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经典因子分析中的 Varimax 旋转具有统计推断作用AI 解读

Abstract In the 1930s, Psychologists began developing Multiple-Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax factor rotation redraws the axes through the multi-dimensional factors to make them sparse and thus make them more interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be…

重新审视簇范围推断：脑活动的量化与定位AI 解读

Abstract Cluster inference based on spatial extent thresholding is a popular analysis method multiple testing in spatial data, and is frequently used for finding activated brain areas in neuroimaging. However, the method has several well-known issues. While powerful for finding regions with some activation, the method as currently defined does not allow any further quantification or localisation of signal. In this paper, we repair this gap. We show that cluster-extent…

利用泊松近似似然对流行病舱室模型进行一致且快速的推断AI 解读

Abstract Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson approximate likelihood (PAL) methods. In contrast to the popular ordinary differential equation (ODE) approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large…

部分线性单指标变系数模型的两阶段估计与偏差校正经验似然AI 解读

Abstract The estimation and empirical likelihood (EL) of the parameters of interest in a partially linear single-index varying-coefficient model are studied. A two-stage method is presented to estimate the regression parameters and the coefficient functions. The asymptotic distributions of the proposed estimators are obtained. Meanwhile, a bias-corrected EL ratio for the regression parameters is proposed. It is shown that the ratio is asymptotically standard chi-squared. The…

利用深度条件生成学习检验时间序列的马尔可夫性AI 解读

Abstract The Markov property is widely imposed in analysis of time series data. Correspondingly, testing the Markov property, and relatedly, inferring the order of a Markov model, are of paramount importance. In this article, we propose a nonparametric test for the Markov property in high-dimensional time series via deep conditional generative learning. We also apply the test sequentially to determine the order of the Markov model. We show that the test controls the type-I…

归一化潜在测度因子模型AI 解读

Abstract We propose a methodology for modelling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalised random measures, we consider a prior distribution for a collection of discrete random measures where each measure is a linear combination of a set of latent measures, interpretable as characteristic traits shared by different distributions, with positive random weights. The model is nonidentified and a method for…

多协变量预期短缺回归的稳健估计与推断AI 解读

Abstract Expected shortfall (ES), also known as superquantile or conditional value-at-risk, is an important measure in risk analysis and stochastic optimisation and has applications beyond these fields. In finance, it refers to the conditional expected return of an asset given that the return is below some quantile of its distribution. In this paper, we consider a joint regression framework recently proposed to model the quantile and ES of a response variable simultaneously,…

通过双臂老虎机过程构造策略性两样本检验AI 解读

Abstract This study aims to improve the power of two-sample tests by analysing whether the difference between two population parameters is larger than a prespecified positive equivalence margin. The classic test statistic treats the original data as exchangeable, while the proposed test statistic breaks the structure and proposes employing a two-armed bandit process to strategically integrate the data and thus a strategy-specific test statistic is constructed by combining…

大规模分布式学习的拟牛顿更新AI 解读

Abstract Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no Hessian matrix inversion or communication is needed. This considerably reduces the computation and communication complexity of the proposed method. Notably, related existing methods only analyse numerical convergence and require a…

Ying Zhou与Xinyi Zhang对Varimax因子分析论文的讨论AI 解读

We congratulate Rohe and Zeng for their inspiring work on providing theoretical support for Varimax rotation in factor analysis. A key contribution of the article is the demonstration that if the factors in the semi-parametric factor model follow heavy-tailed distribution, then performing principal components analysis (PCA) on the observed data matrix along with Varimax rotation applied to the principal components does produce interpretable explanatory variables. We have the…

Van Werde对《Varimax经典因子分析可进行统计推断》的讨论AI 解读

I would like to point out that the author’s results have potential applications in the theory of random graphs beyond those for block models which are explicitly remarked upon in the paper. In particular, the results could be used to resolve the nonidentifiability associated with random dot product graphs (Athreya et al., 2017, Remark 1). The authors are most likely already aware of this connection: they have previously worked on generalized random dot product graphs in Rohe…

We congratulate Rohe and Zeng on their interesting paper and would like to share two comments and propose one question for their consideration. First, it is impressive to see the large variety of models addressed by the ‘vintage sparse PCA’ (vsp) framework, ranging from traditional factor models to explainable and sparse PCA but also including topic models and stochastic block models. In our view, the demonstration of the broad applicability of the ‘compress and rotate’…

