Psychological methods最新文献

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Uses of uncertain statistical power: Designing future studies, not evaluating completed studies. 使用不确定的统计能力:设计未来的研究,而不是评估已完成的研究。
IF 7.6 1区 心理学
Psychological methods Pub Date : 2024-09-19 DOI: 10.1037/met0000577
Jolynn Pek, Kathryn J Hoisington-Shaw, Duane T Wegener
{"title":"Uses of uncertain statistical power: Designing future studies, not evaluating completed studies.","authors":"Jolynn Pek, Kathryn J Hoisington-Shaw, Duane T Wegener","doi":"10.1037/met0000577","DOIUrl":"https://doi.org/10.1037/met0000577","url":null,"abstract":"<p><p>tatistical power is a topic of intense interest as part of proposed methodological reforms to improve the defensibility of psychological findings. Power has been used in disparate ways-some that follow and some that do not follow from definitional features of statistical power. We introduce a taxonomy on three uses of power (comparing the performance of different procedures, designing or planning studies, and evaluating completed studies) in the context of new developments that consider uncertainty due to sampling variability. This review first describes fundamental concepts underlying power, new quantitative developments in power analysis, and the application of power analysis in designing studies. To facilitate the pedagogy of using power for design, we provide web applications to illustrate these concepts and examples of power analysis using newly developed methods. We also describe why using power for evaluating completed studies can be counterproductive. We conclude with a discussion of future directions in quantitative research on power analysis and provide recommendations for applying power in substantive research. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":" ","pages":""},"PeriodicalIF":7.6,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142293953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving variables with Monte Carlo simulation experiments: A stochastic root-solving approach. 用蒙特卡罗模拟实验求解变量:随机求根法
IF 7.6 1区 心理学
Psychological methods Pub Date : 2024-09-19 DOI: 10.1037/met0000689
R Philip Chalmers
{"title":"Solving variables with Monte Carlo simulation experiments: A stochastic root-solving approach.","authors":"R Philip Chalmers","doi":"10.1037/met0000689","DOIUrl":"https://doi.org/10.1037/met0000689","url":null,"abstract":"<p><p>Despite their popularity and flexibility, questions remain regarding how to optimally solve particular unknown variables of interest using Monte Carlo simulation experiments. This article reviews two common approaches based on either performing deterministic iterative searches with noisy objective functions or by constructing interpolation estimates given fitted surrogate functions, highlighting the inefficiencies and inferential concerns of both methods. To address these limitations, and to fill a gap in existing Monte Carlo experimental methodology, a novel algorithm termed the probabilistic bisection algorithm with bolstering and interpolations (ProBABLI) is presented with the goal providing efficient, consistent, and unbiased estimates (with associated confidence intervals) for the stochastic root equations found in Monte Carlo simulation research. Properties of the ProBABLI approach are demonstrated using practical sample size planning applications for independent samples <i>t</i> tests and structural equation models given target power rates, precision criteria, and expected power functions that incorporate prior beliefs. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":" ","pages":""},"PeriodicalIF":7.6,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142293951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Investigating the effects of congruence between within-person associations: A comparison of two extensions of response surface analysis. 调查人内关联之间一致性的影响:响应面分析法两种扩展方法的比较。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-12 DOI: 10.1037/met0000666
Sarah Humberg,Niclas Kuper,Katrin Rentzsch,Tanja M Gerlach,Mitja D Back,Steffen Nestler
{"title":"Investigating the effects of congruence between within-person associations: A comparison of two extensions of response surface analysis.","authors":"Sarah Humberg,Niclas Kuper,Katrin Rentzsch,Tanja M Gerlach,Mitja D Back,Steffen Nestler","doi":"10.1037/met0000666","DOIUrl":"https://doi.org/10.1037/met0000666","url":null,"abstract":"Response surface analysis (RSA) allows researchers to study whether the degree of congruence between two predictor variables is related to a potential psychological outcome. Here, we adapt RSA to the case in which the two predictor variables whose congruence is of interest refer to individual differences in within-person associations (WPAs) between variables that fluctuate over time. For example, a WPA-congruence hypothesis in research on romantic relationships could posit that partners are happier when they have similar social reactivities-that is, when they have similarly strong WPAs between the quantity of their social interactions and their