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Beyond Pearson's Correlation: Modern Nonparametric Independence Tests for Psychological Research. 超越皮尔逊相关性:心理学研究中的现代非参数独立性检验》(Modern Nonparametric Independence Tests for Psychological Research)。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-09-01 Epub Date: 2024-08-04 DOI: 10.1080/00273171.2024.2347960
Julian D Karch, Andres F Perez-Alonso, Wicher P Bergsma

When examining whether two continuous variables are associated, tests based on Pearson's, Kendall's, and Spearman's correlation coefficients are typically used. This paper explores modern nonparametric independence tests as an alternative, which, unlike traditional tests, have the ability to potentially detect any type of relationship. In addition to existing modern nonparametric independence tests, we developed and considered two novel variants of existing tests, most notably the Heller-Heller-Gorfine-Pearson (HHG-Pearson) test. We conducted a simulation study to compare traditional independence tests, such as Pearson's correlation, and the modern nonparametric independence tests in situations commonly encountered in psychological research. As expected, no test had the highest power across all relationships. However, the distance correlation and the HHG-Pearson tests were found to have substantially greater power than all traditional tests for many relationships and only slightly less power in the worst case. A similar pattern was found in favor of the HHG-Pearson test compared to the distance correlation test. However, given that distance correlation performed better for linear relationships and is more widely accepted, we suggest considering its use in place or additional to traditional methods when there is no prior knowledge of the relationship type, as is often the case in psychological research.

在检验两个连续变量是否相关时,通常使用基于皮尔逊、肯德尔和斯皮尔曼相关系数的检验。本文探讨了作为替代方法的现代非参数独立性检验,它与传统检验不同,能够潜在地检测出任何类型的关系。除了现有的现代非参数独立性检验,我们还开发并考虑了现有检验的两个新变体,其中最著名的是 Heller-Heller-Gorfine-Pearson 检验(HHG-Pearson)。我们进行了一项模拟研究,在心理学研究中常见的情况下比较传统的独立性检验(如皮尔逊相关性)和现代的非参数独立性检验。不出所料,在所有关系中,没有哪种检验的效力最高。然而,在许多关系中,距离相关检验和 HHG-Pearson 检验的效力大大高于所有传统检验,而在最坏的情况下,其效力仅略低于传统检验。与距离相关检验相比,HHG-Pearson 检验也有类似的优势。不过,鉴于距离相关检验在线性关系中的表现更好,而且被更广泛地接受,我们建议在没有关于关系类型的先验知识的情况下(如心理学研究中常见的情况),考虑使用距离相关检验来替代或补充传统方法。
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引用次数: 0
Linear Mixed-Effects Models for Dependent Data: Power and Accuracy in Parameter Estimation. 依赖数据的线性混合效应模型:参数估计的功率和准确性。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-09-01 Epub Date: 2024-05-23 DOI: 10.1080/00273171.2024.2350236
Yue Liu, Kit-Tai Hau, Hongyun Liu

Linear mixed-effects models have been increasingly used to analyze dependent data in psychological research. Despite their many advantages over ANOVA, critical issues in their analyses remain. Due to increasing random effects and model complexity, estimation computation is demanding, and convergence becomes challenging. Applied users need help choosing appropriate methods to estimate random effects. The present Monte Carlo simulation study investigated the impacts when the restricted maximum likelihood (REML) and Bayesian estimation models were misspecified in the estimation. We also compared the performance of Akaike information criterion (AIC) and deviance information criterion (DIC) in model selection. Results showed that models neglecting the existing random effects had inflated Type I errors, unacceptable coverage, and inaccurate R-squared measures of fixed and random effects variation. Furthermore, models with redundant random effects had convergence problems, lower statistical power, and inaccurate R-squared measures for Bayesian estimation. The convergence problem is more severe for REML, while reduced power and inaccurate R-squared measures were more severe for Bayesian estimation. Notably, DIC was better than AIC in identifying the true models (especially for models including person random intercept only), improving convergence rates, and providing more accurate effect size estimates, despite AIC having higher power than DIC with 10 items and the most complicated true model.

