Further Exploration of the Effects of Time-varying Covariate in Growth Mixture Models with Nonlinear Trajectories
Jin Liu
备注：
\textcircled{c}2024, Behavior Research Methods. This paper is not the copy of record and may not exactly replicate the final, authoritative version of the article. Please do not copy or cite without authors' permission. The final article will be available, upon publication, via its DOI: https://doi.org/10.3758/s13428-023-02183-5
Growth mixture modeling (GMM) is an analytical tool for identifying multiple unobserved sub-populations of longitudinal processes. In particular, it describes change patterns within each latent sub-population and examines between-individual differences in within-individual change for each sub-group. One research interest in utilizing GMMs is to explore how covariates affect such heterogeneity in change patterns. Liu and Perera (2022c) extended mixture-of-experts (MoE) models, which mainly focus on time-invariant covariates, for allowing the covariates to account for within-group and between-group differences simultaneously and examining the heterogeneity in nonlinear trajectories. The present study further extends Liu and Perera (2022c) and examines the effects on trajectory heterogeneity of time-varying covariates (TVCs). Specifically, we propose methods to decompose a TVC into a trait feature (e.g., the baseline value of the TVC) and a set of state features (e.g., interval-specific slopes or changes). The trait features are allowed to account for within-group differences in growth factors of trajectories (i.e., trait effect), and the state features are allowed to impact observed values of a longitudinal process (i.e., state effect). We examine the proposed models using a simulation study and a real-world data analysis. The simulation study demonstrated that the proposed models are capable of separating trajectories into several clusters and generally generating unbiased and accurate estimates with target coverage probabilities. With the proposed models, we showed the heterogeneity in the trait and state features of reading ability across latent classes of students' mathematics performance. Meanwhile, the trait and state effects on mathematics development of reading ability are also heterogeneous across the clusters of students.
Researchers continue to be interested in exploring the effects that covariates have on the heterogeneity in trajectories. The inclusion of covariates associated with latent classes allows for a more clear understanding of individual differences and a more meaningful interpretation of latent class membership. Many theoretical and empirical studies have focused on investigating heterogeneity in change patterns of a univariate repeated outcome and examining the effects on baseline covariates that inform the cluster formation. However, developmental processes rarely unfold in isolation; therefore,…
Empirical researchers are usually interested in investigating the impacts of baseline covariates have when uncovering sample heterogeneity and separating samples into more homogeneous groups. However, a considerable number of studies in the structural equation modeling (SEM) framework usually start with vague hypotheses in terms of heterogeneity and possible reasons. It suggests that (1) the determination and specification of a proper model with covariates is not straightforward, and (2) the exploration process may be computational intensive given that a model in the SEM framework is usually c…
Standard models assign disease progression to discrete categories or stages based on well-characterized clinical markers. However, such a system is potentially at odds with our understanding of the underlying biology, which in highly complex systems may support a (near-)continuous evolution of disease from inception to terminal state. To learn such a continuous disease score one could infer a latent variable from dynamic "omics" data such as RNA-seq that correlates with an outcome of interest such as survival time. However, such analyses may be confounded by additional data such as clinical co…
Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to asses association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. The most common joint model in this framework is based on a linear m…
Aalto University（阿尔托大学）；University of Helsinki（赫尔辛基大学）
Estimating the effect of a treatment on a given outcome, conditioned on a vector of covariates, is central in many applications. However, learning the impact of a treatment on a continuous temporal response, when the covariates suffer extensively from measurement error and even the timing of the treatments is uncertain, has not been addressed. We introduce a novel data-driven method that can estimate treatment-response trajectories in this challenging scenario. We model personalized treatment-response curves as a combination of parametric response functions, hierarchically sharing information …
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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…
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University of Louisville（路易斯维尔大学）；Case Western Reserve University（凯斯西储大学）；Mass General Brigham, Harvard Medical School（麻省总医院布里格姆医院，哈佛医学院）；University of Missouri（密苏里大学）
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University of California Los Angeles（加州大学洛杉矶分校）；Imperial College London（伦敦帝国理工学院）；Iowa State University（爱荷华州立大学）；KU Leuven（鲁汶大学）；University of Oxford（牛津大学）
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School of Computer Science and Statistics, Trinity College Dublin（都柏林三一学院计算机科学与统计学院）；ADAPT Center（ADAPT中心）；German Research Centre for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））；Trinity Kidney Centre, Trinity College Dublin（都柏林三一学院肾脏病中心）
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their close connection to generalized linear models, it is also natural to incorporate covariate information in them. The current paper presents two universal fitting algorithms for networks with edge covariates: one based on nuclear norm penalization and the other based on projected gradient descent. Both algorithms are motivated by maximizing likelihood for a s…
Although there are many methods for functional data analysis (FDA), little emphasis is put on characterizing variability among volatilities of individual functions. In particular, certain individuals exhibit erratic swings in their trajectory while other individuals have more stable trajectories. There is evidence of such volatility heterogeneity in blood pressure trajectories during pregnancy, for example, and reason to suspect that volatility is a biologically important feature. Most FDA models implicitly assume similar or identical smoothness of the individual functions, and hence can lead …
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Department of Mathematics and Statistics, Binghamton University（数学与统计学系，宾夕法尼亚大学伯灵顿分校）；Department of Mathematics, Illinois State University（数学系，伊利诺伊州立大学）；Department of Biostatistics, The University of North Carolina at Chapel Hill（生物统计学系，北卡罗来纳大学教堂山分校）
We propose a novel semiparametric model for the joint distribution of a continuous longitudinal outcome and the baseline covariates using an enriched Dirichlet process (EDP) prior. This joint model decomposes into a linear mixed model for the outcome given the covariates and marginals for the covariates. The nonparametric EDP prior is placed on the regression and spline coefficients, the error variance, and the parameters governing the predictor space. We predict the outcome at unobserved time points for subjects with data at other time points as well as for new subjects with only baseline cov…
We are interested in survival analysis of hemodialysis patients for whom several biomarkers are recorded over time. Motivated by this challenging problem, we propose a general framework for multivariate joint longitudinal-survival modeling that can be used to examine the association between several longitudinally recorded covariates and a time-to-event endpoint. Our method allows for simultaneous modeling of longitudinal covariates by taking their correlation into account. This leads to a more efficient method for modeling their trajectories over time, and hence, it can better capture their re…
Miller School of Medicine, University of Miami（迈阿密大学米勒医学院）；Heart and Vascular Institute, Cleveland Clinic（克利夫兰诊所心脏与血管研究所）；Kogalur & Company, Inc.（科加卢尔公司）；Goizueta Business School（戈伊祖塔商学院）
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