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1.
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.
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   

3.
Growth models allow for the study of within-person change and between-person differences in within-person change. Typically, these models are applied to continuous variables where the residuals are assumed to be normally distributed. With normally distributed residuals there are a variety of residual structures that can be imposed and tested, which have been shown to affect model fit and parameter estimation. This article concerns residual structures in growth models with binary and ordered categorical outcomes using the probit link function. Different residual structures and their appropriateness for growth data are discussed and their use is illustrated with longitudinal data collected as part of Head Start’s Family and Child Experiences Survey 1997 Cohort. We close with recommendations for the specification and parameterization of growth models that use the probit link.  相似文献   

4.
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   

5.
Grimm KJ  Ram N  Hamagami F 《Child development》2011,82(5):1357-1371
Developmentalists are often interested in understanding change processes, and growth models are the most common analytic tool for examining such processes. Nonlinear growth curves are especially valuable to developmentalists because the defining characteristics of the growth process such as initial levels, rates of change during growth spurts, and asymptotic levels can be estimated. A variety of growth models are described beginning with the linear growth model and moving to nonlinear models of varying complexity. A detailed discussion of nonlinear models is provided, highlighting the added insights into complex developmental processes associated with their use. A collection of growth models are fit to repeated measures of height from participants of the Berkeley Growth and Guidance Studies from early childhood through adulthood.  相似文献   

6.
Latent growth modeling allows social behavioral researchers to investigate within-person change and between-person differences in within-person change. Typically, conventional latent growth curve models are applied to continuous variables, where the residuals are assumed to be normally distributed, whereas categorical variables (i.e., binary and ordinal variables), which do not hold to normal distribution assumptions, have rarely been used. This article describes the latent growth curve model with categorical variables, and illustrates applications using Mplus software that are applicable to social behavioral research. The illustrations use marital instability data from the Iowa Youth and Family Project. We close with recommendations for the specification and parameterization of growth models that use both logit and probit link functions.  相似文献   

7.
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   

8.
Piecewise latent trajectory models for longitudinal data are useful in a wide variety of situations, such as when a simple model is needed to describe nonlinear change, or when the purpose of the analysis is to evaluate hypotheses about change occurring during a particular period of time within a model for a longer overall time frame, such as change that occurs following onset of a treatment or some other event. However, the specification of various forms of piecewise models has not been fully explicated for the structural equation modeling (SEM) framework. This article describes piecewise models as a straightforward extension of the basic SEM model for linear growth, which makes them relatively easy both to specify and to interpret. After presenting models for 2 linear slopes (or pieces) in detail, the article discusses extensions that include additional linear slopes (i.e., a 3-piece model) or a quadratic factor (i.e., a hybrid linear-quadratic model).  相似文献   

9.
This article introduces developmentalists to methods for estimating individual developmental functions from longitudinal data in a multilevel analysis. Quantitative growth curve models for estimating the developmental functions from various types of longitudinal data are discussed in the context of both an investigator's assumptions about individual development on the attribute and the design characteristics of the prospective study. General linear and inherently nonlinear models that estimate population, individual, and prototypic growth curves are illustrated and contrasted when they are fit to speech development data.  相似文献   

10.
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   

11.
Within Bayesian estimation, prior distributions are placed on model parameters and these distributions can take on many different levels of informativeness. Although much of the research conducted within this estimation framework uses what are called diffuse (or noninformative) priors, there are certain models and modeling circumstances where it is more optimal to use what are referred to as informative priors. This study focuses on the latter situation and examines the effects of inaccurate informative priors on the growth parameters within the context of growth mixture modeling. Overall, results indicated that growth mixture modeling is relatively robust to the use of inaccurate mean hyperparameters for the growth parameters, as long as the variance hyperparameters are somewhat large.  相似文献   