线性混合效应模型越来越多地被用于分析心理学研究中的因果数据。尽管与方差分析相比,线性混合效应模型有很多优点,但其分析中的关键问题依然存在。由于随机效应和模型复杂性的增加,估计计算的要求很高,收敛性也变得具有挑战性。应用者需要帮助选择适当的方法来估计随机效应。本蒙特卡罗模拟研究调查了估计过程中限制性最大似然法(REML)和贝叶斯估计模型被错误指定时的影响。我们还比较了 Akaike 信息准则(AIC)和偏差信息准则(DIC)在模型选择中的表现。结果表明,忽略现有随机效应的模型会导致 I 类误差增大、覆盖率不可接受、固定效应和随机效应变异的 R 平方测量不准确。此外,具有冗余随机效应的模型存在收敛问题,统计能力较低,贝叶斯估计的 R 平方测量不准确。REML 的收敛问题更为严重,而贝叶斯估计的统计量降低和 R 平方不准确的情况更为严重。值得注意的是,尽管在 10 个项目和最复杂的真实模型中,AIC 比 DIC 具有更高的功率,但 DIC 在识别真实模型(尤其是仅包括人的随机截距的模型)、提高收敛率和提供更准确的效应大小估计方面优于 AIC。
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引用次数: 0
Killing Two Birds with One Stone: Accounting for Unfolding Item Response Process and Response Styles Using Unfolding Item Response Tree Models. 一石二鸟:使用展开式项目反应树模型考虑展开式项目反应过程和反应风格。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-31 DOI: 10.1080/00273171.2024.2394607
Zhaojun Li, Lingyue Li, Bo Zhang, Mengyang Cao, Louis Tay

Two research streams on responses to Likert-type items have been developing in parallel: (a) unfolding models and (b) individual response styles (RSs). To accurately understand Likert-type item responding, it is vital to parse unfolding responses from RSs. Therefore, we propose the Unfolding Item Response Tree (UIRTree) model. First, we conducted a Monte Carlo simulation study to examine the performance of the UIRTree model compared to three other models - Samejima's Graded Response Model, Generalized Graded Unfolding Model, and Dominance Item Response Tree model, for Likert-type responses. Results showed that when data followed an unfolding response process and contained RSs, AIC was able to select the UIRTree model, while BIC was biased toward the DIRTree model in many conditions. In addition, model parameters in the UIRTree model could be accurately recovered under realistic conditions, and mis-specifying item response process or wrongly ignoring RSs was detrimental to the estimation of key parameters. Then, we used datasets from empirical studies to show that the UIRTree model could fit personality datasets well and produced more reasonable parameter estimates compared to competing models. A strong presence of RS(s) was also revealed by the UIRTree model. Finally, we provided examples with R code for UIRTree model estimation to facilitate the modeling of responses to Likert-type items in future studies.

关于李克特类型项目反应的两个研究流一直在并行发展:(a) 展开模型和 (b) 个人反应风格 (RS)。为了准确理解李克特类型项目的反应,从 RSs 中解析展开式反应至关重要。因此,我们提出了展开项目反应树(UIRTree)模型。首先,我们进行了蒙特卡罗模拟研究,考察了 UIRTree 模型与其他三种模型(Samejima 的分级反应模型、广义分级展开模型和优势项目反应树模型)相比在李克特型反应方面的性能。结果表明,当数据遵循展开式反应过程并包含 RS 时,AIC 能够选择 UIRTree 模型,而 BIC 在许多情况下偏向于 DIRTree 模型。此外,在现实条件下,UIRTree 模型中的模型参数可以准确恢复,而错误地指定项目反应过程或错误地忽略 RSs 则不利于关键参数的估计。然后,我们利用实证研究的数据集表明,UIRTree 模型能很好地拟合个性数据集,与其他竞争模型相比,它能产生更合理的参数估计。UIRTree 模型还揭示了 RS(s)的强烈存在。最后,我们提供了 UIRTree 模型估计的 R 代码示例,以方便在未来的研究中对李克特类型项目的反应进行建模。
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引用次数: 0
Equivalence Testing Based Fit Index: Standardized Root Mean Squared Residual. 基于等效检验的拟合指数:标准化均方根残差。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-17 DOI: 10.1080/00273171.2024.2386686
Nataly Beribisky, Robert A Cribbie

