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1.
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.  相似文献   

2.
Growth mixture modeling (GMM) has become a more popular statistical method for modeling population heterogeneity in longitudinal data, but the performance characteristics of GMM enumeration indexes in correctly identifying heterogeneous growth trajectories are largely unknown. Few empirical studies have addressed this issue. This study considered both homogeneous (a k = 1 growth trajectory) and heterogeneous (k = 3 different but unobserved growth trajectories) situations, and examined the performance of GMM in correctly identifying the latent trajectories in sample data. Four design conditions were manipulated: (a) sample size, (b) latent trajectory class proportions, (c) shapes of latent growth trajectories, and (d) degree of separation among latent growth trajectories. The findings suggest that, for k = 1 condition (1 homogenous growth trajectory), GMM's performance is reasonable in correctly identifying 1 latent growth trajectory (cf. Type I error control). However, for the k = 3 conditions (3 heterogeneous latent growth trajectories), GMM's general performance is very questionable (cf. Type II error). Different enumeration indexes varied considerably in their respective performances. Comparing the current results with previous GMM studies, the limitations of this study and future GMM enumeration research avenues are all discussed.  相似文献   

3.
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   

4.
Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study population. This article presents the results of a simulation study that examines the performance of likelihood-based tests and the traditionally used Information Criterion (ICs) used for determining the number of classes in mixture modeling. We look at the performance of these tests and indexes for 3 types of mixture models: latent class analysis (LCA), a factor mixture model (FMA), and a growth mixture models (GMM). We evaluate the ability of the tests and indexes to correctly identify the number of classes at three different sample sizes (n = 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test proved to be a very consistent indicator of classes across all of the models considered.  相似文献   

5.
For some time, there have been differing recommendations about how and when to include covariates in the mixture model building process. Some have advocated the inclusion of covariates after enumeration, whereas others recommend including them early on in the modeling process. These conflicting recommendations have led to inconsistent practices and unease in trusting modeling results. In an attempt to resolve this discord, we conducted a Monte Carlo simulation to examine the impact of covariate exclusion and misspecification of covariate effects on the enumeration process. We considered population and analysis models with both direct and indirect paths from the covariates to the latent class indicators. As expected, misspecified covariate effects most commonly led to the overextraction of classes. Findings suggest that the number of classes could be reliably determined using the unconditional latent class model, thus our recommendation is that class enumeration be done prior to the inclusion of covariates.  相似文献   

6.
Abstract

Factor 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   

7.
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   

8.
Recent developments in finite mixture modeling allow for the identification of different developmental processes in distinct but unobserved subgroups within a population. The new approach, described within the general growth mixture modeling framework (Muthen, 2001, in press), extends conventional random coefficient growth models to incorporate a categorical latent trajectory variable representing latent classes or mixtures (i.e., the subgroups in the population whose membership must be inferred from the data). This article provides a didactic example of this new methodology with adolescent alcohol use data, which is shown to consist of a mixture of distinct subgroups, defined by unique growth trajectories and differing predictors and sequelae. The method is discussed as a useful tool for mapping hypotheses of development onto appropriate statistical models.  相似文献   

9.
Research Findings: In this research, 487 Chinese children age 3 to 5 years took part in a number line estimation task. This task was used to assess children’s estimation accuracy and their estimation patterns along a number line in two different estimation circumstances. Situation A had the same line lengths for different numeric ranges, whereas situation B held the ratio of line lengths to numeric ranges constant. There were also three different number ranges (1–5/10/20). A new mathematical modeling method was proposed, where the two-dimensional estimation patterns of one child would be modeled as points in a higher dimensional space. Then the Dirichlet process Gaussian mixture model was applied to dynamically estimate the number of classes and assemble the different points into discrete classes based on distance. Three conclusions were drawn as follows: (a) significant differences were found within children for different ages and number ranges; (b) Chinese preschoolers had more estimation patterns than just linear pattern and logarithmic pattern, especially in small number ranges; and (c) mental number distance played an important role in their estimation patterns. Practice or Policy: Implications for early mathematic instruction on children’s understanding of mental number line are discussed.  相似文献   

10.
This article is intended to complement previous research (Sivo, 1997; Sivo & Willson, 1998, in press) by discussing the propriety and practical advantages of specifying multivariate time series models in the context of structural equation modeling for time series and longitudinal panel data. Three practical considerations motivated this article. Unlike Marsh (1993), Sivo and Willson (2000) did not offer multiple indicator (latent order) equivalents to their autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Moreover, such models have yet to be discussed, despite Marsh's (1993) advocacy for multiple indicator models in general. Further motivating multiple indicator extensions of the AR, MA, and ARMA equivalent models is the fact that longitudinal studies often collect data on more than 1 related variable per occasion. Such multiple indicator models capitalize on 1 of the chief analytical advantages of structural equation modeling in that measurement error may be estimated directly.  相似文献   

11.
The purpose of this article is to demonstrate how recent methodological developments in the analysis of individual growth can inform important problems in education policy. Specifically, this article focuses on a method referred to as growth mixture modeling. Growth mixture modeling is a relatively new procedure for the analysis of longitudinal data that relaxes many of the assumptions associated with conventional growth curve modeling. In particular, growth mixture modeling tests for the existence of unique growth trajectory classes through a combination of latent class analysis and standard growth curve modeling. Antecedent predictors of the latent classes can be incorporated as well as relations from the latent classes to specific outcomes. This article applies growth mixture modeling to data from the Early Childhood Longitudinal Study-Kindergarten class of 1998-1999. The specific policy question posed in this article focuses on the estimation of latent growth trajectory classes in reading proficiency and the effects of full-day or part-day kindergarten programs on growth within reading trajectory classes. Results identify a 3-class solution corresponding to slow-developing, normal-developing, and fast-developing reading growth in children. The results further show that full-day kindergarten attendance benefits children in the slow-reading development class relative to the normal and fast-reading development class, but the effect is lessened when holding constant socioeconomic status and age of entry into kindergarten. The implications of the method for quantitative education policy analysis are also discussed.  相似文献   