12.
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   

13.
This article addresses issues of heterogeneity in multiple-stage development as it corresponds to qualitatively different development in alcohol use during adolescence. Using a piecewise growth mixture modeling methodology proposed by Muthén (in press), a 2-piece linear growth model capturing growth trajectories in adolescent alcohol use during the transition from middle school (ages 11 to 13) to high school (ages 14 to 17; N = 81) was examined. It was hypothesized that 2 stages of alcohol use development with varying trajectories would exist in these data, the 1st corresponding to development during middle school (Growth Rate 1), followed by a 2nd stage of continuing growth during high school (Growth Rate 2). Results suggested the tenability of the 2-piece linear development in alcohol use and the emergence of 2 latent classes with individually varying transition points. Class 1 showed linear increases only during high school, whereas Class 2 showed a continued, linear growth throughout the middle and high school years. Findings suggest that the sample population under study is heterogeneous and consists of 2 subpopulations, each defined by its unique growth trajectories and individually varying transitional growth processes. The piecewise growth mixture modeling approach is likely to provide researchers with insightful information regarding qualitative differences in adolescent substance use development as well as a potentially useful modeling technique for intervention studies involving evaluation of program effectiveness.  相似文献   

14.
Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a “black box” to the students. Thus, although correct models are estimated, students often do not obtain a thorough understanding of the nonlinear estimation process. The exercise presented in this article was created to demonstrate to students the need for nonlinear regression estimation—rather than using linear transformations and Ordinary Least Squares (OLS) and subsequently demonstrate the nonlinear optimization process to estimate nonlinear regression models. Using the spreadsheet exercise, students can see effects on the fit of the model by changing the model parameters as they change the values of the decision variables. After applying the spreadsheet to further exercises, students have expressed a deep understanding of the linear regression software. This exercise is innovative because the active learning exercise requires the students to make the logical connections between the structure of the model, the model's parameters, and the objective function.  相似文献   

15.
Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due to its proper and conjugate properties. However, many researchers have pointed out that the inverse Wishart prior might not work as expected. The purpose of this study is to investigate the influence of the inverse Wishart prior and compare it with a class of separation-strategy priors on the parameter estimates of growth curve models. In this article, we illustrate the use of different types of priors with 2 real data analyses, and then conduct simulation studies to evaluate and compare these priors in estimating both linear and nonlinear growth curve models. For the linear model, the simulation study shows that both the inverse Wishart and the separation-strategy priors work well for the fixed effects parameters. For the Level 1 residual variance estimate, the separation-strategy prior performs better than the inverse Wishart prior. For the covariance matrix, the results are mixed. Overall, the inverse Wishart prior is suggested if the population correlation coefficient and at least 1 of the 2 marginal variances are large. Otherwise, the separation-strategy prior is preferred. For the nonlinear growth curve model, the separation-strategy priors work better than the inverse Wishart prior.  相似文献   

16.
A linear latent growth curve mixture model with regime switching is extended in 2 ways. Previously, the matrix of first-order Markov switching probabilities was specified to be time-invariant, regardless of the pair of occasions being considered. The first extension, time-varying transitions, specifies different Markov transition matrices between each pair of occasions. The second extension is second-order time-invariant Markov transition probabilities, such that the probability of switching depends on the states at the 2 previous occasions. The models are implemented using the R package OpenMx, which facilitates data handling, parallel computation, and further model development. It also enables the extraction and display of relative likelihoods for every individual in the sample. The models are illustrated with previously published data on alcohol use observed on 4 occasions as part of the National Longitudinal Survey of Youth, and demonstrate improved fit to the data.  相似文献   

17.
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   

18.
本文研究了后非线性混合信号的盲分离 .后非线性混合信号是由线性混合的每一路信号分别经过一个非线性畸变产生的 .因此分离这种信号需要在适用于线性混合的线性分离结构前放置一个用于补偿非线性畸变的非线性校正部分 .本文用一种最大似然方法推导了一般后非线性分离结构的学习公式 .在前人一些工作的基础上 ,提出了一种用于亚、超高斯信号后非线性混合的盲分离算法 .该算法用多层感知器对分离结构的非线性校正部分进行建模 ,迭代过程中根据一稳定性条件在分别适用于亚、超高斯信号的概率模型间进行切换并以块自适应方式工作 .通过对模拟信号及实际信号 (图像和语音 )的实验证明了该算法的有效性 .  相似文献   

19.
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   

20.
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   

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