momentary well-being. One method for testing a WPA-congruence hypothesis is a two-step approach in which the individuals' WPAs are first estimated as random slopes in respective multilevel models, and then these estimates are used as predictors in a regular RSA. As an alternative, we suggest combining RSA with multilevel structural equation modeling (MSEM) by specifying the WPAs as random slopes in the structural equation and using their latent second-order terms to predict the outcome on Level 2. We introduce both approaches and provide and explain their corresponding computer code templates. We also compared the two approaches with a simulation study and found that the MSEM model-despite its complexities (e.g., nonlinear functions of latent slopes)-has advantages over the two-step approach. We conclude that the MSEM approach should be used in practice. We demonstrate its application using data from a daily diary study and offer guidance for important decisions (e.g., about standardization). (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"10 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Statistical power and optimal design for randomized controlled trials investigating mediation effects. 调查中介效应的随机对照试验的统计功率和最佳设计。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-12 DOI: 10.1037/met0000698
Zuchao Shen,Wei Li,Walter Leite
{"title":"Statistical power and optimal design for randomized controlled trials investigating mediation effects.","authors":"Zuchao Shen,Wei Li,Walter Leite","doi":"10.1037/met0000698","DOIUrl":"https://doi.org/10.1037/met0000698","url":null,"abstract":"Mediation analyses in randomized controlled trials (RCTs) can unpack potential causal pathways between interventions and outcomes and help the iterative improvement of interventions. When designing RCTs investigating these mechanisms, two key considerations are (a) the sample size needed to achieve adequate statistical power and (b) the efficient use of resources. The current study has developed closed-form statistical power formulas for RCTs investigating mediation effects with and without covariates under the Sobel and joint significance tests. The power formulas are functions of sample size, sample allocation between treatment conditions, effect sizes in the treatment-mediator and mediator-outcome paths, and other common parameters (e.g., significance level, one- or two-tailed test). The power formulas allow us to assess how covariates impact the magnitude of mediation effects and statistical power. Accounting for the potential unequal sampling costs between treatment conditions, we have further developed an optimal design framework to identify optimal sample allocations that provide the maximum statistical power under a fixed budget or use the minimum resources to achieve a target power. Illustrations show that the proposed method can identify more efficient and powerful sample allocations than conventional designs with an equal number of individuals in each treatment condition. We have implemented the methods in the R package odr to improve the accessibility of the work. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"263 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixture multigroup structural equation modeling: A novel method for comparing structural relations across many groups. 混合多组结构方程模型:一种比较多组结构关系的新方法。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-12 DOI: 10.1037/met0000667
Andres F Perez Alonso,Yves Rosseel,Jeroen K Vermunt,Kim De Roover
{"title":"Mixture multigroup structural equation modeling: A novel method for comparing structural relations across many groups.","authors":"Andres F Perez Alonso,Yves Rosseel,Jeroen K Vermunt,Kim De Roover","doi":"10.1037/met0000667","DOIUrl":"https://doi.org/10.1037/met0000667","url":null,"abstract":"Behavioral scientists often examine the relations between two or more latent variables (e.g., how emotions relate to life satisfaction), and structural equation modeling (SEM) is the state-of-the-art for doing so. When comparing these \"structural relations\" among many groups, they likely differ across the groups. However, it is equally likely that some groups share the same relations so that clusters of groups emerge. Latent variables are measured indirectly by questionnaires and, for validly comparing their relations among groups, the measurement of the latent variables should be invariant across the groups (i.e., measurement invariance). However, across many groups, often at least some measurement parameters differ. Restricting these measurement parameters to be invariant, when they are not, causes the structural relations to be estimated incorrectly and invalidates their comparison. We propose mixture multigroup SEM (MMG-SEM) to gather groups with equivalent structural relations in clusters while accounting for the reality of measurement noninvariance. Specifically, MMG-SEM obtains a clustering of groups focused on the structural relations by making them cluster-specific, while capturing measurement noninvariances with group-specific measurement parameters. In this way, MMG-SEM ensures that the clustering is valid and unaffected by differences in measurement. This article proposes an estimation procedure built around the R package \"lavaan\" and evaluates MMG-SEM's performance through two simulation studies. The results demonstrate that MMG-SEM successfully recovers the group-clustering as well as the cluster-specific relations and the partially group-specific measurement parameters. To illustrate its empirical value, we apply MMG-SEM to cross-cultural data on the relations between experienced emotions and life satisfaction. