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1.
The purpose of this study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that Step 1 of the 3-step approach shows adequate results in class enumeration, we suggest using an alternative approach: (a) decide the number of latent classes without predictors of latent classes, and (b) bring the latent class predictors into the model with the inclusion of hypothesized direct covariate effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students’ academic achievement outcome. Implications of the study are discussed. 相似文献
2.
Yan Wang Eunsook Kim John M. Ferron Robert F. Dedrick Tony X. Tan Stephen Stark 《Educational and psychological measurement》2021,81(1):61
Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed. 相似文献
3.
Roberto Di Mari Daniel L. Oberski Jeroen K. Vermunt 《Structural equation modeling》2016,23(5):649-660
Latent Markov models with covariates can be estimated via 1-step maximum likelihood. However, this 1-step approach has various disadvantages, such as that the inclusion of covariates in the model might alter the formation of the latent states and that parameter estimation could become infeasible with large numbers of time points, responses, and covariates. This is why researchers typically prefer performing the analysis in a stepwise manner; that is, they first construct the measurement model, then obtain the latent state classifications, and subsequently study the relationship between covariates and latent state memberships. However, such a stepwise approach yields downward-biased estimates of the covariate effects on initial state and transition probabilities. This article, shows how to overcome this problem using a generalization of the bias-corrected 3-step estimation method proposed for latent class analysis (Asparouhov & Muthén, 2014; Bolck, Croon, & Hagenaars, 2004; Vermunt, 2010). We give a formal derivation of the generalization to latent Markov models and discuss how it can be used with many time points by incorporating it into a Baum–Welch type of expectation-maximization algorithm. We evaluate the method through a simulation study and illustrate it using an application on household financial portfolio change. Our study shows that the proposed correction method yields unbiased parameter estimates and accurate standard errors, except for situations with very poorly separated classes and a small sample. 相似文献
4.
Relatively few empirical studies have examined the performance of enumeration indices in correctly identifying longitudinal population heterogeneity when present, and these studies have produced mixed results. In light of these findings, Muthén (2003) suggested that the inclusion of time-invariant (antecedent) and time-varying (concurrent) covariates, as well as allowing the extracted growth mixture classes to predict a distal outcome (consequent covariate), could improve the performance of enumeration indices. This Monte Carlo simulation study examined the performance of a large set of enumeration indices within these generalized growth mixture model (GGMM) conditions, as suggested by Muthén, by manipulating 4 design conditions: (a) sample size, (b) separation distance between adjacent latent growth trajectories, (c) growth trajectory membership proportions, and (d) the amount of mixture model variance explained by the covariates. The findings suggest: (a) at smaller (N = 500) sample sizes, enumeration indices were much more likely to select an incorrect model than the correct one, (b) at larger (N = 3,000) sample sizes, correct model identification occurred only in the largest separation distance and trajectory membership equality conditions, and (c) the inclusion of covariates had a negligible effect at smaller sample sizes, but covariate inclusion had a more favorable effect on data generation model identification in the largest sample size, largest trajectory separation distance, and equal trajectory membership proportions conditions. Suggestions for researchers and future empirical study possibilities are discussed. 相似文献
5.
AbstractFactor mixture models are designed for the analysis of multivariate data obtained from a population consisting of distinct latent classes. A common factor model is assumed to hold within each of the latent classes. Factor mixture modeling involves obtaining estimates of the model parameters, and may also be used to assign subjects to their most likely latent class. This simulation study investigates aspects of model performance such as parameter coverage and correct class membership assignment and focuses on covariate effects, model size, and class-specific versus class-invariant parameters. When fitting true models, parameter coverage is good for most parameters even for the smallest class separation investigated in this study (0.5 SD between 2 classes). The same holds for convergence rates. Correct class assignment is unsatisfactory for the small class separation without covariates, but improves dramatically with increasing separation, covariate effects, or both. Model performance is not influenced by the differences in model size investigated here. Class-specific parameters may improve some aspects of model performance but negatively affect other aspects. 相似文献
6.
Jungkyu Park 《Structural equation modeling》2018,25(5):778-790
The inclusion of covariates improves the prediction of class memberships in latent class analysis (LCA). Several methods for examining covariate effects have been developed over the past decade; however, researchers have limited to the comparisons of the performance among these methods in cases of the single-level LCA. The present study investigated the performance of three different methods for examining covariate effects in a multilevel setting. We conducted a simulation to compare the performance of the three methods when level-1 and level-2 covariates were simultaneously incorporated into the nonparametric multilevel latent class model to predict latent class membership at each level. The simulation results revealed that the bias-adjusted three-step maximum likelihood method performed equally well as the one-step method when the sample sizes were sufficiently large and the latent classes were distinct from each other. However, the unadjusted three-step method significantly underestimated the level-1 covariate effect in most conditions.
7.
