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1.
Change over time often takes on a nonlinear form. Furthermore, change patterns can be characterized by heterogeneity due to unobserved subpopulations. Nonlinear mixed-effects mixture models provide one way of addressing both of these issues. This study attempts to extend these models to accommodate time-unstructured data. We develop methods to fit these models in both the structural equation modeling framework as well as the Bayesian framework and evaluate their performance. Simulations show that the success of these methods is driven by the separation between latent classes. When classes are well separated, a sample of 200 is sufficient. Otherwise, a sample of 1,000 or more is required before parameters can be accurately recovered. Ignoring individually varying measurement occasions can also lead to substantial bias, particularly in the random-effects parameters. Finally, we demonstrate the application of these techniques to a data set involving the development of reading ability in children. 相似文献
2.
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
3.
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
4.
This article investigates three types of stage-sequential growth mixture models in the structural equation modeling framework for the analysis of multiple-phase longitudinal data. These models can be important tools for situations in which a single-phase growth mixture model produces distorted results and can allow researchers to better understand population heterogeneity and growth over multiple phases. Through theoretical and empirical comparisons of the models, the authors discuss strategies with respect to model selection and interpreting outcomes. The unique attributes of each approach are illustrated using ecological momentary assessment data from a tobacco cessation study. Transitional discrepancy between phases as well as growth factors are examined to see whether they can give us useful information related to a distal outcome, abstinence at 6 months postquit. It is argued that these statistical models are powerful and flexible tools for the analysis of complex and detailed longitudinal data. 相似文献
5.
When conducting longitudinal research, the investigation of between-individual differences in patterns of within-individual change can provide important insights. In this article, we use simulation methods to investigate the performance of a model-based exploratory data mining technique—structural equation model trees (SEM trees; Brandmaier, Oertzen, McArdle, & Lindenberger, 2013)—as a tool for detecting population heterogeneity. We use a latent-change score model as a data generation model and manipulate the precision of the information provided by a covariate about the true latent profile as well as other factors, including sample size, under the possible influences of model misspecifications. Simulation results show that, compared with latent growth curve mixture models, SEM trees might be very sensitive to model misspecification in estimating the number of classes. This can be attributed to the lower statistical power in identifying classes, resulting from smaller differences of parameters prescribed by the template model between classes. 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.
In recent years, longitudinal data have become increasingly relevant in many applications, heightening interest in selecting the best longitudinal model to analyze them. Too often, traditional practice rather than substantive theory guides the specific model selected. This opens the possibility that alternative models might better correspond to the data. In this paper, we present a general longitudinal model that we call the Latent Variable-Autoregressive Latent Trajectory (LV-ALT) model that includes most other longitudinal models with continuous outcomes as special cases. It is capable of specializing to most models dictated by theory or prior research while having the capacity to compare them to alternative ones. If there is little guidance on the best model, the LV-ALT provides a way to determine the appropriate empirical match to the data. We present the model, discuss its identification and estimation, and illustrate how the LV-ALT reveals new things about a widely used empirical example. 相似文献
8.
Wynne W. Chin 《Structural equation modeling》2013,20(2):196-201
STATISTICA 5.0. StatSoft, 2325 East 13th Street, Tulsa, OK 74104, (918) 583–4149. $995 retail, academic site license—$2,000 for 10 copies. Requirements: 386 or better, 4 Meg RAM, Microsoft Windows 3.1 or 95. 相似文献
9.
Gabriela Stegmann Ross Jacobucci Jeffrey R. Harring Kevin J. Grimm 《Structural equation modeling》2018,25(1):160-165
In this software review, we provide a brief overview of four R functions to estimate nonlinear mixed-effects programs: nlme (linear and nonlinear mixed-effects model), nlmer (from the lme4 package, linear mixed-effects models using Eigen and S4), saemix (stochastic approximation expectation maximization), and brms (Bayesian regression models using Stan). We briefly describe the approaches used, provide a sample code, and highlight strengths and weaknesses of each. 相似文献
10.
Naoya Todo 《Structural equation modeling》2016,23(5):695-712
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
11.
First-order latent growth curve models (FGMs) estimate change based on a single observed variable and are widely used in longitudinal research. Despite significant advantages, second-order latent growth curve models (SGMs), which use multiple indicators, are rarely used in practice, and not all aspects of these models are widely understood. In this article, our goal is to contribute to a better understanding of theoretical and practical differences between FGMs and SGMs. We define the latent variables in FGMs and SGMs explicitly on the basis of latent state–trait (LST) theory and discuss insights that arise from this approach. We show that FGMs imply a strict trait-like conception of the construct under study, whereas SGMs allow for both trait and state components. Based on a simulation study and empirical applications to the Center for Epidemiological Studies Depression Scale (Radloff, 1977) we illustrate that, as an important practical consequence, FGMs yield biased reliability estimates whenever constructs contain state components, whereas reliability estimates based on SGMs were found to be accurate. Implications of the state–trait distinction for the measurement of change via latent growth curve models are discussed. 相似文献
12.