A popular measure of model fit in structural equation modeling (SEM) is the standardized root mean squared residual (SRMR) fit index. Equivalence testing has been used to evaluate model fit in structural equation modeling (SEM) but has yet to be applied to SRMR. Accordingly, the present study proposed equivalence-testing based fit tests for the SRMR (ESRMR). Several variations of ESRMR were introduced, incorporating different equivalence bounds and methods of computing confidence intervals. A Monte Carlo simulation study compared these novel tests with traditional methods for evaluating model fit. The results demonstrated that certain ESRMR tests based on an analytic computation of the confidence interval correctly reject poor-fitting models and are well-powered for detecting good-fitting models. We also present an illustrative example with real data to demonstrate how ESRMR may be incorporated into model fit evaluation and reporting. Our recommendation is that ESRMR tests be presented in addition to descriptive fit indices for model fit reporting in SEM.

在结构方程建模(SEM)中,衡量模型拟合度的常用指标是标准化均方根残差(SRMR)拟合指数。等效检验已被用于评估结构方程建模(SEM)中的模型拟合度,但尚未应用于 SRMR。因此,本研究提出了基于等效检验的 SRMR(ESRMR)拟合检验。本研究引入了 ESRMR 的几种变体,结合了不同的等效边界和计算置信区间的方法。蒙特卡罗模拟研究将这些新型检验与传统的模型拟合度评估方法进行了比较。结果表明,某些基于置信区间分析计算的 ESRMR 检验能正确拒绝拟合度较差的模型,并能很好地检测拟合度较好的模型。我们还用真实数据举例说明了如何将 ESRMR 纳入模型拟合度评估和报告中。我们的建议是,在 SEM 的模型拟合报告中,除了描述性拟合指数外,还应提供 ESRMR 检验。
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引用次数: 0
Latent Reciprocal Engagement and Accuracy Variables in Social Relations Structural Equation Modeling. 社会关系结构方程模型中的潜在互惠参与和准确性变量。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-08-07 DOI: 10.1080/00273171.2024.2386060
David Jendryczko, Fridtjof W Nussbeck

The social relations model (SRM) is the standard approach for analyzing dyadic data stemming from round-robin designs. The model can be used to estimate correlation-coefficients that reflect the overall reciprocity or accuracy of judgements for individual and dyads on the sample- or population level. Within the social relations structural equation modeling framework and on the statistical grounding of stochastic measurement and classical test theory, we show how the multiple indicator SRM can be modified to capture inter-individual and inter-dyadic differences in reciprocal engagement or inter-individual differences in reciprocal accuracy. All models are illustrated on an open-access round-robin data set containing measures of mimicry, liking, and meta-liking (the belief to be liked). Results suggest that people who engage more strongly in reciprocal mimicry are liked more after an interaction with someone and that overestimating one's own popularity is strongly associated with being liked less. Further applications, advantages and limitations of the models are discussed.

社会关系模型(SRM)是分析由循环设计产生的二元数据的标准方法。该模型可用于估算相关系数,以反映样本或总体层面上个体和二元组判断的整体互惠性或准确性。在社会关系结构方程模型框架内,基于随机测量和经典测试理论的统计基础,我们展示了如何对多指标 SRM 进行修改,以捕捉互惠参与的个体间和社群间差异或互惠准确性的个体间差异。所有模型都在一个包含模仿、喜欢和元喜欢(被喜欢的信念)测量指标的开放式循环数据集上进行了说明。结果表明,参与互惠模仿的人在与某人互动后会得到更多的喜欢,而高估自己的受欢迎程度与被人喜欢的程度较低密切相关。本文讨论了模型的进一步应用、优势和局限性。
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引用次数: 0
Clustering Individuals Based on Similarity in Idiographic Factor Loading Patterns. 基于图像因子加载模式的相似性对个体进行聚类。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-23 DOI: 10.1080/00273171.2024.2374826
Cara J Arizmendi, Kathleen M Gates

