Assessing how adequate clusters fit a dataset and finding an optimum number of clusters is a difficult process. A membership matrix and the degree of membership matrix is suggested to determine the homogeneity of a cluster fit. Maximisation of the ratio of the overall degree of membership at cluster number lag 1 is also suggested as a method to optimise the number of clusters in a dataset. A threshold factor upon the degree of membership is also suggested for homogeneous clusters. Cluster simulations were given to compare how well the proposed method compares against established methods. This method may be applied to the output of both hierarchical and k-means clustering.
The micro-randomized trial (MRT) is a sequential randomized experimental design to empirically evaluate the effectiveness of mobile health (mHealth) intervention components that may be delivered at hundreds or thousands of decision points. MRTs have motivated a new class of causal estimands, termed "causal excursion effects", for which semiparametric inference can be conducted via a weighted, centered least squares criterion (Boruvka et al., 2018). Existing methods assume between-subject independence and non-interference. Deviations from these assumptions often occur. In this paper, causal exc…
The average treatment effect (ATE) is popularly used to assess the treatment effect. However, the ATE implicitly assumes a homogenous treatment effect even amongst individuals with different characteristics. In this paper, we mainly focus on assessing the treatment effect heterogeneity, which has important implications in designing the optimal individual treatment regimens and in policy making. The treatment benefit rate (TBR) and treatment harm rate (THR) have been defined to characterize the magnitude of heterogeneity for binary outcomes. When the outcomes are continuous, we extend the defin…
One size fits all approaches to medicine have become a thing of the past as the understanding of individual differences grows. The paper introduces a test for the presence of heterogeneity in treatment effects in a clinical trial. Heterogeneity is assessed on the basis of the predicted individual treatment effects (PITE) framework and a permutation test is utilized to establish if significant heterogeneity is present. We first use the novel test to show that heterogeneity in the effects of interventions exists in the Amyotrophic Lateral Sclerosis Clinical Trials. We then show, using two differ…
Treatment effect heterogeneity occurs when individual characteristics influence the effect of a treatment. We propose a novel approach that combines prognostic score matching and conditional inference trees to characterize effect heterogeneity of a randomized binary treatment. One key feature that distinguishes our method from alternative approaches is that it controls the Type I error rate, i.e., the probability of identifying effect heterogeneity if none exists and retains the underlying subgroups. This feature makes our technique particularly appealing in the context of clinical trials, whe…
Replication is complicated in psychological research because studies of a given psychological phenomenon can never be direct or exact replications of one another, and thus effect sizes vary from one study of the phenomenon to the next--an issue of clear importance for replication. Current large scale replication projects represent an important step forward for assessing replicability, but provide only limited information because they have thus far been designed in a manner such that heterogeneity either cannot be assessed or is intended to be eliminated. Consequently, the non-trivial degree of…
Assessing the impact of variance heterogeneity and misspecification in mixed-effects location-scale models
MRC Biostatistics Unit, University of Cambridge（剑桥大学 MRC 生物统计学单元）；Department of Biomedical Informatics, Columbia University（哥伦比亚大学生物医学信息学系）；Population, Policy and Practice Research and Teaching Department, UCL Great Ormond Street Institute of Child Health（UCL 大奥蒙德街儿童健康研究所人口、政策和实践研究与教学部）
There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation index, this paper proposes to set up null models that capture structural features of the data that cannot be interpreted as indicating clustering. Artificial datasets are sampled from the null model with parameters estimated from the original dataset. This can be used for testing the null hypothesis of a homogeneous population against a clustering alternative…
Cross-level interactions among fixed effects in linear mixed models (also known as multilevel models) are often complicated by the variances stemming from random effects and residuals. When these variances change across clusters, tests of fixed effects (including cross-level interaction terms) are subject to inflated Type I or Type II error. While the impact of variance change/heterogeneity has been noticed in the literature, few methods have been proposed to detect this heterogeneity in a simple, systematic way. In addition, when heterogeneity among clusters is detected, researchers often wis…
In diverse fields ranging from finance to omics, it is increasingly common that data is distributed and with multiple individual sources (referred to as ``clients'' in some studies). Integrating raw data, although powerful, is often not feasible, for example, when there are considerations on privacy protection. Distributed learning techniques have been developed to integrate summary statistics as opposed to raw data. In many of the existing distributed learning studies, it is stringently assumed that all the clients have the same model. To accommodate data heterogeneity, some federated learnin…