Latent profile analysis (LPA) has become a popular statistical method for modeling unobserved population heterogeneity in cross-sectionally sampled data, but very few empirical studies have examined the question of how well enumeration indexes accurately identify the correct number of latent profiles present. This Monte Carlo simulation study examined the ability of several classes of enumeration indexes to correctly identify the number of latent population profiles present under 3 different research design conditions: sample size, the number of observed variables used for LPA, and the separation distance among the latent profiles measured in Mahalanobis D units. Results showed that, for the homogeneous population (i.e., the population has k = 1 latent profile) conditions, many of the enumeration indexes used in LPA were able to correctly identify the single latent profile if variances and covariances were freely estimated. However, for a heterogeneous population (i.e., the population has k = 3 distinct latent profiles), the correct identification rate for the enumeration indexes in the k = 3 latent profile conditions was typically very low. These results are compared with the previous cross-sectional mixture modeling studies, and the limitations of this study, as well as future cross-sectional mixture modeling and enumeration index research possibilities, are discussed. 相似文献
8.
Mike W.L. Cheung 《Structural equation modeling》2013,20(2):227-246
Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models. 相似文献
9.
Popular longitudinal models allow for prediction of growth trajectories in alternative ways. In latent class growth models (LCGMs), person-level covariates predict membership in discrete latent classes that each holistically define an entire trajectory of change (e.g., a high-stable class vs. late-onset class vs. moderate-desisting class). In random coefficient growth models (RCGMs, also known as latent curve models), however, person-level covariates separately predict continuously distributed latent growth factors (e.g., an intercept vs. slope factor). This article first explains how complex and nonlinear interactions between predictors and time are recovered in different ways via LCGM versus RCGM specifications. Then a simulation comparison illustrates that, aside from some modest efficiency differences, such predictor relationships can be recovered approximately equally well by either model—regardless of which model generated the data. Our results also provide an empirical rationale for integrating findings about prediction of individual change across LCGMs and RCGMs in practice. 相似文献
10.
This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as well as sample reallocation to latent classes. The results show that the clarity of remaining latent classes, as measured by the entropy statistic depends on the number of observations in the omitted latent class—but this statistic is not reliable. Specification error in the latent Markov model focuses on the transition probabilities when a longitudinal Guttman process is incorrectly specified. The findings show that specifying a longitudinal Guttman process that is not true in the population impacts other transition probabilities through the covariance matrix of the logit parameters used to calculate those probabilities. 相似文献
11.
Recently, several bias-adjusted stepwise approaches to latent class modeling with continuous distal outcomes have been proposed in the literature and implemented in generally available software for latent class analysis. In this article, we investigate the robustness of these methods to violations of underlying model assumptions by means of a simulation study. Although each of the 4 investigated methods yields unbiased estimates of the class-specific means of distal outcomes when the underlying assumptions hold, 3 of the methods could fail to different degrees when assumptions are violated. Based on our study, we provide recommendations on which method to use under what circumstances. The differences between the various stepwise latent class approaches are illustrated by means of a real data application on outcomes related to recidivism for clusters of juvenile offenders. 相似文献
12.
Eun Sook Kim Seang-Hwane Joo Philseok Lee Yan Wang Stephen Stark 《Structural equation modeling》2016,23(6):870-887
This simulation study examines the efficacy of multilevel factor mixture modeling (ML FMM) for measurement invariance testing across unobserved groups when the groups are at the between level of multilevel data. To this end, latent classes are generated with class-specific item parameters (i.e., factor loading and intercept) across the between-level classes. The efficacy of ML FMM is evaluated in terms of class enumeration, class assignment, and the detection of noninvariance. Various classification criteria such as Akaike’s information criterion, Bayesian information criterion, and bootstrap likelihood ratio tests are examined for the correct enumeration of between-level latent classes. For the detection of measurement noninvariance, free and constrained baseline approaches are compared with respect to true positive and false positive rates. This study evidences the adequacy of ML FMM. However, its performance heavily depends on the simulation factors such as the classification criteria, sample size, and the magnitude of noninvariance. Practical guidelines for applied researchers are provided. 相似文献
13.
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. 相似文献
14.
A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates
Jeffrey R. Harring Nidhi Kohli Rebecca D. Silverman Deborah L. Speece 《Structural equation modeling》2013,20(1):118-136
A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a nonlinear manner are common to all subjects. In this article we describe how a variant of the Michaelis–Menten (M–M) function can be fit within this modeling framework using Mplus 6.0. We demonstrate how observed and latent covariates can be incorporated to help explain individual differences in growth characteristics. Features of the model including an explication of key analytic decision points are illustrated using longitudinal reading data. To aid in making this class of models accessible, annotated Mplus code is provided. 相似文献
15.
W. Holmes Finch 《Educational and psychological measurement》2021,81(3):523
Social scientists are frequently interested in identifying latent subgroups within the population, based on a set of observed variables. One of the more common tools for this purpose is latent class analysis (LCA), which models a scenario involving k finite and mutually exclusive classes within the population. An alternative approach to this problem is presented by the grade of membership (GoM) model, in which individuals are assumed to have partial membership in multiple population subgroups. In this respect, it differs from the hard groupings associated with LCA. The current Monte Carlo simulation study extended on prior work on the GoM by investigating its ability to recover underlying subgroups in the population for a variety of sample sizes, latent group size ratios, and differing group response profiles. In addition, this study compared the performance of GoM with that of LCA. Results demonstrated that when the underlying process conforms to the GoM model form, the GoM approach yielded more accurate classification results than did LCA. In addition, it was found that the GoM modeling paradigm yielded accurate results for samples as small as 200, even when latent subgroups were very unequal in size. Implications for practice were discussed. 相似文献
16.
