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1.
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   

2.
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   

3.
The 3-step approach has been recently advocated over the simultaneous 1-step approach to model a distal outcome predicted by a latent categorical variable. We generalize the 3-step approach to situations where the distal outcome is predicted by multiple and possibly associated latent categorical variables. Although the simultaneous 1-step approach has been criticized, simulation studies have found that the performance of the two approaches is similar in most situations (Bakk & Vermunt, 2016). This is consistent with our findings for a 2-LV extension when all model assumptions are satisfied. Results also indicate that under various degrees of violation of the normality and conditional independence assumption for the distal outcome and indicators, both approaches are subject to bias but the 3-step approach is less sensitive. The differences in estimates using the two approaches are illustrated in an analysis of the effects of various childhood socioeconomic circumstances on body mass index at age 50.  相似文献   

4.
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   

5.
A problem central to structural equation modeling is measurement model specification error and its propagation into the structural part of nonrecursive latent variable models. Full-information estimation techniques such as maximum likelihood are consistent when the model is correctly specified and the sample size large enough; however, any misspecification within the model can affect parameter estimates in other parts of the model. The goals of this study included comparing the bias, efficiency, and accuracy of hypothesis tests in nonrecursive latent variable models with indirect and direct feedback loops. We compare the performance of maximum likelihood, two-stage least-squares and Bayesian estimators in nonrecursive latent variable models with indirect and direct feedback loops under various degrees of misspecification in small to moderate sample size conditions.  相似文献   

6.
Growth mixture modeling (GMM) is a useful statistical method for longitudinal studies because it includes features of both latent growth modeling (LGM) and finite mixture modeling. This Monte Carlo simulation study explored the impact of ignoring 3 types of time series processes (i.e., AR(1), MA(1), and ARMA(1,1)) in GMM and manipulated the separation of the latent classes, the strength of the time series process, and whether the errors conformed to the time series process in 1 or 2 latent classes. The results showed that omitting time series processes resulted in more serious bias in parameter estimation as the distance between classes increased. However, when the class distances were small, ignoring time series processes contributed to the selection of the correct number of classes. When the GMM models correctly specified the time series process, only models with an AR(1) time series process produced unbiased parameter estimates in most conditions. It was also found that among design factors manipulated, the distance between classes prominently affected the identification of the number of classes and parameter estimation.  相似文献   

7.
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   

8.
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   

9.
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   

10.
Propensity score (PS) analysis aims to reduce bias in treatment effect estimates obtained from observational studies, which may occur due to non-random differences between treated and untreated groups with respect to covariates related to the outcome. We demonstrate how to use structural equation modeling (SEM) for PS analysis to remove selection bias due to latent covariates and estimate treatment effects on latent outcomes. Following the discussion of the design and analysis stages of PS analysis with SEM, an example is presented which uses the Mplus software to analyze data from the 1999 School and Staffing Survey (SASS) and 2000 Teacher Follow-up Survey (TFS) to estimate the effects teacher’s participation in a network of teachers on the teacher’s perception of workload manageability.  相似文献   

11.
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   

12.
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   

13.
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   

14.
The purpose of this article is to examine the use of sample weights in the latent variable modeling context. A sample weight is the inverse of the probability that the unit in question was sampled and is used to obtain unbiased estimates of population parameters when units have unequal probabilities of inclusion in a sample. Although sample weights are discussed at length in survey research literature, virtually no discussion of sample weights can be found in the latent variable modeling literature. This article examines sample weights in latent variable models applied to the case where a simple random sample is drawn from a population containing a mixture of strata. A bootstrap simulation study is used to compare raw and normalized sample weights to conditions where weights are ignored. The results show that ignoring weights can lead to serious bias in latent variable model parameters and that this bias is mitigated by the incorporation of sample weights. Standard errors appear to be underestimated when sample weights are applied. Results on goodness‐of‐fit statistics demonstrate the advantages of utilizing sample weights.  相似文献   