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"10 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Latent growth mixture models as latent variable multigroup factor models: Comment on McNeish et al. (2023). 作为潜在变量多组因子模型的潜在增长混合模型:对 McNeish 等人(2023 年)的评论。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-12 DOI: 10.1037/met0000693
Phillip K Wood,Wolfgang Wiedermann,Jules K Wood
{"title":"Latent growth mixture models as latent variable multigroup factor models: Comment on McNeish et al. (2023).","authors":"Phillip K Wood,Wolfgang Wiedermann,Jules K Wood","doi":"10.1037/met0000693","DOIUrl":"https://doi.org/10.1037/met0000693","url":null,"abstract":"McNeish et al. argue for the general use of covariance pattern growth mixture models because these models do not involve the assumption of random effects, demonstrate high rates of convergence, and are most likely to identify the correct number of latent subgroups. We argue that the covariance pattern growth mixture model is a single random intercept model. It and other models considered in their article are special cases of a general model involving slope and intercept factors. We argue growth mixture models are multigroup invariance hypotheses based on unknown subgroups. Psychometric models in which trajectories are modeled using slope factor loadings which vary by latent subgroup are often conceptually preferable. Convergence rates for mixture models can be substantially improved by using a variance component start value taken from analyses with one fewer class and by specifying multifactor models in orthogonal form. No single latent growth model is appropriate across all research contexts and, instead, the most appropriate latent mixture model must be \"right-sized\" to the data under consideration. Reanalysis of a real-world longitudinal data set of posttraumatic stress disorder symptomatology reveals a three-group model involving exponential decline, further suggesting that the four-group \"cat's cradle\" pattern frequently reported is artefactual. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"41 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Bayesian reservoir model of psychological regulation. 心理调节的贝叶斯水库模型。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-12 DOI: 10.1037/met0000690
Mirinda M Whitaker,Cindy S Bergeman,Pascal R Deboeck
{"title":"The Bayesian reservoir model of psychological regulation.","authors":"Mirinda M Whitaker,Cindy S Bergeman,Pascal R Deboeck","doi":"10.1037/met0000690","DOIUrl":"https://doi.org/10.1037/met0000690","url":null,"abstract":"Social and behavioral scientists are increasingly interested the dynamics of the processes they study. Despite the wide array of processes studied, a fairly narrow set of models are applied to characterize dynamics within these processes. For social and behavioral research to take the next step in modeling dynamics, a wider variety of models need to be considered. The reservoir model is one model of psychological regulation that helps expand the models available (Deboeck & Bergeman, 2013). The present article implements the Bayesian reservoir model for both single time series and multilevel data. Simulation 1 compares the performance of the original version of the reservoir model fit using structural equation modeling (Deboeck & Bergeman, 2013) to the proposed Bayesian estimation approach. Simulation 2 expands this to a multilevel data scenario and compares this to the single-level version. The Bayesian estimation approach performs substantially better than the original estimation approach and produces low-bias estimates even with time series as short as 25 observations. Combining Bayesian estimation with a multilevel modeling approach allows for relatively unbiased estimation with sample sizes as small as 15 individuals and/or with time series as short as 15 observations. Finally, a substantive example is presented that applies the Bayesian reservoir model to perceived stress, examining how the model parameters relate to psychological variables commonly expected to relate to resilience. The current expansion of the reservoir model demonstrates the benefits of leveraging the combined strengths of Bayesian estimation and multilevel modeling, with new dynamic models that have been tailored to match the process of psychological regulation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"1 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Clustering methods: To optimize or to not optimize? 聚类方法:优化还是不优化?
