Growth Mixture Modeling With Nonnormal Distributions: Implications for Data Transformation

2020 ◽  
pp. 001316442097677
Author(s):  
Yeji Nam ◽  
Sehee Hong
Keyword(s):  
Repeated Measures ◽  
Growth Mixture Modeling ◽  
Computation Time ◽  
Data Transformation ◽  
Mixture Modeling ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Nonnormal Distributions ◽  
Normality Assumption ◽  
Growth Mixture

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality assumption and using data transformation on repeated measures. Based on unconditional GMM with two latent trajectories, data were generated under different sample sizes (300, 800, and 1500), skewness (0.7, 1.2, and 1.6) and kurtosis (2 and 4) of outcomes, numbers of time points (4 and 8), and class proportions (0.5:0.5 and 0.25:0.75). Of the four distributions, it was found that skew- t GMM had the highest accuracy in terms of parameter estimation. In GMM based on data transformations, the adjusted logarithmic method was more effective in obtaining unbiased parameter estimates than the use of van der Waerden quantile normal scores. Even though adjusted logarithmic transformation in nonnormal GMM reduced computation time, skew- t GMM produced much more accurate estimation and was more robust over a range of simulation conditions. This study is significant in that it considers different levels of kurtosis and class proportions, which has not been investigated in depth in previous studies. The present study is also meaningful in that investigated the applicability of data transformation to nonnormal GMM.

Modern Methods for Modeling Change in Obesity Research in Nursing

2017 ◽  
Vol 39 (8) ◽  
pp. 1028-1044 ◽  
Author(s):  
Susan M. Sereika ◽  
Yaguang Zheng ◽  
Lu Hu ◽  
Lora E. Burke
Keyword(s):  
Weight Loss ◽  
Repeated Measures ◽  
Latent Class ◽  
Growth Mixture Modeling ◽  
Mixture Modeling ◽  
Calorie Intake ◽  
Lifestyle Behaviors ◽  
Trajectory Modeling ◽  
Growth Mixture ◽  
Time Dependent Covariates

Persons receiving treatment for weight loss often demonstrate heterogeneity in lifestyle behaviors and health outcomes over time. Traditional repeated measures approaches focus on the estimation and testing of an average temporal pattern, ignoring the interindividual variability about the trajectory. An alternate person-centered approach, group-based trajectory modeling, can be used to identify distinct latent classes of individuals following similar trajectories of behavior or outcome change as a function of age or time and can be expanded to include time-invariant and time-dependent covariates and outcomes. Another latent class method, growth mixture modeling, builds on group-based trajectory modeling to investigate heterogeneity within the distinct trajectory classes. In this applied methodologic study, group-based trajectory modeling for analyzing changes in behaviors or outcomes is described and contrasted with growth mixture modeling. An illustration of group-based trajectory modeling is provided using calorie intake data from a single-group, single-center prospective study for weight loss in adults who are either overweight or obese.

scholarly journals Exploring Class Enumeration in Bayesian Growth Mixture Modeling Based on Conditional Medians

2021 ◽  
Vol 6 ◽  
Author(s):  
Seohyun Kim ◽  
Xin Tong ◽  
Zijun Ke
Keyword(s):  
Model Selection ◽  
Model Comparison ◽  
Growth Mixture Modeling ◽  
Information Criterion ◽  
Mixture Modeling ◽  
Latent Classes ◽  
Normality Assumption ◽  
Selection Accuracy ◽  
Growth Mixture ◽  
Bayesian Model Comparison

Growth mixture modeling is a popular analytic tool for longitudinal data analysis. It detects latent groups based on the shapes of growth trajectories. Traditional growth mixture modeling assumes that outcome variables are normally distributed within each class. When data violate this normality assumption, however, it is well documented that the traditional growth mixture modeling mislead researchers in determining the number of latent classes as well as in estimating parameters. To address nonnormal data in growth mixture modeling, robust methods based on various nonnormal distributions have been developed. As a new robust approach, growth mixture modeling based on conditional medians has been proposed. In this article, we present the results of two simulation studies that evaluate the performance of the median-based growth mixture modeling in identifying the correct number of latent classes when data follow the normality assumption or have outliers. We also compared the performance of the median-based growth mixture modeling to the performance of traditional growth mixture modeling as well as robust growth mixture modeling based on t distributions. For identifying the number of latent classes in growth mixture modeling, the following three Bayesian model comparison criteria were considered: deviance information criterion, Watanabe-Akaike information criterion, and leave-one-out cross validation. For the median-based growth mixture modeling and t-based growth mixture modeling, our results showed that they maintained quite high model selection accuracy across all conditions in this study (ranged from 87 to 100%). In the traditional growth mixture modeling, however, the model selection accuracy was greatly influenced by the proportion of outliers. When sample size was 500 and the proportion of outliers was 0.05, the correct model was preferred in about 90% of the replications, but the percentage dropped to about 40% as the proportion of outliers increased to 0.15.

