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1.
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   

2.
The factor mixture model (FMM) uses a hybrid of both categorical and continuous latent variables. The FMM is a good model for the underlying structure of psychopathology because the use of both categorical and continuous latent variables allows the structure to be simultaneously categorical and dimensional. This is useful because both diagnostic class membership and the range of severity within and across diagnostic classes can be modeled concurrently. Although the conceptualization of the FMM has been explained in the literature, the use of the FMM is still not prevalent. One reason is that there is little research about how such models should be applied in practice and, once a well-fitting model is obtained, how it should be interpreted. In this article, the FMM is explored by studying a real data example on conduct disorder. By exploring this example, this article aims to explain the different formulations of the FMM, the various steps in building a FMM, and how to decide between an FMM and alternative models.  相似文献   

3.
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   

4.
Regression mixture models are a new approach for finding differential effects which have only recently begun to be used in applied research. This approach comes at the cost of the assumption that error terms are normally distributed within classes. The current 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 which 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 which 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   

5.
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   

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.
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   

8.
Latent class analysis often aims to relate the classes to continuous external consequences (“distal outcomes”), but estimating such relationships necessitates distributional assumptions. Lanza, Tan, and Bray (2013) suggested circumventing such assumptions with their LTB approach: Linear logistic regression of latent class membership on each distal outcome is first used, after which this estimated relationship is reversed using Bayes’ rule. However, the LTB approach currently has 3 drawbacks, which we address in this article. First, LTB interchanges the assumption of normality for one of homoskedasticity, or, equivalently, of linearity of the logistic regression, leading to bias. Fortunately, we show introducing higher order terms prevents this bias. Second, we improve coverage rates by replacing approximate standard errors with resampling methods. Finally, we introduce a bias-corrected 3-step version of LTB as a practical alternative to standard LTB. The improved LTB methods are validated by a simulation study, and an example application demonstrates their usefulness.  相似文献   

9.
The standardized generalized dimensionality discrepancy measure and the standardized model‐based covariance are introduced as tools to critique dimensionality assumptions in multidimensional item response models. These tools are grounded in a covariance theory perspective and associated connections between dimensionality and local independence. Relative to their precursors, they allow for dimensionality assessment in a more readily interpretable metric of correlations. A simulation study demonstrates the utility of the discrepancy measures’ application at multiple levels of dimensionality analysis, and compares them to factor analytic and item response theoretic approaches. An example illustrates their use in practice.  相似文献   

10.
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   

11.
This article introduces a new inferential test for acyclic structural equation models (SEM) without latent variables or correlated errors. The test is based on the independence relations predicted by the directed acyclic graph of the SEMs, as given by the concept of d-separation. A wide range of distributional assumptions and structural functions can be accommodated. No iterative fitting procedures are used, precluding problems involving convergence. Exact probability estimates can be obtained, thus permitting the testing of models with small data sets.  相似文献   

12.
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   

13.
Two simulation studies investigated Type I error performance of two statistical procedures for detecting differential item functioning (DIF): SIBTEST and Mantel-Haenszel (MH). Because MH and SIBTEST are based on asymptotic distributions requiring "large" numbers of examinees, the first study examined Type 1 error for small sample sizes. No significant Type I error inflation occurred for either procedure. Because MH has the potential for Type I error inflation for non-Rasch models, the second study used a markedly non-Rasch test and systematically varied the shape and location of the studied item. When differences in distribution across examinee group of the measured ability were present, both procedures displayed inflated Type 1 error for certain items; MH displayed the greater inflation. Also, both procedures displayed statistically biased estimation of the zero DIF for certain items, though SIBTEST displayed much less than MH. When no latent distributional differences were present, both procedures performed satisfactorily under all conditions.  相似文献   

14.
In this article, 3-step methods to include predictors and distal outcomes in commonly used mixture models are evaluated. Two Monte Carlo simulation studies were conducted to compare the pseudo class (PC), Vermunt’s (2010), and the Lanza, Tan, and Bray (LTB) 3-step approaches with respect to bias of parameter estimates in latent class analysis (LCA) and latent profile analysis (LPA) models with auxiliary variables. For coefficients of predictors of class membership, results indicated that Vermunt’s method yielded more accurate estimates for LCA and LPA compared to the PC method. With distal outcomes of latent classes and latent profiles, the LTB method produced the lowest relative bias of coefficient estimates and Type I error rates close to nominal levels.  相似文献   

15.
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   

16.
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17.
Latent class models are often used to assign values to categorical variables that cannot be measured directly. This “imputed” latent variable is then used in further analyses with auxiliary variables. The relationship between the imputed latent variable and auxiliary variables can only be correctly estimated if these auxiliary variables are included in the latent class model. Otherwise, point estimates will be biased. We develop a method that correctly estimates the relationship between an imputed latent variable and external auxiliary variables, by updating the latent variable imputations to be conditional on the external auxiliary variables using a combination of multiple imputation of latent classes and the so-called three-step approach. In contrast with existing “one-step” and “three-step” approaches, our method allows the resulting imputations to be analyzed using the familiar methods favored by substantive researchers.  相似文献   

18.
In longitudinal design, investigating interindividual differences of intraindividual changes enables researchers to better understand the potential variety of development and growth. Although latent growth curve mixture models have been widely used, unstructured finite mixture models (uFMMs) are also useful as a preliminary tool and are expected to be more robust in identifying classes under the influence of possible model misspecifications, which are very common in actual practice. In this study, large-scale simulations were performed in which various normal uFMMs and nonnormal uFMMs were fit to evaluate their utility and the performance of each model selection procedure for estimating the number of classes in longitudinal designs. Results show that normal uFMMs assuming invariance of variance–covariance structures among classes perform better on average. Among model selection procedures, the Calinski–Harabasz statistic, which has a nonparametric nature, performed better on average than information criteria, including the Bayesian information criterion.  相似文献   

19.
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   

20.
The assumption of conditional independence between the responses and the response times (RTs) for a given person is common in RT modeling. However, when the speed of a test taker is not constant, this assumption will be violated. In this article we propose a conditional joint model for item responses and RTs, which incorporates a covariance structure to explain the local dependency between speed and accuracy. To obtain information about the population of test takers, the new model was embedded in the hierarchical framework proposed by van der Linden ( 2007 ). A fully Bayesian approach using a straightforward Markov chain Monte Carlo (MCMC) sampler was developed to estimate all parameters in the model. The deviance information criterion (DIC) and the Bayes factor (BF) were employed to compare the goodness of fit between the models with two different parameter structures. The Bayesian residual analysis method was also employed to evaluate the fit of the RT model. Based on the simulations, we conclude that (1) the new model noticeably improves the parameter recovery for both the item parameters and the examinees’ latent traits when the assumptions of conditional independence between the item responses and the RTs are relaxed and (2) the proposed MCMC sampler adequately estimates the model parameters. The applicability of our approach is illustrated with an empirical example, and the model fit indices indicated a preference for the new model.  相似文献   

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