Pargent、Goretzko 与 von Oertzen 对《经典因子分析结合 Varimax 可进行统计推断》的讨论AI 解读

As psychologists, we appreciate Rohe & Zeng’s (R&Z; Rohe & Zeng, 2022) new insights into ‘vintage’ principal component analysis with varimax rotation (PCA+VR). Theories of intelligence and personality, perhaps psychology’s contributions best known outside of our field, have been a direct product of PCA. PCA+VR is still widely used for developing and evaluating psychological tests and questionnaires, although the literature has fought against it in favour of more complex…

Bickel 等对《Varimax 经典因子分析实现统计推断》的讨论意见AI 解读

We compliment the authors for their unification of old and new latent variable models. Their motivation seems to have come from Thurstone’s Factor Analysis and the wish to explain the somewhat mysterious success of Kaiser’s Varimax rule in that context. However, their major applications and notation stem from overlapping network community detection and Latent Dirichlet Allocation (LDA) (Blei et al., 2003). Inference for these models can be unified in another way via a…

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VanderWeele对《Varimax传统因子分析可进行统计推断》的讨论AI 解读

Rohe and Zeng (2022) have provided important results concerning properties of ‘vintage factor analysis’ that assist with interpretability, especially for non-Gaussian and leptokurtic data. I would like to focus my remarks on one particular comment, also present in Thurstone (1935) that, one aims “to ensure that each factor…. corresponds to a ‘scientifically meaningful category.’” This is an important goal, but I would argue that (i) questions of the meaning of factors always…

Tao Wang 对《Varimax 旋转的经典因子分析可进行统计推断》的讨论AI 解读

I congratulate the authors on their excellent paper studying the fundamental mechanism of PCA with the Varimax rotation. The paper thoughtfully establishes theorems to demonstrate that the Varimax rotation can supply an unified estimating technique for a wide range of semiparametric factor models. My discussion will be primarily centred on clarification and potential extensions. The paper illustrates that if PCA is performed on a matrix with independent elements, PCA with…

Yang Liu对《采用Varimax旋转的传统因子分析可实现统计推断》的讨论AI 解读

I congratulate Rohe and Zeng for the fascinating piece of work. They discovered that sparse principle components analysis (PCA) with Varimax rotation (vsp) identifies and consistently recovers latent factors in a broad class of semi-parametric factor models. I have a number of comments to share regarding identification assumptions, asymptotic results, and interpretation of factors. Identification Assumptions. The identification of the low-rank matrix M=ZBY⊤ (when treated as…

Kaizheng Wang 对《采用 Varimax 的传统因子分析可实现统计推断》的讨论AI 解读

I congratulate Drs. Rohe and Zeng for their elegant paper that advances our understanding of the classical Varimax algorithm. Varimax was originally proposed by Kaiser (1958) as an analytic criterion for determining interpretable factors. Despite its extensive applications and tremendous success, theoretical understanding is still lacking. Statisticians are further perplexed by negative results showing the nonidentifiability of Gaussian factor models. Toward resolving the…

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倪晓月对《Varimax 旋转的传统因子分析可进行统计推断》的讨论AI 解读

I want to congratulate Rohe and Zeng on solving a long-time puzzle (and fight between statisticians and practitioners) of ‘why/whether the varimax rotation works’. Their inspiring results have some implications in the literature of latent space models for social networks (Hoff, 2021; Hoff et al., 2002). One of the appealing features of the latent space model is that one can extract the latent factors and analyse the unobserved features through the latent positions. However,…

Anru Zhang; Rungang Han and Anru R Zhang’s contribution to the Discussion of “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe &

Mark Pilling 对《采用 Varimax 的传统因子分析可进行统计推断》的讨论AI 解读

Thanks to the authors for their very interesting, thoughtful, and thorough reconsideration of the topic of factor analysis. We know to be a weakness of factor analysis that an issue is that analysts must chose the type of rotation (e.g., SPSS lists Varimax, Direct Oblimin, Quartimax, Equamax, & Promax) to use, and this choice tends to be subjectively based on how useful or interpretable the rotation was in the context of the study. So multiple rotations might be considered.…

Joshua Cape 对《采用 Varimax 的经典因子分析实现统计推断》的讨论AI 解读

I congratulate Professor Rohe and Dr Zeng on their illuminating paper. Their broad contributions will no doubt redouble contemporary research activity in multivariate analysis for years to come. Even the paper’s appendices are full of valuable gems, not to be overlooked by readers. Rohe and Zeng contextualize their findings vis-à-vis classical developments in psychometrics and statistics. This choice is apt, for the authors champion a newfound understanding of varimax factor…