A New Semiparametric Approach to Finite Mixture of Regressions using Penalized Regression via Fusion

Austin, Erin; Pan, Wei; Shen, Xiaotong

doi:10.5705/ss.202016.0531

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…Ma and Huang (2017) proposed a concave pairwise fusion approach to identify sub-groups with pairwise penalization on subject-specific intercepts. Austin et al (2020) proposed a grouping fusion approach to identify unknown sub-groups and their corresponding regression models. Tang et al (2020) proposed a method to simultaneously achieve individualized variable selection and sub-grouping.…”

Section: Discussionmentioning

confidence: 99%

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Pursuing sources of heterogeneity in modeling clustered population

Zhao

et al. 2021

Biometrics

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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 differences of the clusters and propose a regularized finite mixture effects regression to achieve heterogeneity pursuit and feature selection simultaneously. We develop an efficient algorithm and show that our approach can achieve both estimation and selection consistency. Simulation studies further demonstrate the effectiveness of our method under various practical scenarios. Three applications are presented, namely, an imaging genetics study for linking genetic factors and brain neuroimaging traits in Alzheimer's disease, a public health study for exploring the association between suicide risk among adolescents and their school district characteristics, and a sport analytics study for understanding how the salary levels of baseball players are associated with their performance and contractual status.

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Section: Discussionmentioning

confidence: 99%

“…Austin et al . (2020) proposed a grouping fusion approach to identify unknown sub‐groups and their corresponding regression models. Tang et al .…”

Section: Discussionmentioning

confidence: 99%

Pursuing sources of heterogeneity in modeling clustered population

Zhao

et al. 2021

Biometrics

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“…To mention a few, Ma and Huang (2017) proposed a concave pairwise fusion approach to identify sub-groups with pairwise penalization on subject-specific intercepts. Austin et al (2020) proposed a grouping fusion approach to simultaneously identify unknown sub-groups and their corresponding regression models. Tang ϑ ∈ ω.…”

Section: Discussionmentioning

confidence: 99%

Pursuing Sources of Heterogeneity in Modeling Clustered Population

Li¹,

Yu²,

Zhao³

et al. 2020

Preprint

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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 differences of the clusters and propose a regularized finite mixture effects regression to achieve heterogeneity pursuit and feature selection simultaneously. As the name suggests, the problem is formulated under an effects-model parameterization, in which the cluster labels are missing and the effect of each predictor on the outcome is decomposed to a common effect term and a set of cluster-specific terms. A constrained sparse estimation of these effects leads to the identification of both the variables with common effects and those with heterogeneous effects. We propose an efficient algorithm and show that our approach can achieve both estimation and selection consistency. Simulation studies further demonstrate the effectiveness of our method under various practical scenarios. Three applications are presented, namely, an imaging genetics study for linking genetic factors and brain neuroimaging traits in Alzheimer's disease, a public health study for exploring the association between suicide risk among adolescents and their school district characteristics, and a sport analytics study for understanding how the salary levels of baseball players are associated with their performance and contractual status.

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“…Recent developments of clustering methods based on the penalized regression model make it feasible to model heterogeneous effects and select the number of subgroups automatically for clustering subjects. Pan et al (2013) propose a center-based subgrouping method for multivariate vectors using grouping pursuit; Chi and Lange (2015) formulate clustering as a splitting problem using convex optimization; Ma and Huang (2017) cluster subjects through modeling subject-specific intercepts; Ma and Huang (2016) further extend their approach to incorporate subject-specific coefficients for treatment variables; and Austin et al (2016) propose a pairwise penalized regression model with a truncated L 1 -penalty. However, the above methods mainly target responses under the linear regression model framework for independent data, which is not applicable for longitudinal binary responses.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal clustering for heterogeneous binary data

Zhu¹,

Tang²,

Qu³

2021

STAT SINICA

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Personalized marketing has emerged as a critical marketing strategy due to the success of E-commerce and the accessibility of digital marketing data.It is well-known that different groups of customers might react rather differently to the same marketing strategy due to their individual preferences. In this paper, we propose a pairwise subgrouping approach to identify subgroups and categorize similar marketing effects into groups. Specifically, we model customers' purchase decisions as binary responses under the generalized linear model framework while incorporating their longitudinal correlation. We impose penalization on pairwise distances of heterogeneous effects to formulate subgroups, where different subgroups are associated with different marketing effects. In theory, we establish the consistency of subgroup identification in the sense that the true underlying segmentation structure can be recovered successfully, in addition to parameter estimation consistency. We conduct numerical studies and a real data application using IRI marketing data on in-store display marketing effects, where the proposed method outperforms other competing methods in terms of subgrouping identification and marketing effects estimation.

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A New Semiparametric Approach to Finite Mixture of Regressions using Penalized Regression via Fusion

Cited by 4 publications

References 13 publications

Pursuing sources of heterogeneity in modeling clustered population

Pursuing sources of heterogeneity in modeling clustered population

Pursuing Sources of Heterogeneity in Modeling Clustered Population

Longitudinal clustering for heterogeneous binary data

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