Die Identifikation früher Veränderungsmuster in der ambulanten Psychotherapie

2007 ◽  
Vol 36 (2) ◽  
pp. 93-104 ◽  
Author(s):  
Wolfgang Lutz ◽  
Niklaus Stulz ◽  
David W. Smart ◽  
Michael J. Lambert
Keyword(s):  
Growth Mixture Modeling ◽  
Mixture Modeling ◽  
Growth Mixture

Zusammenfassung. Theoretischer Hintergrund: Im Rahmen einer patientenorientierten Psychotherapieforschung werden Patientenausgangsmerkmale und Veränderungsmuster in einer frühen Therapiephase genutzt, um Behandlungsergebnisse und Behandlungsdauer vorherzusagen. Fragestellung: Lassen sich in frühen Therapiephasen verschiedene Muster der Veränderung (Verlaufscluster) identifizieren und durch Patientencharakteristika vorhersagen? Erlauben diese Verlaufscluster eine Vorhersage bezüglich Therapieergebnis und -dauer? Methode: Anhand des Growth Mixture Modeling Ansatzes wurden in einer Stichprobe von N = 2206 ambulanten Patienten einer US-amerikanischen Psychotherapieambulanz verschiedene latente Klassen des frühen Therapieverlaufs ermittelt und unter Berücksichtigung unterschiedlicher Patientenausgangscharakteristika als Prädiktoren der frühen Veränderungen mit dem Therapieergebnis und der Therapiedauer in Beziehung gesetzt. Ergebnisse: Für leicht, mittelschwer und schwer beeinträchtigte Patienten konnten je vier unterschiedliche Verlaufscluster mit jeweils spezifischen Prädiktoren identifiziert werden. Die Identifikation der frühen Verlaufsmuster ermöglichte weiterhin eine spezifische Vorhersage für die unterschiedlichen Verlaufscluster bezüglich des Therapieergebnisses und der Therapiedauer. Schlussfolgerungen: Frühe Psychotherapieverlaufsmuster können einen Beitrag zu einer frühzeitigen Identifikation günstiger sowie ungünstiger Therapieverläufe leisten.

A Monte Carlo evaluation of growth mixture modeling

2021 ◽  
pp. 1-14
Author(s):  
Tiffany M. Shader ◽  
Theodore P. Beauchaine
Keyword(s):  
Monte Carlo ◽  
Growth Mixture Modeling ◽  
Mixture Modeling ◽  
Fit Indices ◽  
Linear Quadratic ◽  
Growth Mixture ◽  
True Number ◽  
Monte Carlo Evaluation ◽  
Wrong Number ◽  
State Of Affairs

Abstract Growth mixture modeling (GMM) and its variants, which group individuals based on similar longitudinal growth trajectories, are quite popular in developmental and clinical science. However, research addressing the validity of GMM-identified latent subgroupings is limited. This Monte Carlo simulation tests the efficiency of GMM in identifying known subgroups (k = 1–4) across various combinations of distributional characteristics, including skew, kurtosis, sample size, intercept effect size, patterns of growth (none, linear, quadratic, exponential), and proportions of observations within each group. In total, 1,955 combinations of distributional parameters were examined, each with 1,000 replications (1,955,000 simulations). Using standard fit indices, GMM often identified the wrong number of groups. When one group was simulated with varying skew and kurtosis, GMM often identified multiple groups. When two groups were simulated, GMM performed well only when one group had steep growth (whether linear, quadratic, or exponential). When three to four groups were simulated, GMM was effective primarily when intercept effect sizes and sample sizes were large, an uncommon state of affairs in real-world applications. When conditions were less ideal, GMM often underestimated the correct number of groups when the true number was between two and four. Results suggest caution in interpreting GMM results, which sometimes get reified in the literature.

scholarly journals Methods and Measures: Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups

2009 ◽  
Vol 33 (6) ◽  
pp. 565-576 ◽  
Author(s):  
Nilam Ram ◽  
Kevin J. Grimm
Keyword(s):  
Stress Response ◽  
Growth Curve ◽  
Growth Modeling ◽  
Growth Mixture Modeling ◽  
Mixture Modeling ◽  
Longitudinal Change ◽  
Growth Curve Model ◽  
Growth Mixture ◽  
Multiple Group ◽  
Curve Model

Growth mixture modeling (GMM) is a method for identifying multiple unobserved sub-populations, describing longitudinal change within each unobserved sub-population, and examining differences in change among unobserved sub-populations. We provide a practical primer that may be useful for researchers beginning to incorporate GMM analysis into their research. We briefly review basic elements of the standard latent basis growth curve model, introduce GMM as an extension of multiple-group growth modeling, and describe a four-step approach to conducting a GMM analysis. Example data from a cortisol stress-response paradigm are used to illustrate the suggested procedures.

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