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.

scholarly journals Extracting Spurious Latent Classes in Growth Mixture Modeling With Nonnormal Errors

2016 ◽  
Vol 76 (6) ◽  
pp. 933-953 ◽  
Author(s):  
Kiero Guerra-Peña ◽  
Douglas Steinley
Keyword(s):  
Likelihood Ratio ◽  
Growth Mixture Modeling ◽  
Information Criterion ◽  
Mixture Modeling ◽  
Latent Classes ◽  
Ratio Test ◽  
Fit Statistics ◽  
Growth Mixture ◽  
Modeling Analysis ◽  
Time Invariant

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This can lead to the overextraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study are (1) to explore the performance of the Bayesian information criterion, sample-adjusted BIC, and bootstrap likelihood ratio test in growth mixture modeling analysis with nonnormal distributed outcome variables and (2) to examine the effects of nonnormal time invariant covariates in the estimation of the number of latent classes when outcome variables are normally distributed. For both of these goals, we will include nonnormal conditions not considered previously in the literature. Two simulation studies were conducted. Results show that spurious classes may be selected and optimal solutions obtained in the data analysis when the population departs from normality even when the nonnormality is only present in time invariant covariates.

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.

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.

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