Latent Growth Modeling and Latent Class Analysis

Geared towards capturing change, longitudinal research is able to provide insight into a variety of phenomena of interest to IS researchers, especially IT adoption and use. However, its potential is constrained by the data analysis methods typically used. In this paper, I introduce an advanced technique – Latent Curve Modeling – and demonstrate how this technique supports longitudinal data analysis using system use data collected at an international management consulting firm. Latent Curve Modeling helps capture temporal patterns better than existing methods, and provides methods to identify the causes of change in patterns. With rich information in the discussion of the technique and the results of the empirical tests, I recommend it as a valuable option for IS researchers who are interested in research involving temporal changes

Integrating Person-Centered and Variable-Centered Analyses: Growth Mixture Modeling With Latent Trajectory Classes

Background: Many alcohol research questions require methods that take a person-centered approach because the interest is in finding heterogeneous groups of individuals, such as those who are susceptible to alcohol dependence and those who are not. A person-centered focus also is useful with longitudinal data to represent heterogeneity in developmental trajectories. In alcohol, drug, and mental health research the recognition of heterogeneity has led to theories of multiple developmental pathways. Methods: This paper gives a brief overview of new methods that integrate variable-and person-centered analyses. Methods discussed include latent class analysis, latent transition analysis, latent class growth analysis, growth mixture modeling, and general growth mixture modeling. These methods are presented in a general latent variable modeling framework that expands traditional latent variable modeling by including not only continuous latent variables but also categorical latent variables. Results: Four examples that use the National Longitudinal Survey of Youth (NLSY) data are presented to illustrate latent class analysis, latent class growth analysis, growth mixture modeling, and general growth mixture modeling. Latent class analysis of antisocial behavior found four classes. Four heavy drinking trajectory classes were found. The relationship between the latent classes and background variables and consequences was studied. Conclusions: Person-centered and variable-centered analyses typically have been seen as different activities that use different types of models and software. This paper gives a brief overview of new methods that integrate variable-and person-centered analyses. The general framework makes it possible to combine these models and to study new models serving as a stimulus for asking research questions that have both person-and variable-centered aspects

Building latent class growth trees

Researchers use latent class growth (LCG) analysis to detect meaningful subpopulations that display different growth curves. However, especially when the number of classes required to obtain a good fit is large, interpretation of the encountered class-specific curves might not be straightforward. To overcome this problem, we propose an alternative way of performing LCG analysis, which we call LCG tree (LCGT) modeling. For this purpose, a recursive partitioning procedure similar to divisive hierarchical cluster analysis is used: Classes are split until a certain criterion indicates that the fit does not improve. The advantage of the LCGT approach compared to the standard LCG approach is that it gives a clear insight into how the latent classes are formed and how solutions with different numbers of classes relate. The practical use of the approach is illustrated using applications on drug use during adolescence and mood regulation during the day

The impact of ignoring a level of nesting structure in multilevel growth mixture model: a Monte Carlo study

The number of longitudinal studies has increased steadily in various social science disciplines over the last decade. Growth Mixture Modeling (GMM) has emerged among the new approaches for analyzing longitudinal data. It can be viewed as a combination of Hierarchical Linear Modeling, Latent Growth Curve Modeling and Finite Mixture Modeling. The combination of both continuous and categorical latent variables makes GMM a flexible analysis procedure. However, when researchers analyze their data using GMM, some may assume that the units are independent of each other even though it may not always be the case. The purpose of this dissertation was to examine the impact of ignoring a higher nesting structure in Multilevel Growth Mixture Modeling on the accuracy of classification of individuals and the accuracy on tests of significance (i.e., Type I error rate and statistical power) of the parameter estimates for the model in each subpopulation. Two simulation studies were conducted. In the first study, the impact of misspecifying the multilevel mixture model is investigated by ignoring a level of nesting structure in cross-sectional data. In the second study, longitudinal clustered data (e.g., repeated measures nested within units and units nested within clusters) are analyzed correctly and with a misspecification ignoring the highest level of the nesting structure. Results indicate that ignoring a higher level nesting structure results in lower classification accuracy, less accurate fixed effect estimates, inflation of lower-level variance estimates, and less accurate standard error estimates, the latter result which in turn affects the accuracy of tests of significance for the fixed effects. The magnitude of the intra-class correlation (ICC) coefficient has a substantial impact when a higher level nesting structure is ignored; the higher the ICC, the more variance at the highest level is ignored, and the worse the performance of the model. The implication for applied researchers is that it is important to model the multilevel data structure in (growth) mixture modeling. In addition, researchers should be cautious in interpreting their results if ignoring a higher level nesting structure is inevitable. Limitations concerning appropriate use of latent class analysis in growth modeling include unknown effects of incorrect estimation of the number of latent classes, non-normal distribution effects, and different growth patterns within-group and between-group

Hybridizing two-step growth mixture model and exploratory factor analysis to examine heterogeneity in nonlinear trajectories

