共查询到20条相似文献，搜索用时 46 毫秒
1.
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
2.
In a recent article, Castro-Schilo, Widaman, and Grimm (2013) compared different approaches for relating multitrait–multimethod (MTMM) data to external variables. Castro-Schilo et al. reported that estimated associations with external variables were in part biased when either the correlated traits–correlated uniqueness (CT-CU) or correlated traits–correlated (methods–1) [CT-C(M–1)] models were fit to data generated from the correlated traits–correlated methods (CT-CM) model, whereas the data-generating CT-CM model accurately reproduced these associations. Castro-Schilo et al. argued that the CT-CM model adequately represents the data-generating mechanism in MTMM studies, whereas the CT-CU and CT-C(M–1) models do not fully represent the MTMM structure. In this comment, we question whether the CT-CM model is more plausible as a data-generating model for MTMM data than the CT-C(M–1) model. We show that the CT-C(M–1) model can be formulated as a reparameterization of a basic MTMM true score model that leads to a meaningful and parsimonious representation of MTMM data. We advocate the use confirmatory factor analysis MTMM models in which latent trait, method, and error variables are explicitly and constructively defined based on psychometric theory. 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.
Nonlinear models are effective tools for the analysis of longitudinal data. These models provide a flexible means for describing data that follow complex forms of change. Exponential and logistic functions that include a parameter to represent an asymptote, for instance, are useful for describing responses that tend to level off with time. There are forms of nonlinear latent curve models and nonlinear mixed-effects model that are equivalent, and so given the same set of data, growth function, distributional assumptions, and method of estimation, the 2 models yield equivalent results. There are also forms that are strikingly different and can yield different interpretations for a given set of data. This article discusses cases in which nonlinear mixed-effects models and nonlinear latent curve models are equivalent and those in which they are different and clarifies the estimation needs of the different models. Examples based on empirical data help to illustrate these points. 相似文献
5.
Shu-Ping Chen 《Structural equation modeling》2013,20(1):94-101
Estimating nonlinear effects between constructs is an important concern in the social sciences. In empirical studies, researchers often focus more on mediated moderation or moderated mediation as opposed to moderation by itself. This article generalizes the constrained approach with noncentered observed variables to a matrix form that encompasses the latent nonlinear effects of not only exogenous variables, but also endogenous variables or a combination of the two. Constraints are specified in matrix form and the matrices involved in model specification are partitioned to fit into the nonlinear model framework. The usage and validity of the procedure is demonstrated with a simulated data set example using the Mx program. 相似文献
6.
There has been a great deal of work in the literature on the equivalence between the mixed-effects modeling and structural equation modeling (SEM) frameworks in specifying growth models (Willett &; Sayer, 1994). However, there has been little work on the correspondence between the latent growth curve model (LGM) and the latent change score model (see Grimm, Zhang, Hamagami, &; Mazzocco, 2013). We demonstrate that four popular variants of the latent change score model – the no change, constant change, proportional change, and dual change models – have LGM equivalents. We provide equations that allow the translation of parameters from one approach to the other and vice versa. We then illustrate this equivalence using mathematics achievement data from the National Longitudinal Survey of Youth. 相似文献
7.
Axel Mayer Nora Umbach Barbara Flunger Augustin Kelava 《Structural equation modeling》2017,24(4):556-570
In this article, we present an approach for comprehensive analysis of the effectiveness of interventions based on nonlinear structural equation mixture models (NSEMM). We provide definitions of average and conditional effects and show how they can be computed. We extend the traditional moderated regression approach to include latent continous and discrete (mixture) variables as well as their higher order interactions, quadratic or more general nonlinear relationships. This new approach can be considered a combination of the recently proposed EffectLiteR approach and the NSEMM approach. A key advantage of this synthesis is that it gives applied researchers the opportunity to gain greater insight into the effectiveness of the intervention. For example, it makes it possible to consider structural equation models for situations where the treatment is noneffective for extreme values of a latent covariate but is effective for medium values, as we illustrate using an example from the educational sciences. 相似文献
8.
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
9.