Using Individualized Treatment Effects to Assess Treatment Effect Heterogeneity
Advanced Methodology and Data Science, Novartis Pharma AG（诺华制药AG高级方法与数据科学）；China Novartis Institutes for Bio-medical Research CO.（中国诺华生物医学研究院有限公司）；Advanced Methodology and Data Science, Novartis Pharmaceuticals Corporation（诺华制药有限公司高级方法与数据科学）；Department of Statistics, Stanford University（斯坦福大学统计学系）
Inter-rater reliability (IRR), which is a prerequisite of high-quality ratings and assessments, may be affected by contextual variables such as the rater's or ratee's gender, major, or experience. Identification of such heterogeneity sources in IRR is important for implementation of policies with the potential to decrease measurement error and to increase IRR by focusing on the most relevant subgroups. In this study, we propose a flexible approach for assessing IRR in cases of heterogeneity due to covariates by directly modeling differences in variance components. We use Bayes factors to selec…
Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-clu…
Cluster-induced target shift and synthetic approximation for high-dimensional clustered data
Florida International University（佛罗里达国际大学）；University of Nottingham Ningbo China（诺丁汉大学宁波校区）；University of Pennsylvania（宾夕法尼亚大学）；Dartmouth College（达特茅斯学院）；Oklahoma State University（俄克拉荷马州立大学）
We propose a multidimensional tensor clustering approach for studying how professional basketball players' shooting patterns vary over court locations and game time. Unlike most existing methods that only study continuous-valued tensors or have to assume the same cluster structure along different tensor directions, we propose a Bayesian nonparametric model that deals with count-valued tensors and projects the heterogeneity among players onto tensor dimensions while allowing cluster structures to be different over directions. Our method is fully probabilistic; hence allows simultaneous inferenc…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of effects that have to be estimated. A recursive partitioning (or tree based) method is proposed that identifies clusters of units that share the same effect. The approach reduces the number of parameters to be estimated and is useful in particular if one is interested in identifying clusters with the same effect on a response variable. It is shown that the met…
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly consistent estimates of degree-corrected latent positions, with asymptotically Gaussian error. In the special case of a degree-corrected stochastic block model, the embedding concentrates about K distinct points, representing communities. These can be recovered perfectly, asymptotically, through a subsequent clustering step, without spherical projection, as co…
Dissecting Microbial Community Structure and Heterogeneity via Multivariate Covariate-Adjusted Clustering
University of Connecticut Health Center（康涅狄格大学健康中心）；Department of Biostatistics, University of Michigan（密歇根大学生物统计系）；Department of Statistics, University of Connecticut（康涅狄格大学统计学系）
We provide a novel inferential framework to estimate the exact affine Stone index (EASI) model, and analyze welfare implications due to price changes caused by taxes. Our inferential framework is based on a non-parametric specification of the stochastic errors in the EASI incomplete demand system using Dirichlet processes. Our proposal enables to identify consumer clusters due to unobserved preference heterogeneity taking into account, censoring, simultaneous endogeneity and non-linearities. We perform an application based on a tax on electricity consumption in the Colombian economy. Our resul…
University of Connecticut（康涅狄格大学）；Jiangxi University of Finance and Economics（江西财经大学）；Yale School of Public Health（耶鲁公共卫生学院）；University of California, Riverside（加州大学河滨分校）；University of Connecticut Health Center（康涅狄格大学健康中心）
Researchers often have to deal with heterogeneous population with mixed regression relationships, increasingly so in the era of data explosion. In such problems, when there are many candidate predictors, it is not only of interest to identify the predictors that are associated with the outcome, but also to distinguish the true sources of heterogeneity, i.e., to identify the predictors that have different effects among the clusters and thus are the true contributors to the formation of the clusters. We clarify the concepts of the source of heterogeneity that account for potential scale differen…
A recent literature in econometrics models unobserved cross-sectional heterogeneity in panel data by assigning each cross-sectional unit a one-dimensional, discrete latent type. Such models have been shown to allow estimation and inference by regression clustering methods. This paper is motivated by the finding that the clustered heterogeneity models studied in this literature can be badly misspecified, even when the panel has significant discrete cross-sectional structure. To address this issue, we generalize previous approaches to discrete unobserved heterogeneity by allowing each unit to ha…
The multilevel model (MLM) is the popular approach to describe dependences of hierarchically clustered observations. A main feature is the capability to estimate (cluster-specific) random effect parameters, while their distribution describes the variation across clusters. However, the MLM can only model positive associations among clustered observations, and it is not suitable for small sample sizes. The limitation of the MLM becomes apparent when estimation methods produce negative estimates for random effect variances, which can be seen as an indication that observations are negatively corre…
