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.
Inference about a scalar parameter of interest is a core statistical task that has attracted immense research in statistics. The Wald statistic is a prime candidate for the task, on the grounds of the asymptotic validity of the standard normal approximation to its finite-sample distribution, simplicity and low computational cost. It is well known, though, that this normal approximation can be inadequate, especially when the sample size is small or moderate relative to the number of parameters. A novel, algebraic adjustment to the Wald statistic is proposed, delivering significant improvements …
Dimension Correction for Hierarchical Latent Class Models
Aalborg University（奥尔堡大学）
模型复杂性是在选择图形模型时要考虑的一个重要因素。当所有变量都被观察到时，模型的复杂性可以通过其标准维度来衡量，即独立参数的数量。但是，当存在隐藏变量时，标准尺寸可能不再适用。应该使用有效维数（Geiger et al. 1996）。本文讨论了有效维数的计算问题。首先，我们提出了一个上界的潜在类（LC）模型的有效维数。该界是紧的，计算简单.然后，我们考虑LC模型的一个推广，称为分层潜在类（HLC）模型（Zhang 2002）。我们证明了HLC模型的有效维数可以由一些相关LC模型的有效维数得到。我们还实证证明，使用有效维度代替标准维度可以提高从数据中学习的模型的质量。
Georgia Institute of Technology（佐治亚理工学院）；Utrecht University（乌得勒支大学）
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the posterior distribution not only for one instance of data, but a distribution of data pertaining to a specific inverse problem. During inference, the neural network -- in our case a conditional normalizing flow -- provides posterior samples at virtually no cost. However, the accuracy of amortized variational inference relies on the availability of high-fidelit…
Labeling data for modern machine learning is expensive and time-consuming. Latent variable models can be used to infer labels from weaker, easier-to-acquire sources operating on unlabeled data. Such models can also be trained using labeled data, presenting a key question: should a user invest in few labeled or many unlabeled points? We answer this via a framework centered on model misspecification in method-of-moments latent variable estimation. Our core result is a bias-variance decomposition of the generalization error, which shows that the unlabeled-only approach incurs additional bias unde…
Efficient Bayesian inference remains a computational challenge in hierarchical models. Simulation-based approaches such as Markov Chain Monte Carlo methods are still popular but have a large computational cost. When dealing with the large class of Latent Gaussian Models, the INLA methodology embedded in the R-INLA software provides accurate Bayesian inference by computing deterministic mixture representation to approximate the joint posterior, from which marginals are computed. The INLA approach has from the beginning been targeting to approximate univariate posteriors. In this paper we lay ou…
Propensity score analysis with latent covariates: Measurement error bias correction using the covariate's posterior mean, aka the inclusive factor score
Johns Hopkins Bloomberg School of Public Health（约翰斯·霍普金斯大学彭博公共卫生学院）