Steffen Nestler 《Structural equation modeling》2013,20(4):542-551
The relations between the latent variables in structural equation models are typically assumed to be linear in form. This article aims to explain how a specification error test using instrumental variables (IVs) can be employed to detect unmodeled interactions between latent variables or quadratic effects of latent variables. An empirical example is presented, and the results of a simulation study are reported to evaluate the sensitivity and specificity of the test and compare it with the commonly employed chi-square model test. The results show that the proposed test can identify most unmodeled latent interactions or latent quadratic effects in moderate to large samples. Furthermore, its power is higher when the number of indicators used to define the latent variables is large. Altogether, this article shows how the IV-based test can be applied to structural equation models and that it is a valuable tool for researchers using structural equation models. 相似文献
10.
Tiffany A. Whittaker S. Natasha Beretvas Toni Falbo 《Structural equation modeling》2013,20(2):303-317
The analysis of longitudinal data collected from nonexchangeable dyads presents a challenge for applied researchers for various reasons. This article introduces the dyadic curve-of-factors model (D–COFM), which extends the curve-of-factors model (COFM) proposed by McArdle (1988) for use with nonexchangeable dyadic data. The D–COFM overcomes problems with modeling composite scores across time and instead permits examination of the growth in latent constructs over time. The D–COFM also appropriately models the interdependency among nonexchangeable dyads. Different parameterizations of the D–COFM are illustrated and discussed using a real data set to aid applied researchers when analyzing dyadic longitudinal data. 相似文献
11.
This Monte Carlo simulation study investigated different strategies for forming product indicators for the unconstrained approach in analyzing latent interaction models when the exogenous factors are measured by unequal numbers of indicators under both normal and nonnormal conditions. Product indicators were created by (a) multiplying parcels of the larger scale by items of the smaller scale, and (b) matching items according to reliability to create several product indicators, ignoring those items with lower reliability. Two scaling approaches were compared where parceling was not involved: (a) fixing the factor variances, and (b) fixing 1 loading to 1 for each factor. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. Results showed that under normal conditions, the LMS approach was preferred because the biases of its interaction estimates and associated standard errors were generally smaller, and its power was higher than that of the unconstrained approach. Under nonnormal conditions, however, the unconstrained approach was generally more robust than the LMS approach. It is recommended to form product indicators by using items with higher reliability (rather than parceling) in the matching and then to specify the model by fixing 1 loading of each factor to unity when adopting the unconstrained approach. 相似文献
12.
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
13.
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
14.
We consider a multivariate generalized latent variable model to investigate the effects of observable and latent explanatory variables on multiple responses of interest. Various types of correlated responses, such as continuous, count, ordinal, and nominal variables, are considered in the regression. A generalized confirmatory factor analysis model that is capable of managing mixed-type data is proposed to characterize latent variables via correlated observed indicators. In addressing the complicated structure of the proposed model, we introduce continuous underlying measurements to provide a unified model framework for mixed-type data. We develop a multivariate version of the Bayesian adaptive least absolute shrinkage and selection operator procedure, which is implemented with a Markov chain Monte Carlo (MCMC) algorithm in a full Bayesian context, to simultaneously conduct estimation and model selection. The empirical performance of the proposed methodology is demonstrated through a simulation study. An application of the proposed method to a study of adolescent substance abuse based on the National Longitudinal Survey of Youth is presented. 相似文献
15.
Conventionally, moderated mediation analysis is conducted through adding relevant interaction terms into a mediation model of interest. In this study, we illustrate how to conduct moderated mediation analysis by directly modeling the relation between the indirect effect components including a and b and the moderators, to permit easier specification and interpretation of moderated mediation. With this idea, we introduce a general moderated mediation model that can be used to model many different moderated mediation scenarios including the scenarios described in Preacher, Rucker, and Hayes (2007). Then we discuss how to estimate and test the conditional indirect effects and to test whether a mediation effect is moderated using Bayesian approaches. How to implement the estimation in both BUGS and Mplus is also discussed. Performance of Bayesian methods is evaluated and compared to that of frequentist methods including maximum likelihood (ML) with 1st-order and 2nd-order delta method standard errors and mL with bootstrap (percentile or bias-corrected confidence intervals) via a simulation study. The results show that Bayesian methods with diffuse (vague) priors implemented in both BUGS and Mplus yielded unbiased estimates, higher power than the ML methods with delta method standard errors, and the ML method with bootstrap percentile confidence intervals, and comparable power to the ML method with bootstrap bias-corrected confidence intervals. We also illustrate the application of these methods with the real data example used in Preacher et al. (2007). Advantages and limitations of applying Bayesian methods to moderated mediation analysis are also discussed. 相似文献
16.
