Piecewise Growth Mixture Models Research Articles

Developmental trajectories of depression, anxiety, and stress among college students: a piecewise growth mixture model analysis

Mental health issues are becoming increasingly common among college students, but not all students follow the same developmental trends of mental health. This study aims to identify the developmental trajectories of depression, anxiety, and stress among college students and the related factors for different trajectory classes. The data were collected from a longitudinal survey of college students over four consecutive years, and 2473 students were included in the analysis. The study used a piecewise growth mixture model to determine the subtrajectories, and a multinomial logistic regression model was constructed to investigate the related factors affecting students in subtrajectories. The results revealed that subtrajectories include the low and stable class, increasing class, decreasing then stable class, increasing then decreasing class, and decreasing and high class. The decreasing and high class only presents in the trajectories of anxiety and stress. Regarding related factors, high BMI and high sleep hours were identified as related factors for the increasing class of depression; gender and high sleep hours were associated with the increasing class of anxiety; and hometown location was related to the increasing class of stress. Extroversion personality, relationship with classmates, siblings, and father’s education level are related factors for other subtrajectories. Considering that college students experience multiple trajectories of depression, anxiety, and stress, mental health education and psychological intervention should be carried out for students in each class.

Trajectories and risk factors of fatigue following colorectal cancer diagnosis.

This study sought to identify groups of colorectal cancer patients based upon trajectories of fatigue and examine how demographic, clinical and behavioural risk factors differentiate these groups. Patients were from six cancer centres in the United States and Germany. Fatigue was measured using the fatigue subscale of the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire (EORTC QLQ-C30) at five time points (baseline/enrolment and 3, 6, 12 and 24 months after diagnosis). Piecewise growth mixture models identified latent trajectories of fatigue. Logistic regression models examined differences in demographic, clinical and behavioural characteristics between fatigue trajectory groups. Among 1615 participants (57% men, 86% non-Hispanic White, mean age 61 ± 13 years at diagnosis), three distinct groups were identified. In the high fatigue group (36%), fatigue significantly increased in the first 6 months after diagnosis and then showed statistically and clinically significant improvement from 6 to 24 months (P values < 0.01). Throughout the study period, average fatigue met or exceeded cutoffs for clinical significance. In the moderate (34%) and low (30%) fatigue groups, fatigue levels remained below or near population norms across the study period. Patients who were diagnosed with Stage II-IV disease and/or current smokers were more likely to be in the high fatigue than in the moderate fatigue group (P values < 0.05). A large proportion of colorectal cancer patients experienced sustained fatigue after initiation of cancer treatment. Patients with high fatigue at the time of diagnosis may benefit from early supportive care.

Heterogeneity in resilience patterns and its prediction of 1-year quality of life outcomes among patients with newly diagnosed cancer: An exploratory piecewise growth mixture model analysis

PurposeThis study was designed to explore the impact of a new cancer diagnosis on resilience of patients and whether the resilience patterns could predict Quality of Life (QoL) in the first year. MethodsAn exploratory linear piecewise growth mixture modeling (PGMM) with one hypothetical dot (3 months since diagnosis, T1) was employed to identify different resilience patterns and growth in 289 patients with different cancer diagnoses at five assessment occasions (T0-T4). Logistic regression analysis was performed to select potential predictors and receiver operating characteristic (ROC) curve analysis was utilized to test PGMM’s discriminative ability against 1-year QoL. ResultsFive discrete resilience trajectories with two growing trends were identified, including “Transcendence” (7.3%), “Resilient” (47.4%), “Recovery” (18.7%), “Damaged” (14.9%) and “Maladaption” (11.8%). Advanced stage, colorectal cancer, and receiving surgery therapy were significant predictors of negative resilience trajectories (“Damaged” or “Maladaption”). Discriminative ability was good for PGMM (AUC = 0.81, 95%CI, 0.76–0.85, P < 0.0001). ConclusionHeterogeneity is identified in resilience growth before and after 3 months since diagnosis. 26.7% newly diagnosed patients need additional attention especially for those with advanced colorectal cancer and receiving surgery therapy.