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 complicated and the pool of candidate covariates is usually huge in the psychological and educational domain where the SEM framework is widely employed. Following \citet{Bakk2017two}, this article presents a two-step growth mixture model (GMM) that examines the relationship between latent classes of nonlinear trajectories and baseline characteristics. Our simulation studies demonstrate that the proposed model is capable of clustering the nonlinear change patterns, and estimating the parameters of interest unbiasedly, precisely, as well as exhibiting appropriate confidence interval coverage. Considering the pool of candidate covariates is usually huge and highly correlated, this study also proposes implementing exploratory factor analysis (EFA) to reduce the dimension of covariate space. We illustrate how to use the hybrid method, the two-step GMM and EFA, to efficiently explore the heterogeneity of nonlinear trajectories of longitudinal mathematics achievement data.Comment: Draft version 1.6, 08/08/2020. This paper has not been peer reviewed. Please do not copy or cite without author's permissio

LONGITUDINAL MEASUREMENT NON-INVARIANCE ON GROWTH PARAMETERS RECOVERY AND CLASSIFICATION ACCURACY IN GROWTH MIXTURE MODELING

First-order growth mixture model (1-GMM) has received increased attention over the past decade. It models class-specific latent growth trajectory and individual classification using composite scores computed over items of the same scale across multiple time points. By default, using composite scores assumes identical item-to-construct relationship over time (longitudinal measurement invariance; L-MI), which is not necessarily the case in research practice. Violation of L-MI assumption has been studied using latent growth curve modeling where subjects are assumed to be sampled from one latent class. Deviation from L-MI assumption impacted the growth characteristics, thus producing invalid conclusions on the pattern of change. This study extends the prior research on the impact of L-MI violation to the situation where multiple latent classes exist. A Monte Carlo study was performed to examine how systematically varied measurement non-invariance impacted class-specific growth factor parameter recovery and classification accuracy. Five factors were systematically manipulated in studying the impact of L-MI assumption violation: directional change in non-invariant item intercepts, patterns of item loadings and item intercepts, percent of items containing a set of non-invariant item parameters, presence of time-adjacent within-item correlated measurement error, and latent class distances. Additionally, three GMMs were compared to assess their robustness against longitudinal measurement non-invariance, including 1-GMM, second order GMM with constrained measurement invariance, and second order GMM with freely estimated item factor loadings and item intercepts. Accuracy, precision, Type I error, and power were examined on the slope factor parameter estimates. Additionally, mixture proportion and individual classification were assessed. Results show that the second order GMM with freely estimated item loadings and item intercepts was robust under various violation of L-MI and able to produce accurate estimates of slope factor parameters. Performance of the second order GMM with constrained measurement invariance on slope factor parameters recovery depended on the specific generating measurement non-invariance configuration. 1-GMM, on the other hand, was not able to recover the slope factor parameters with deviation from the L-MI assumption. With extremely unbalanced mixture proportions, class membership assignment was found not satisfactory regardless of simulated measurement non-invariance condition and analysis model

Latent class analysis was accurate but sensitive in data simulations

Objectives: Latent class methods are increasingly being used in analysis of developmental trajectories. A recent simulation study by Twisk and Hoekstra (2012) suggested caution in use of these methods because they failed to accurately identify developmental patterns that had been artificially imposed on a real data set. This article tests whether existing developmental patterns within the data set used might have obscured the imposed patterns.<p></p> Study Design and Setting: Data were simulated to match the latent class pattern in the previous article, but with varying levels of randomly generated variance, rather than variance carried over from a real data set. Latent class analysis (LCA) was then used to see if the latent class structure could be accurately identified.<p></p> Results: LCA performed very well at identifying the simulated latent class structure, even when the level of variance was similar to that reported in the previous study, although misclassification began to be more problematic with considerably higher levels of variance.<p></p> Conclusion: The failure of LCA to replicate the imposed patterns in the previous study may have been because it was sensitive enough to detect residual patterns of population heterogeneity within the altered data. LCA performs well at classifying developmental trajectories.<p></p&gt

Latent classes of nonresponders, rapid responders, and gradual responders in depressed outpatients receiving antidepressant medication and psychotherapy

BackgroundWe used growth mixture modeling (GMM) to identify subsets of patients with qualitatively distinct symptom trajectories resulting from treatment. Existing studies have focused on 12-week antidepressant trials. We used data from a concurrent antidepressant and psychotherapy trial over a 6-month period. MethodEight hundred twenty-one patients were randomized to receive either fluoxetine or tianepine and received cognitive-behavioral therapy, supportive therapy, or psychodynamic therapy. Patients completed the Montgomery-angstrom sberg depression rating scale (MADRS) at the 0, 1, 3, and 6-month periods. Patients also completed measures of dysfunctional attitudes, functioning, and personality. GMM was conducted using MADRS scores and the number of growth classes to be retained was based on the Bayesian information criterion. ResultsCriteria supported the presence of four distinct latent growth classes representing gradual responders of high severity (42% of sample), gradual responders of moderate severity (31%), nonresponders (15%), and rapid responders (11%). Initial severity, greater use of emotional coping strategies, less use of avoidance coping strategies, introversion, and less emotional stability predicted nonresponder status. Growth classes were not associated with different treatments or with proportion of dropouts. ConclusionsThe longer time period used in this study highlights potential overestimates of nonresponders in previous research and the need for continued assessments. Our findings demonstrate distinct growth trajectories that are independent of treatment modality and generalizable to most psychotherapy patients. The correlates of class membership provide directions for future studies, which can refine methods to predict likely nonresponders as a means to facilitate personalized treatments