We evaluate the performance of the most common estimators of latent Markov (LM) models with covariates in the presence of direct effects of the covariates on the indicators of the LM model. In LM modeling it is common practice not to model such direct effects, ignoring the consequences that might have on the overall model fit and the parameters of interest. However, in the general literature about latent variable modeling it is well known that unmodeled direct effects can severely bias the parameter estimates of the model at hand. We evaluate how the presence of direct effects in?uences the bias and efficiency of the 3 most common estimators of LM models, the 1-step, 2-step, and 3-step approaches. Furthermore, we propose amendments (that were thus far not used in the context of LM modeling) to the 2- and 3-step approaches that make it possible to account for direct effects and eliminate bias as a consequence. This is done by modeling the (possible) direct effects in the first step of the stepwise estimation procedures. We evaluate the proposed estimators through an extensive simulation study, and illustrate them via a real data application. Our results show, first, that the augmented 2-step and 3-step approaches are unbiased and efficient estimators of LM models with direct effects. Second, ignoring the direct effects leads to biased estimates with all existing estimators, the 1-step approach being the most sensitive. 相似文献
17.
In this simulation study, we explored the effect of introducing covariates to a growth mixture model when covariates were also generated by a mixture model. We varied the association between the latent classes underlying the growth trajectories and the covariates, the degree of separation between the latent classes underlying the covariates, the number of covariates included, and amount of missing data in the growth data. We found that adding covariates to the growth mixture model generally hurt class recovery except where the latent classes underlying the growth trajectories and the covariates were the same or very strongly associated, and there was a large degree of separation between the classes underlying the covariates. We found that when covariates were introduced, entropy might no longer be an accurate indicator of the distinctiveness of the growth trajectory classes. 相似文献
18.
Martha A. O’Daniel Rinsland 《Journal of Experimental Education》2013,81(3):307-317
Latent class analysis is an analytic technique often used in educational and psychological research to identify meaningful groups of individuals within a larger heterogeneous population based on a set of variables. This technique is flexible, encompassing not only a static set of variables but also longitudinal data in the form of growth mixture modeling, as well as the application to complex multilevel sampling designs. The goal of this study was to investigate—through a Monte Carlo simulation study—the performance of several methods for parameterizing multilevel latent class analysis. Of particular interest was the comparison of several such models to adequately fit Level 1 (individual) data, given a correct specification of the number of latent classes at both levels (Level 1 and Level 2). Results include the parameter estimation accuracy as well as the quality of classification at Level 1. 相似文献
19.
Rens van de Schoot Marit Sijbrandij Sonja D. Winter Sarah Depaoli Jeroen K. Vermunt 《Structural equation modeling》2017,24(3):451-467
Estimating models within the mixture model framework, like latent growth mixture modeling (LGMM) or latent class growth analysis (LCGA), involves making various decisions throughout the estimation process. This has led to a wide variety in how results of latent trajectory analysis are reported. To overcome this issue, using a 4-round Delphi study, we developed Guidelines for Reporting on Latent Trajectory Studies (GRoLTS). The purpose of GRoLTS is to present criteria that should be included when reporting the results of latent trajectory analysis across research fields. We have gone through a systematic process to identify key components that, according to a panel of experts, are necessary when reporting results for trajectory studies. We applied GRoLTS to 38 papers where LGMM or LCGA was used to study trajectories of posttraumatic stress after a traumatic event. 相似文献
20.
This purpose of this paper is to identify risk profiles of youth who are victimized by on- and offline harassment and to explore the consequences of victimization on school outcomes. Latent class analysis is used to explore the overlap and co-occurrence of different clusters of victims and to examine the relationship between class membership and school exclusion and delinquency. Participants were a random sample of youth between the ages of 12 and 18 selected for inclusion to participate in the 2011 National Crime Victimization Survey: School Supplement. The latent class analysis resulted in four categories of victims: approximately 3.1% of students were highly victimized by both bullying and cyberbullying behaviors; 11.6% of youth were classified as being victims of relational bullying, verbal bullying and cyberbullying; a third class of students were victims of relational bullying, verbal bullying and physical bullying but were not cyberbullied (8%); the fourth and final class, characteristic of the majority of students (77.3%), was comprised of non-victims. The inclusion of covariates to the latent class model indicated that gender, grade and race were significant predictors of at least one of the four victim classes. School delinquency measures were included as distal outcomes to test for both overall and pairwise associations between classes. With one exception, the results were indicative of a significant relationship between school delinquency and the victim subtypes. Implications for these findings are discussed. 相似文献