Trajectories of college students' general self-efficacy, the related predictors, and depression: A piecewise growth mixture modeling approach

General self-efficacy plays a critical role in the development of college students, and mastering the development of students' general self-efficacy is helpful to explain students' behavior and psychological performance. Based on the data from the same cohort of college students for four consecutive years, this study used the piecewise growth mixture model to identify the developmental trajectories of general self-efficacy, built a multinomial logistic regression model to analyze the related predictors on different trajectories, and further compared the differences in depression symptoms in general self-efficacy trajectories. Three trajectories of college students' general self-efficacy were identified: stable-rising (8.7%), stable-decreasing (2.4%), and moderate and stable (88.9%). With the moderate and stable class as the reference, gender and extraversion are the predictors of students in the stable-increasing class; gender, extraversion, mother’s education level, and university tier significantly predict students who fall into the stable-decreasing class. With the stable-increasing class as the reference, gender also has a significant predictive effect on students who belong to the stable-decreasing class. However, age, ethnicity, siblings, hometown location, father’s education level, BMI, sleep, and major were not related predictors. Furthermore, mean differences in depression between latent classes of general self-efficacy trajectories were significant, and the depression scores of the stable-decreasing class were beyond the normal range in the third and fourth years. To promote college students' mental health, we suggest that colleges provide more specific psychological interventions to students based on the classification.

Fitting a Nonlinear Piecewise Growth Mixture Model into the Seoul Education Longitudinal Study to Discover Change Points

Fitting a Nonlinear Piecewise Growth Mixture Model into the Seoul Education Longitudinal Study to Discover Change Points

Trajectories of Self-Esteem Development for Adolescence Based on China Family Panel Studies: A Piecewise Growth Mixture Model Analysis

Self-esteem has always been a hot research object in the field of adolescent mental health. But in longitudinal research, using a single slope to describe the trajectory of adolescent self-esteem is unrealistic. The piecewise growth mixture model (PGMM) was used to fit the data in this study. Selecting from China Family Panel Studies database, a total of 1,759 individuals were selected and their self-esteem (RSES) scores over the years were used as the tracking index. Based on the characteristics of the development trajectories of three latent classes, class 1 was referred to as “stable low level group,” class 2 was named “rapidly rising group,” and class 3 was referred to as “rapidly decrease group.” And there were two stages in the development process of self-esteem in the adolescent group. The slope of the stable low level group showed a significant downward trend in the first stage and a significant upward trend in the second stage, with a relatively flat development trajectory and relatively low self-esteem on the whole. The slope of the rapidly rising group showed an insignificant upward trend in the first stage and a significant rapid upward trend in the second stage. The rapidly decrease group showed a significant and rapid downward trend in the first stage and a significant and rapid upward trend in the second stage. In the development of self-esteem in adolescence, there were three latent classes in which the characteristics of development trajectories were different. Age of 14 is the turning point between the two stages of development.

Discontinuous Piecewise Growth Mixture Model with Distal Outcome: A Comparison of Three-Step ML and BCH Approaches

본 연구는 비연속 분할함수 성장혼합모형의 접근법에 따라 계층 간 원격 결과변인 추정치에 어떠한 차이가 있는지를 확인하는 데 목적이 있다. 이를 위하여 본 연구는 3단계 ML접근법과 3단계 BCH 접근법을 적용하여 모의실험 연구를 수행하였다. 모의실험에 계층 분류정도(1.3, 2.6), 계층 혼합비율(90:10, 70:30, 50:50), 표본크기(200, 500, 1000, 2000)의 조건을 설정하였다. 분석결과, 3단계 ML접근법과 3단계 BCH접근법의 원격 결과변인에서 양호도의 차이는 미미한 것으로 나타났지만, 소표본일 때 3단계 BCH접근법이 3단계 ML접근법에 비해 상대적으로 효율성이 높은 것으로 나타났다. 본 연구는 원격 결과변인의 보조변수 접근법에 기존에 활용되지 않았던 비연속 분할함수 성장혼합모형을 적용하고, 다양한 모의실험 조건을 설정하여 모의실험 연구를 수행하였다는 점에서 의의가 있다. 본 연구가 연구자들에게 실질적인 모형 활용 방안을 제시할 수 있을 것으로 기대하며, 연구의 제한점을 바탕으로 후속연구를 제언하였다.The purpose of this study was to compare the estimates of distal outcome variable in discontinuous growth mixture model. For this purpose, this study carried out a simulation study using a three-step maximum likelihood (ML) approach and a three-step BCH approach. The manipulated conditions were the class separation (1.3, 2.6), the mixing proportions (90:10, 70:30, 50:50), and the sample size (200, 500, 1000, 2000). The differences between ML and a three-step BCH approaches were not substantial, however, the three-step BCH approach was relatively more efficient than the three-step ML approach in the conditions of relatively small sample sizes. In particular, the bias of standard error was smaller in the conditions of the relatively less mixing proportions when three-step BCH approach was used. Limitations of the current study and suggestions for future study were provided.