Idiographic measurement models such as p-technique and dynamic factor analysis (DFA) assess latent constructs at the individual level. These person-specific methods may provide more accurate models than models obtained from aggregated data when individuals are heterogeneous in their processes. Developing clustering methods for the grouping of individuals with similar measurement models would enable researchers to identify if measurement model subtypes exist across individuals as well as assess if the different models correspond to the same latent concept or not. In this paper, methods for clustering individuals based on similarity in measurement model loadings obtained from time series data are proposed. We review literature on idiographic factor modeling and measurement invariance, as well as clustering for time series analysis. Through two studies, we explore the utility and effectiveness of these measures. In Study 1, a simulation study is conducted, demonstrating the recovery of groups generated to have differing factor loadings using the proposed clustering method. In Study 2, an extension of Study 1 to DFA is presented with a simulation study. Overall, we found good recovery of simulated clusters and provide an example demonstrating the method with empirical data.

P技术和动态因素分析(DFA)等等位测量模型可以评估个体层面的潜在结构。当个人的过程存在异质性时,这些针对个人的方法可能会比从综合数据中获得的模型更准确。开发对具有相似测量模型的个体进行分组的聚类方法,将使研究人员能够确定个体间是否存在测量模型亚型,并评估不同模型是否对应于同一潜在概念。本文提出了根据从时间序列数据中获得的测量模型载荷的相似性对个体进行分组的方法。我们回顾了有关特异性因子建模和测量不变性以及时间序列分析聚类的文献。通过两项研究,我们探讨了这些措施的实用性和有效性。在研究 1 中,我们进行了一项模拟研究,证明了使用所提议的聚类方法生成的具有不同因子载荷的组的恢复情况。在研究 2 中,通过模拟研究将研究 1 扩展到 DFA。总之,我们发现模拟聚类的恢复效果很好,并提供了一个用经验数据演示该方法的例子。
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引用次数: 0
Causal Latent Class Analysis with Distal Outcomes: A Modified Three-Step Method Using Inverse Propensity Weighting. 远端结果的因果潜类分析:使用反倾向加权的修正三步法。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-22 DOI: 10.1080/00273171.2024.2367485
Trà T Lê, Felix J Clouth, Jeroen K Vermunt

Bias-adjusted three-step latent class (LC) analysis is a popular technique for estimating the relationship between LC membership and distal outcomes. Since it is impossible to randomize LC membership, causal inference techniques are needed to estimate causal effects leveraging observational data. This paper proposes two novel strategies that make use of propensity scores to estimate the causal effect of LC membership on a distal outcome variable. Both strategies modify the bias-adjusted three-step approach by using propensity scores in the last step to control for confounding. The first strategy utilizes inverse propensity weighting (IPW), whereas the second strategy includes the propensity scores as control variables. Classification errors are accounted for using the BCH or ML corrections. We evaluate the performance of these methods in a simulation study by comparing it with three existing approaches that also use propensity scores in a stepwise LC analysis. Both of our newly proposed methods return essentially unbiased parameter estimates outperforming previously proposed methods. However, for smaller sample sizes our IPW based approach shows large variability in the estimates and can be prone to non-convergence. Furthermore, the use of these newly proposed methods is illustrated using data from the LISS panel.

经过偏差调整的三步潜类(LC)分析是估算 LC 成员与远端结果之间关系的常用技术。由于不可能随机化 LC 成员,因此需要因果推断技术来利用观察数据估计因果效应。本文提出了两种新策略,利用倾向分数来估计 LC 成员资格对远端结果变量的因果效应。这两种策略都修改了偏差调整三步法,在最后一步使用倾向分数来控制混杂因素。第一种策略采用反倾向加权法(IPW),而第二种策略则将倾向得分作为控制变量。分类误差采用 BCH 或 ML 校正。我们在模拟研究中评估了这些方法的性能,并将其与同样在逐步 LC 分析中使用倾向分数的三种现有方法进行了比较。我们新提出的两种方法都能返回基本无偏的参数估计值,优于之前提出的方法。然而,对于较小的样本量,我们基于 IPW 的方法在估计值上显示出较大的变异性,并且容易出现不收敛现象。此外,我们还利用 LISS 面板数据说明了这些新提出方法的使用情况。
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引用次数: 0
Multiple Imputation with Factor Scores: A Practical Approach for Handling Simultaneous Missingness Across Items in Longitudinal Designs. 因子得分多重估算:在纵向设计中处理各项目同时缺失的实用方法。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-12 DOI: 10.1080/00273171.2024.2371816
Yanling Li, Zita Oravecz, Linying Ji, Sy-Miin Chow