15.
Latent growth curve mediation models are increasingly used to assess mechanisms of behavior change. For latent growth mediation model, like any another mediation model, even with random treatment assignment, a critical but untestable assumption for valid and unbiased estimates of the indirect effects is that there should be no omitted variable that confounds indirect effects. One way to address this untestable assumption is to conduct sensitivity analysis to assess whether the inference about an indirect effect would change under varying degrees of confounding bias. We developed a sensitivity analysis technique for a latent growth curve mediation model. We compute the biasing effect of confounding on point and confidence interval estimates of the indirect effects in a structural equation modeling framework. We illustrate sensitivity plots to visualize the effects of confounding on each indirect effect and present an empirical example to illustrate the application of the sensitivity analysis.  相似文献   

16.
Multilevel Structural equation models are most often estimated from a frequentist framework via maximum likelihood. However, as shown in this article, frequentist results are not always accurate. Alternatively, one can apply a Bayesian approach using Markov chain Monte Carlo estimation methods. This simulation study compared estimation quality using Bayesian and frequentist approaches in the context of a multilevel latent covariate model. Continuous and dichotomous variables were examined because it is not yet known how different types of outcomes—most notably categorical—affect parameter recovery in this modeling context. Within the Bayesian estimation framework, the impact of diffuse, weakly informative, and informative prior distributions were compared. Findings indicated that Bayesian estimation may be used to overcome convergence problems and improve parameter estimate bias. Results highlight the differences in estimation quality between dichotomous and continuous variable models and the importance of prior distribution choice for cluster-level random effects.  相似文献   

17.
Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes and illustrates key features of Bayesian approaches to model diagnostics and assessing data–model fit of structural equation models, discussing their merits relative to traditional procedures.  相似文献   

18.
A challenge facing nearly all studies in the psychological sciences is how to best combine multiple items into a valid and reliable score to be used in subsequent modeling. The most ubiquitous method is to compute a mean of items, but more contemporary approaches use various forms of latent score estimation. Regardless of approach, outside of large-scale testing applications, scoring models rarely include background characteristics to improve score quality. This article used a Monte Carlo simulation design to study score quality for different psychometric models that did and did not include covariates across levels of sample size, number of items, and degree of measurement invariance. The inclusion of covariates improved score quality for nearly all design factors, and in no case did the covariates degrade score quality relative to not considering the influences at all. Results suggest that the inclusion of observed covariates can improve factor score estimation.  相似文献   

19.
Estimation of the direct effect of an exposure on an outcome requires adjustment for confounders of the exposure–outcome and mediator–outcome relationships. When some of the latter confounders have been affected by the exposure, then standard regression adjustment is prone to possibly severe bias. The use of inverse probability weighting under so-called marginal structural models has recently been suggested as a solution in the psychological literature. In this article, we show how progress can alternatively be made via G-estimation. We show that this estimation method can be easily embedded within the structural equation modeling framework and could in particular be used for estimating direct effects in the presence of latent variables. Moreover, by avoiding inverse probability weighting, it accommodates the typical problem of unstable weights in the alternative estimation approaches based on marginal structural models. We illustrate the approach both by simulations and by the analysis of a longitudinal study in individiduals who ended a romantic relationship. In this example we explore whether the effect of attachment anxiety during the relationship on mental distress 2 years after the breakup is mediated by rumination or not.  相似文献   

20.
Researchers have devoted some time and effort to developing methods for fitting nonlinear relationships among latent variables. In particular, most of these have focused on correctly modeling interactions between 2 exogenous latent variables, and quadratic relationships between exogenous and endogenous variables. All of these approaches require prespecification of the nonlinearity by the researcher, and are limited to fairly simple nonlinear relationships. Other work has been done using mixture structural equation models (SEMM) in an attempt to fit more complex nonlinear relationships. This study expands on this earlier work by introducing the 2-stage generalized additive model (2SGAM) approach for fitting regression splines in the context of structural equation models. The model is first described and then investigated through the use of simulated data, in which it was compared with the SEMM approach. Results demonstrate that the 2SGAM is an effective tool for fitting a variety of nonlinear relationships between latent variables, and can be easily and accurately extended to models including multiple latent variables. Implications of these results are discussed.  相似文献   

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