Guo Jia, Wall Melanie, Amemiya Yasuo
Division of Biostatistics, School of Public Health, University of Minnesota, A460 Mayo Building, MMC 303, Minneapolis, 55455-0378, USA.
Biostatistics. 2006 Jan;7(1):145-63. doi: 10.1093/biostatistics/kxi046. Epub 2005 Aug 3.
In the research of public health, psychology, and social sciences, many research questions investigate the relationship between a categorical outcome variable and continuous predictor variables. The focus of this paper is to develop a model to build this relationship when both the categorical outcome and the predictor variables are latent (i.e. not observable directly). This model extends the latent class regression model so that it can include regression on latent predictors. Maximum likelihood estimation is used and two numerical methods for performing it are described: the Monte Carlo expectation and maximization algorithm and Gaussian quadrature followed by quasi-Newton algorithm. A simulation study is carried out to examine the behavior of the model under different scenarios. A data example involving adolescent health is used for demonstration where the latent classes of eating disorders risk are predicted by the latent factor body satisfaction.
在公共卫生、心理学和社会科学研究中，许多研究问题探讨的是分类结果变量与连续预测变量之间的关系。本文的重点是开发一个模型，用于在分类结果变量和预测变量均为潜在变量（即不能直接观测）时建立这种关系。该模型扩展了潜在类别回归模型，使其能够包含对潜在预测变量的回归。使用最大似然估计，并描述了执行该估计的两种数值方法：蒙特卡罗期望最大化算法和高斯求积法，随后是拟牛顿算法。进行了一项模拟研究，以检验该模型在不同场景下的表现。使用一个涉及青少年健康的数据示例进行演示，其中饮食失调风险的潜在类别由潜在因素身体满意度来预测。