Missingness in intensive longitudinal data triggered by latent factors constitute one type of nonignorable missingness that can generate simultaneous missingness across multiple items on each measurement occasion. To address this issue, we propose a multiple imputation (MI) strategy called MI-FS, which incorporates factor scores, lag/lead variables, and missing data indicators into the imputation model. In the context of process factor analysis (PFA), we conducted a Monte Carlo simulation study to compare the performance of MI-FS to listwise deletion (LD), MI with manifest variables (MI-MV, which implements MI on both dependent variables and covariates), and partial MI with MVs (PMI-MV, which implements MI on covariates and handles missing dependent variables via full-information maximum likelihood) under different conditions. Across conditions, we found MI-based methods overall outperformed the LD; the MI-FS approach yielded lower root mean square errors (RMSEs) and higher coverage rates for auto-regression (AR) parameters compared to MI-MV; and the PMI-MV and MI-MV approaches yielded higher coverage rates for most parameters except AR parameters compared to MI-FS. These approaches were also compared using an empirical example investigating the relationships between negative affect and perceived stress over time. Recommendations on when and how to incorporate factor scores into MI processes were discussed.

由潜在因素引发的密集纵向数据中的缺失是一种不可忽略的缺失,它可能在每个测量场合的多个项目中同时产生缺失。为了解决这个问题,我们提出了一种称为 MI-FS 的多重估算(MI)策略,它将因子得分、滞后/先导变量和缺失数据指标纳入估算模型。在过程因子分析(PFA)的背景下,我们进行了蒙特卡罗模拟研究,比较了 MI-FS 与列表删除法(LD)、带显变量的 MI(MI-MV,对因变量和协变量均实施 MI)以及带 MV 的部分 MI(PMI-MV,对协变量实施 MI,并通过全信息最大似然法处理缺失的因变量)在不同条件下的性能。在不同条件下,我们发现基于 MI 的方法总体上优于 LD;与 MI-MV 相比,MI-FS 方法产生的均方根误差(RMSE)更低,自动回归(AR)参数的覆盖率更高;与 MI-FS 相比,PMI-MV 和 MI-MV 方法产生的除 AR 参数外的大多数参数的覆盖率更高。我们还使用一个实证例子对这些方法进行了比较,该例子调查了负面情绪和感知压力随时间变化的关系。会上还讨论了何时以及如何将因子得分纳入多元智能过程的建议。
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引用次数: 0
Understanding the Consequences of Collinearity for Multilevel Models: The Importance of Disaggregation Across Levels. 了解多层次模型的共线性后果:跨层次分解的重要性。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-01 Epub Date: 2024-05-09 DOI: 10.1080/00273171.2024.2315549
Haley E Yaremych, Kristopher J Preacher

In multilevel models, disaggregating predictors into level-specific parts (typically accomplished via centering) benefits parameter estimates and their interpretations. However, the importance of level-specificity has been sparsely addressed in multilevel literature concerning collinearity. In this study, we develop novel insights into the interactivity of centering and collinearity in multilevel models. After integrating the broad literatures on centering and collinearity, we review level-specific and conflated correlations in multilevel data. Next, by deriving formal relationships between predictor collinearity and multilevel model estimates, we demonstrate how the consequences of collinearity change across different centering specifications and identify data characteristics that may exacerbate or mitigate those consequences. We show that when all or some level-1 predictors are uncentered, slope estimates can be greatly biased by collinearity. Disaggregation of all predictors eliminates the possibility that fixed effect estimates will be biased due to collinearity alone; however, under some data conditions, collinearity is associated with biased standard errors and random effect (co)variance estimates. Finally, we illustrate the importance of disaggregation for diagnosing collinearity in multilevel data and provide recommendations for the use of level-specific collinearity diagnostics. Overall, the necessity of disaggregation for identifying and managing collinearity's consequences in multilevel models is clarified in novel ways.