Latent growth modeling (LGM) is a popular and flexible technique that may be used when data are collected across several different measurement occasions. Modeling the appropriate growth trajectory has important implications with respect to the accurate interpretation of parameter estimates of interest in a latent growth model that may impact educational policy decisions. A Monte Carlo simulation study was conducted to examine the accuracy of six information-based criteria (i.e., AIC, CAIC, AICC, BIC, nBIC, and HQIC) when selecting among various growth trajectories modeled using LGM under different sample size, number of time points, and growth trajectory scenarios. The accuracy of the information criteria generally improved as sample size increased. The cubic and linear growth models were distinguished most accurately by the information criteria. All of the nonlinear models were more easily distinguished as the number of time points increased. The comparative performance of the six information criteria was dependent upon the manipulated conditions. Implications of the findings are discussed. 相似文献
17.
Karen Nylund-Gibson Ryan P. Grimm Katherine E. Masyn 《Structural equation modeling》2013,20(6):967-985
Including auxiliary variables such as antecedent and consequent variables in mixture models provides valuable insight in understanding the population heterogeneity embodied by a latent class variable. The model building process regarding how to include predictors/correlates and outcomes of the latent class variables into mixture models is an area of active research. As such, new methods of including these variables continue to emerge and best practices for the application of these methods in real data settings (including simple guidelines for choosing amongst them) are still not well established. This paper focuses on one type of auxiliary variable—distal outcomes—providing an overview of the methods currently available for estimating the effects of latent class membership on subsequent distal outcomes. We illustrate the recommended methods in the software packages Mplus and Latent Gold using a latent class model to capture population heterogeneity in students’ mathematics attitudes, linking latent class membership to two distal outcomes. 相似文献
18.
An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R 2 indexes associated with repeatedly followed measures in longitudinal studies. In addition to facilitating evaluation of local model fit, the approach is helpful for purposes of differentiating between plausible models stipulating different patterns of change over time, and in particular in empirical situations characterized by large samples and high statistical power. The procedure is also applicable in cross-sectional studies, as well as with general structural equation models. The method is illustrated using data from a nationally representative study of older adults. 相似文献
19.
Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we describe a nonlinear structural equation mixture approach that integrates the strength of parametric approaches (specification of the nonlinear functional relationship) and the flexibility of semiparametric structural equation mixture approaches for approximating the nonnormality of latent predictor variables. In a comparative simulation study, the advantages of the proposed mixture procedure over contemporary approaches [Latent Moderated Structural Equations approach (LMS) and the extended unconstrained approach] are shown for varying degrees of skewness of the latent predictor variables. Whereas the conventional approaches show either biased parameter estimates or standard errors of the nonlinear effects, the proposed mixture approach provides unbiased estimates and standard errors. We present an empirical example from educational research. Guidelines for applications of the approaches and limitations are discussed. 相似文献
20.
Christian Geiser Samuel D. Mandelman Mei Tan Elena L. Grigorenko 《Structural equation modeling》2016,23(1):76-90
Although the use of multiple criteria and informants is one of the most universally agreed on practices in the identification of gifted children, few studies to date have examined the convergent validity of multiple informants and objective ability tests in gifted identification. In this study, we illustrate the use of the correlated traits–correlated (methods – 1) or CT–C(M – 1) model (Eid, Lischetzke, Nussbeck, & Trierweiler, 2003) to examine the convergent validity of self, parent, and teacher ratings relative to objective cognitive ability tests in a sample of 145 4th to 6th graders. The CT–C(M – 1) analyses revealed that teacher ratings showed the highest convergence with the objective assessments, whereas self-ratings had the lowest reliabilities and insufficient validity. Parent ratings were more reliable and valid than self-reports, but were outperformed by teacher ratings for most abilities. Overall, the CT–C(M – 1) analyses showed that the convergent validity of the ratings relative to the objective test battery was highest for numerical and lowest for creative abilities. Furthermore, whereas part of the shared variance between parent and teacher ratings reflected true convergent validity, agreement between parent and self-reports was entirely due to a shared rater variance. Our analyses demonstrate the usefulness and proper interpretation of the CT–C(M – 1) approach for examining convergent validity and method effects in multitrait–multimethod data. 相似文献