비연속 분할함수 성장혼합모형에서 계층 분류과정의 공변인 접근법 비교

비연속 분할함수 성장혼합모형에서 계층 분류과정의 공변인 접근법 비교

Erratum to: Effects of Distance and Shape on the Estimation of the Piecewise Growth Mixture Model

The authors missed an important reference “Liu, Luo, & Liu, 2014” on the original version of this article.

Effects of Distance and Shape on the Estimation of the Piecewise Growth Mixture Model

The piecewise growth mixture model is used in longitudinal studies to tackle non-continuous trajectories and unobserved heterogeneity in a compound way. This study investigated how factors such as latent distance and shape influence the model. Two simulation studies were used exploring the 2- and 3-class situation with sample size, latent distance (Mahalanobis distance), and shape being considered as the influencing factor. The results of two simulations showed that a non-parallel shape led to a slightly better overall model fit. Parameter estimation is affected by the shape, mainly through the parameter differences between latent classes.

Linear-linear piecewise growth mixture models with unknown random knots: A primer for school psychology

Studying change over time requires rigorous and sometimes novel statistical methods that can support increasingly complex applied research questions. In this article, we provide an overview of the potential of piecewise growth mixture models. This type of longitudinal model can be used to advance our understanding of group and individual growth that may follow a segmented, or disjointed, pattern of change, and where the data come from a mixture of two or more latent classes. We then demonstrate the practical utility of piecewise growth mixture models by applying it to a subsample of students from the Early Childhood Longitudinal Study – Kindergarten Cohort of 1998 (ECLS-K) to ascertain whether mathematics achievement is characterized by one or two latent classes akin to students with and without mathematics difficulties. We discuss the applicability for school psychological research and provide supplementary online files that include an instructional sample dataset and corresponding R routine with explanatory annotations to assist in understanding the R routine before applying this approach in novel applications (https://doi.org/10.1016/j.jsp.2019.03.004).

Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models.

Piecewise growth mixture models are a flexible and useful class of methods for analyzing segmented trends in individual growth trajectory over time, where the individuals come from a mixture of two or more latent classes. These models allow each segment of the overall developmental process within each class to have a different functional form; examples include two linear phases of growth, or a quadratic phase followed by a linear phase. The changepoint (knot) is the time of transition from one developmental phase (segment) to another. Inferring the location of the changepoint(s) is often of practical interest, along with inference for other model parameters. A random changepoint allows for individual differences in the transition time within each class. The primary objectives of our study are as follows: (1) to develop a PGMM using a Bayesian inference approach that allows the estimation of multiple random changepoints within each class; (2) to develop a procedure to empirically detect the number of random changepoints within each class; and (3) to empirically investigate the bias and precision of the estimation of the model parameters, including the random changepoints, via a simulation study. We have developed the user-friendly package BayesianPGMM for R to facilitate the adoption of this methodology in practice, which is available at https://github.com/lockEF/BayesianPGMM . We describe an application to mouse-tracking data for a visual recognition task.

Bayesian analysis of piecewise growth mixture models with skew-t distributions: Application to AIDS studies

ABSTRACTA major problem in HIV/AIDS studies is the development of drug resistance to antiretroviral (ARV) drug or therapy. Estimating the time at which such drug resistance would develop is usually sought. The goal of this article is to perform this estimation by developing growth mixture models with change-points and skew-t distributions based on longitudinal data. For such data, following ARV treatment, the profile of each subject’s viral load tends to follow a ‘broken stick’ like growth trajectory, indicating multiple phases of decline and increase in viral loads. These multiple phases with multiple change-points are captured by subject-specific random parameters of growth curve models. To account for heterogeneity of drug resistance among subjects, the change-points are also allowed to differ by subgroups (subpopulations) of patients classified into latent classes on the basis of trajectories of observed viral loads. The proposed methods are illustrated using real data from an AIDS clinical study.

Piecewise growth mixture models and its current researches

Piecewise growth mixture models and its current researches

Factors of Piecewise Growth Mixture Model: Distance and Pattern

Factors of Piecewise Growth Mixture Model: Distance and Pattern

General Piecewise Growth Mixture Model: Word Recognition Development for Different Learners in Different Phases

The General Piecewise Growth Mixture Model (GPGMM), without losing generality to other fields of study, can answer six crucial research questions regarding children’s word recognition development. Using child word recognition data as an example, this study demonstrates the flexibility and versatility of the GPGMM in investigating growth trajectories that are potentially phasic and heterogeneous. The strengths and limitations of the GPGMM and lessons learned from this hands-on experience are discussed.