is developed. PLS describes data generation by an underlying response approach, and uses a least squares (LS) fitting function to construct a penalized estimation criterion. A numerical simulation was used to compare PLS with existing penalized likelihood (PL) in terms of averaged mean square error, absolute bias, and the correctness of the model. Based on these empirical findings, a hybrid PLS was also proposed to improve both PL and PLS. The hybrid PLS first chooses an optimal sparsity pattern by PL, then estimates model parameters by an unpenalized LS under the model selected by PL. We also extended PLS to cases of mixed type data and multi-group analysis. All proposed methods could be realized in the R package lslx.
具有稀疏性的统计建模已成为统计学和机器学习领域的一个活跃研究课题。由于模型的真实稀疏模式通常事先未知，因此通常通过稀疏估计程序（如最小绝对收缩和选择算子（lasso））来探索。在本研究中，开发了一种用于有序数据结构方程建模（SEM）的惩罚最小二乘法（PLS）。PLS通过潜在响应方法描述数据生成，并使用最小二乘（LS）拟合函数来构建惩罚估计准则。使用数值模拟在平均均方误差、绝对偏差和模型正确性方面将PLS与现有的惩罚似然法（PL）进行比较。基于这些实证结果，还提出了一种混合PLS以改进PL和PLS。混合PLS首先通过PL选择最优稀疏模式，然后在PL选择的模型下通过无惩罚的LS估计模型参数。我们还将PLS扩展到混合类型数据和多组分析的情况。所有提出的方法都可以在R包lslx中实现。