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-12 DOI: 10.1037/met0000688
Michael Brusco,Douglas Steinley,Ashley L Watts
{"title":"Clustering methods: To optimize or to not optimize?","authors":"Michael Brusco,Douglas Steinley,Ashley L Watts","doi":"10.1037/met0000688","DOIUrl":"https://doi.org/10.1037/met0000688","url":null,"abstract":"Many clustering problems are associated with a particular objective criterion that is sought to be optimized. There are often several methods that can be used to tackle the optimization problem, and one or more of them might guarantee a globally optimal solution. However, it is quite possible that, relative to one or more suboptimal solutions, a globally optimal solution might be less interpretable from the standpoint of psychological theory or be less in accordance with some known (i.e., true) cluster structure. For example, in simulation experiments, it has sometimes been observed that there is not a perfect correspondence between the optimized clustering criterion and recovery of the underlying known cluster structure. This can lead to the misconception that clustering methods with a tendency to produce suboptimal solutions might, in some instances, be preferable to superior methods that provide globally optimal (or at least better locally optimal) solutions. In this article, we present results from simulation studies in the context of K-median clustering where departure from global optimality was carefully controlled. Although the results showed that suboptimal solutions sometimes produced marginally better recovery for experimental cells where the known cluster structure was less well-defined, capriciously accepting inferior solutions is an unwise practice. However, there are instances in which some sacrifice in the optimization criterion value to meet certain desirable constraints or to improve the value of one or more other relevant criteria is principled. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"17 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142174794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
So is it better than something else? Using the results of a random-effects meta-analysis to characterize the magnitude of an effect size as a percentile. 那么,它比其他东西更好吗?用随机效应荟萃分析的结果来描述效应大小的百分位数。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-09 DOI: 10.1037/met0000704
Peter Boedeker,Gena Nelson,Hannah Carter
{"title":"So is it better than something else? Using the results of a random-effects meta-analysis to characterize the magnitude of an effect size as a percentile.","authors":"Peter Boedeker,Gena Nelson,Hannah Carter","doi":"10.1037/met0000704","DOIUrl":"https://doi.org/10.1037/met0000704","url":null,"abstract":"The characterization of an effect size is best made in reference to effect sizes found in the literature. A random-effects meta-analysis is the systematic synthesis of related effects from across a literature, producing an estimate of the distribution of effects in the population. We propose using the estimated mean and variance from a random-effects meta-analysis to inform the characterization of an observed effect size. The percentile of an observed effect size within the estimated distribution of population effects can describe the magnitude of the observed effect. Because there is uncertainty in the population estimates, we propose using the prediction distribution (used frequently to estimate the prediction interval in a meta-analysis) to serve as the reference distribution when characterizing an effect size. Doing so, the percentile of an observed effect and the limits of the effect size's 95% confidence interval within the prediction distribution are calculated. With numerous meta-analyses available including various outcomes and contexts, the presented method can be useful to many researchers and practitioners. We demonstrate the application of an easy-to-use Excel worksheet to automate these percentile calculations. We follow this with a simulation study evaluating the method's performance over a range of conditions. Recommendations (and cautions) for meta-analysts and researchers conducting a single study are provided. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"5 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unidimensional community detection: A monte carlo simulation, grid search, and comparison. 单维群落检测:蒙特卡罗模拟、网格搜索和比较。
IF 7 1区 心理学
Psychological methods Pub Date : 2024-09-09 DOI: 10.1037/met0000692
Alexander P Christensen
{"title":"Unidimensional community detection: A monte carlo simulation, grid search, and comparison.","authors":"Alexander P Christensen","doi":"10.1037/met0000692","DOIUrl":"https://doi.org/10.1037/met0000692","url":null,"abstract":"Unidimensionality is fundamental to psychometrics. Despite the recent focus on dimensionality assessment in network psychometrics, unidimensionality assessment remains a challenge. Community detection algorithms are the most common approach to estimate dimensionality in networks. Many community detection algorithms maximize an objective criterion called modularity. A limitation of modularity is that it penalizes unidimensional structures in networks, favoring two or more communities (dimensions). In this study, this penalization is discussed and a solution is offered. Then, a Monte Carlo simulation using one- and two-factor models is performed. Key to the simulation was the condition of model error or the misfit of the population factor model to the generated data. Based on previous simulation studies, several community detection algorithms that have performed well with unidimensional structures (Leading Eigenvalue, Leiden, Louvain, and Walktrap) were compared. A grid search was performed on the tunable parameters of these algorithms to determine the optimal trade-off between unidimensional and bidimensional recovery. The best-performing parameters for each algorithm were then compared against each other as well as maximum likelihood factor analysis and parallel analysis (PA) with mean and 95th percentile eigenvalues. Overall, the Leiden and Louvain algorithms and PA methods were the most accurate methods to recover unidimensional and bidimensional structures and were the most robust to model error. More nuanced method recommendations for specific unidimensional and bidimensional conditions are provided. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":"5 1","pages":""},"PeriodicalIF":7.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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