在多层次模型中,将预测因子分解为特定层次的部分(通常通过居中来实现)有利于参数估计及其解释。然而,在有关共线性的多层次文献中,却很少涉及水平特异性的重要性。在本研究中,我们对多层次模型中中心化和共线性的交互作用提出了新的见解。在整合了关于中心化和共线性的大量文献之后,我们回顾了多层次数据中特定层次的相关性和混合相关性。接下来,通过推导预测因子共线性与多层次模型估计值之间的正式关系,我们展示了共线性的后果在不同的中心化规范中是如何变化的,并确定了可能加剧或减轻这些后果的数据特征。我们表明,当所有或部分一级预测因子未居中时,斜率估计值会因共线性而产生很大偏差。对所有预测因子进行分解后,固定效应估计值就不会仅仅因为共线性而出现偏差;但是,在某些数据条件下,共线性会导致标准误差和随机效应(共)方差估计值出现偏差。最后,我们说明了分解对诊断多层次数据中的共线性的重要性,并提出了使用特定层次共线性诊断的建议。总之,我们以新颖的方式阐明了在多层次模型中识别和管理共线性后果的分类必要性。
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引用次数: 0
Counterfactual Mediation Analysis with a Latent Class Exposure. 潜类暴露的反事实中介分析。
IF 5.3 3区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2024-07-01 Epub Date: 2024-05-31 DOI: 10.1080/00273171.2024.2335394
Gemma Hammerton, Jon Heron, Katie Lewis, Kate Tilling, Stijn Vansteelandt

Latent classes are a useful tool in developmental research, however there are challenges associated with embedding them within a counterfactual mediation model. We develop and test a new method "updated pseudo class draws (uPCD)" to examine the association between a latent class exposure and distal outcome that could easily be extended to allow the use of any counterfactual mediation method. UPCD extends an existing group of methods (based on pseudo class draws) that assume that the true values of the latent class variable are missing, and need to be multiply imputed using class membership probabilities. We simulate data based on the Avon Longitudinal Study of Parents and Children, examine performance for existing techniques to relate a latent class exposure to a distal outcome ("one-step," "bias-adjusted three-step," "modal class assignment," "non-inclusive pseudo class draws," and "inclusive pseudo class draws") and compare bias in parameter estimates and their precision to uPCD when estimating counterfactual mediation effects. We found that uPCD shows minimal bias when estimating counterfactual mediation effects across all levels of entropy. UPCD performs similarly to recommended methods (one-step and bias-adjusted three-step), but provides greater flexibility and scope for incorporating the latent grouping within any commonly-used counterfactual mediation approach.

潜类是发展研究中的一个有用工具,但将其嵌入反事实中介模型却面临挑战。我们开发并测试了一种新方法 "更新伪类抽样(uPCD)",用于检验潜类暴露与远端结果之间的关联,这种方法可以很容易地扩展到任何反事实中介方法。UPCD 扩展了现有的一组方法(基于伪类抽样),这些方法假定潜类变量的真实值是缺失的,需要使用类成员概率进行多重估算。我们模拟了雅芳父母与子女纵向研究(Avon Longitudinal Study of Parents and Children)的数据,考察了将潜类暴露与远端结果相关联的现有技术("一步法"、"偏差调整三步法"、"模态类分配"、"非包容性伪类抽样 "和 "包容性伪类抽样")的性能,并在估计反事实中介效应时,比较了参数估计的偏差及其与 uPCD 的精度。我们发现,uPCD 在估计所有熵水平的反事实中介效应时,偏差最小。UPCD 的表现与推荐方法(一步法和偏差调整三步法)相似,但提供了更大的灵活性和范围,可将潜在分组纳入任何常用的反事实中介方法中。
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引用次数: 0
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Multivariate Behavioral Research
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