论文标题
潜在变量模型中WALD测试的小样品校正
Small sample corrections for Wald tests in Latent Variable Models
论文作者
论文摘要
潜在变量模型（LVM）通常用于心理学，并越来越多地用于分析脑成像数据。这样的研究通常涉及少数参与者（n <100），其中标准的渐近结果通常无法适当控制1型误差。本文提出了两个校正，以改善使用最大似然（ML）估计的LVM中WALD测试1型误差的控制。首先，我们得出了对方差参数的ML估计量偏置的校正。这使我们能够估算模型参数和校正的WALD统计数据的校正标准错误。其次，我们使用学生的T分布而不是高斯分布来说明方差估计器的可变性。使用Satterthwaite近似估算学生的T-分布的自由度。一项基于两项已发表脑成像研究的数据的模拟研究表明，与未校正的WALD检验相比，这两个校正对1型错误率的控制提供了较高的控制，尽管对某些参数是保守的。提出的方法在R lavasearch2中实现，网址为https://cran.r-project.org/web/packages/lavasearch2。
Latent variable models (LVMs) are commonly used in psychology and increasingly used for analyzing brain imaging data. Such studies typically involve a small number of participants (n<100), where standard asymptotic results often fail to appropriately control the type 1 error. This paper presents two corrections improving the control of the type 1 error of Wald tests in LVMs estimated using maximum likelihood (ML). First, we derive a correction for the bias of the ML estimator of the variance parameters. This enables us to estimate corrected standard errors for model parameters and corrected Wald statistics. Second, we use a Student's t-distribution instead of a Gaussian distribution to account for the variability of the variance estimator. The degrees of freedom of the Student's t-distributions are estimated using a Satterthwaite approximation. A simulation study based on data from two published brain imaging studies demonstrates that combining these two corrections provides superior control of the type 1 error rate compared to the uncorrected Wald test, despite being conservative for some parameters. The proposed methods are implemented in the R package lavaSearch2 available at https://cran.r-project.org/web/packages/lavaSearch2.