12.
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   

13.
Stage-sequential (or multiphase) growth mixture models are useful for delineating potentially different growth processes across multiple phases over time and for determining whether latent subgroups exist within a population. These models are increasingly important as social behavioral scientists are interested in better understanding change processes across distinctively different phases, such as before and after an intervention. One of the less understood issues related to the use of growth mixture models is how to decide on the optimal number of latent classes. The performance of several traditionally used information criteria for determining the number of classes is examined through a Monte Carlo simulation study in single- and multiphase growth mixture models. For thorough examination, the simulation was carried out in 2 perspectives: the models and the factors. The simulation in terms of the models was carried out to see the overall performance of the information criteria within and across the models, whereas the simulation in terms of the factors was carried out to see the effect of each simulation factor on the performance of the information criteria holding the other factors constant. The findings not only support that sample size adjusted Bayesian Information Criterion would be a good choice under more realistic conditions, such as low class separation, smaller sample size, or missing data, but also increase understanding of the performance of information criteria in single- and multiphase growth mixture models.  相似文献   

14.
Mixture Rasch models have been used to study a number of psychometric issues such as goodness of fit, response strategy differences, strategy shifts, and multidimensionality. Although these models offer the potential for improving understanding of the latent variables being measured, under some conditions overextraction of latent classes may occur, potentially leading to misinterpretation of results. In this study, a mixture Rasch model was applied to data from a statewide test that was initially calibrated to conform to a 3‐parameter logistic (3PL) model. Results suggested how latent classes could be explained and also suggested that these latent classes might be due to applying a mixture Rasch model to 3PL data. To support this latter conjecture, a simulation study was presented to demonstrate how data generated to fit a one‐class 2‐parameter logistic (2PL) model required more than one class when fit with a mixture Rasch model.  相似文献   

15.
This study investigates the effect of multidimensionality on extraction of latent classes in mixture Rasch models. In this study, two‐dimensional data were generated under varying conditions. The two‐dimensional data sets were analyzed with one‐ to five‐class mixture Rasch models. Results of the simulation study indicate the mixture Rasch model tended to extract more latent classes than the number of dimensions simulated, particularly when the multidimensional structure of the data was more complex. In addition, the number of extracted latent classes decreased as the dimensions were more highly correlated regardless of multidimensional structure. An analysis of the empirical multidimensional data also shows that the number of latent classes extracted by the mixture Rasch model is larger than the number of dimensions measured by the test.  相似文献   

16.
Dynamic structural equation modeling (DSEM) is a novel, intensive longitudinal data (ILD) analysis framework. DSEM models intraindividual changes over time on Level 1 and allows the parameters of these processes to vary across individuals on Level 2 using random effects. DSEM merges time series, structural equation, multilevel, and time-varying effects models. Despite the well-known properties of these analysis areas by themselves, it is unclear how their sample size requirements and recommendations transfer to the DSEM framework. This article presents the results of a simulation study that examines the estimation quality of univariate 2-level autoregressive models of order 1, AR(1), using Bayesian analysis in Mplus Version 8. Three features are varied in the simulations: complexity of the model, number of subjects, and number of time points per subject. Samples with many subjects and few time points are shown to perform substantially better than samples with few subjects and many time points.  相似文献   

17.
The purpose of this ITEMS module is to provide an introduction to differential item functioning (DIF) analysis using mixture item response models. The mixture item response models for DIF analysis involve comparing item profiles across latent groups, instead of manifest groups. First, an overview of DIF analysis based on latent groups, called latent DIF analysis, is provided and its applications in the literature are surveyed. Then, the methodological issues pertaining to latent DIF analysis are described, including mixture item response models, parameter estimation, and latent DIF detection methods. Finally, recommended steps for latent DIF analysis are illustrated using empirical data.  相似文献   

18.
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   

19.
A latent variable modeling procedure for examining whether a studied population could be a mixture of 2 or more latent classes is discussed. The approach can be used to evaluate a single-class model vis-à-vis competing models of increasing complexity for a given set of observed variables without making any assumptions about their within-class interrelationships. The method is helpful in the initial stages of finite mixture analyses to assess whether models with 2 or more classes should be subsequently considered as opposed to a single-class model. The discussed procedure is illustrated with a numerical example.  相似文献   

20.
The effects of misspecifying intercept-covariate interactions in a 4 time-point latent growth model were the focus of this investigation. The investigation was motivated by school growth studies in which students' entry-level skills may affect their rate of growth. We studied the latent interaction of intercept and a covariate in predicting growth with respect to 3 factors: sample size (100, 200, and 500), 4 levels of magnitude of interaction effect, and 3 correlation values between intercept and covariate (.3, .5, and .7). Correctly specified models were examined to determine power and Type I error rates, and misspecified models were examined to evaluate the effects on power, parameter estimation, bias, and fit indexes. Results showed that, under correctly specified models, power increased as expected with increasing sample size, larger magnitude of interaction, and larger intercept-covariate correlation. Under misspecification, omitting a non-null interaction results in significant change in the estimation of the direct effects of both covariate and intercept in both magnitude and direction, with results dependent on sign of parameter values for main effects and interaction. Including a spurious interaction does not affect estimation of direct effects of intercept and covariate but does increase standard errors. The primary problem in ignoring a non-null interaction lies in misinterpretation of the model, as interactions yield important insights into the nature of the processes being studied.  相似文献   

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