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
13.
Sonya K. Sterba 《Structural equation modeling》2013,20(4):630-647
Individual growth trajectories of psychological phenomena are often theorized to be nonlinear. Additionally, individuals’ measurement schedules might be unique. In a structural equation framework, latent growth curve model (LGM) applications typically have either (a) modeled nonlinearity assuming some degree of balance in measurement schedules, or (b) accommodated truly individually varying time points, assuming linear growth. This article describes how to fit 4 popular nonlinear LGMs (polynomial, shape-factor, piecewise, and structured latent curve) with truly individually varying time points, via a definition variable approach. The extension is straightforward for certain nonlinear LGMs (e.g., polynomial and structured latent curve) but in the case of shape-factor LGMs requires a reexpression of the model, and in the case of piecewise LGMs requires introduction of a general framework for imparting piecewise structure, along with tools for its automation. All 4 nonlinear LGMs with individually varying time scores are demonstrated using an empirical example on infant weight, and software syntax is provided. The discussion highlights some advantages of modeling nonlinear growth within structural equation versus multilevel frameworks, when time scores individually vary. 相似文献
14.
A potential weakness of quantitative methods is the intrusive nature of testing in general, and pretesting specifically. The Solomon four-group design ameliorates this difficulty, but because of statistical issues there are few published examples. W. Braver and Braver (1988) suggested the use of meta-analytic Stouffer's Z to combine the data from all four groups. Sawilowsky and Markman (1990a, 1990b, 1990c, 1990d) and Braver and W. Braver (1990a, 1990b) exchanged differing opinions on this approach. The present study is a Monte Carlo demonstration that the experiment-wise error rate inflates nearly triple nominal alpha. However, when not conducted as conditional tests, traditional procedures are more powerful than this meta-analytic approach, despite the ability of Stouffer's Z to combine all available data into a single statistic. 相似文献
15.
Su-Young Kim 《Structural equation modeling》2013,20(2):263-279
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
16.
Growth mixture models combine latent growth curve models and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. Analyses based on these models are becoming quite common in social and behavioral science research because of recent advances in computing, the availability of specialized statistical programs, and the ease of programming. In this article, we show how mixture models can be fit to examine the presence of multiple latent classes by algorithmically grouping or clustering individuals who follow the same estimated growth trajectory based on an evaluation of individual case residuals. The approach is illustrated using empirical longitudinal data along with an easy to use computerized implementation. 相似文献
17.
Todd E. Bodner 《Structural equation modeling》2013,20(4):651-675
When using multiple imputation in the analysis of incomplete data, a prominent guideline suggests that more than 10 imputed data values are seldom needed. This article calls into question the optimism of this guideline and illustrates that important quantities (e.g., p values, confidence interval half-widths, and estimated fractions of missing information) suffer from substantial imprecision with a small number of imputations. Substantively, a researcher can draw categorically different conclusions about null hypothesis rejection, estimation precision, and missing information in distinct multiple imputation runs for the same data and analysis with few imputations. This article explores the factors associated with this imprecision, demonstrates that precision improves by increasing the number of imputations, and provides practical guidelines for choosing a reasonable number of imputations to reduce imprecision for each of these quantities. 相似文献
18.
Katerina M. Marcoulides 《Structural equation modeling》2018,25(5):687-699
Latent growth curve models are widely used in the social and behavioral sciences to study complex developmental patterns of change over time. The trajectories of these developmental patterns frequently exhibit distinct segments in the studied variables. Latent growth models with piecewise functions for repeated measurements of variables have become increasingly popular for modeling such developmental trajectories. A major problem with using piecewise models is determining the precise location of the point where the change in the process has occurred and uncovering the related number of segments. The purpose of this paper is to introduce an optimization procedure that can be used to determine both the segments and location of the knots in piecewise linear latent growth models. The procedure is illustrated using empirical data in order to detect the number of segments and change points. The results demonstrate the capabilities of the procedure for fitting latent growth curve models. 相似文献
19.
Su-Young Kim 《Structural equation modeling》2013,20(3):457-476
Just as growth mixture models are useful with single-phase longitudinal data, multiphase growth mixture models can be used with multiple-phase longitudinal data. One of the practically important issues in single- and multiphase growth mixture models is the sample size requirements for accurate estimation. In a Monte Carlo simulation study, the sample sizes required for using these models are investigated under various theoretical and realistic conditions. In particular, the relationship between the sample size requirement and the number of indicator variables is examined, because the number of indicators can be relatively easily controlled by researchers in many multiphase data collection settings such as ecological momentary assessment. The findings not only provide tangible information about required sample sizes under various conditions to help researchers, but they also increase understanding of sample size requirements in single- and multiphase growth mixture models. 相似文献
20.
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