多阶段增长模型的方法比较

多阶段增长模型（Piecewise Growth Modeling,PGM）可以解决发展趋势中具有转折点的情形,并且相对其他复杂的曲线增长模型,解释更简单.已有的统计方法主要通过多层线性模型和潜变量增长模型对多阶段模型进行估计.通过模拟研究,用HLM6.0和Mplus6.0对上述两种模型分别进行估计,结果发现在参数估计的精度上,两种估计方法没有差异,只是在犯一类错误的概率上后者略小.进一步通过对错误模型的探讨发现,在样本量小（n=50）,斜率变化小（△b=0.2）时,用线性模型拟合数据而非PGM所犯错误概率较小,整体拟合更佳.但随着样本的增加和斜率变化的增加,错误模型的犯错概率明显增大.故在实际应用中,为了能更好拟合数据,研究者应根据数据本身的情况选择恰当的模型.     

Modeling Incomplete Longitudinal Substance Use Data Using Latent Variable Growth Curve Methodology

Longitudinal data sets typically suffer from attrition and other forms of missing data. When this common problem occurs, several researchers have demonstrated that correct maximum likelihood estimation with missing data can be obtained under mild assumptions concerning the missing data mechanism. With reasonable substantive theory, a mixture of cross-sectional and longitudinal methods developed within multiple-group structural equation modeling can provide a strong basis for inference about developmental change. Using an approach to the analysis of missing data, the present study investigated developmental trends in adolescent (N = 759) alcohol, marijuana, and cigarette use across a 5-year period using multiple-group latent growth modeling. An associative model revealed that common developmental trends existed for all three substances. Age and gender were included in the model as predictors of initial status and developmental change. Findings discuss the utility of latent variable structural equation modeling techniques and missing data approaches in the study of developmental change.     

老年人认知功能的变化轨迹：基于潜变量增长模型的分析

摘 要 本研究采用中国老年健康影响因素跟踪调查（CLHLS）的4次数据（2002,2005,2008,2011）,对老年人认知功能的变化趋势以及影响因素进行了探讨。结果显示：（1）老年人认知功能在4次测查中呈非线性的下降趋势。（2）日常生活活动能力较低的个体其认知功能也较低;老年人读书年限越高,其认知功能水平越高;女性的认知功能水平低于男性;不饮酒的老年人认知功能低于饮酒的老年人。（3）读书年限与饮酒会正向预测模型的斜率。     

Testing Group Mean Differences of Latent Variables in Multilevel Data Using Multiple-Group Multilevel CFA and Multilevel MIMIC Modeling

Considering that group comparisons are common in social science, we examined two latent group mean testing methods when groups of interest were either at the between or within level of multilevel data: multiple-group multilevel confirmatory factor analysis (MG ML CFA) and multilevel multiple-indicators multiple-causes modeling (ML MIMIC). The performance of these methods were investigated through three Monte Carlo studies. In Studies 1 and 2, either factor variances or residual variances were manipulated to be heterogeneous between groups. In Study 3, which focused on within-level multiple-group analysis, six different model specifications were considered depending on how to model the intra-class group correlation (i.e., correlation between random effect factors for groups within cluster). The results of simulations generally supported the adequacy of MG ML CFA and ML MIMIC for multiple-group analysis with multilevel data. The two methods did not show any notable difference in the latent group mean testing across three studies. Finally, a demonstration with real data and guidelines in selecting an appropriate approach to multilevel multiple-group analysis are provided.     

Latent Growth Modeling for Logistic Response Functions

Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following logistic (sigmoidal; S-shape) response functions. Such trajectories are assumed in a variety of psychological and educational settings where learning occurs over time, and yet applications using the logistic model in growth modeling methodology have been sparse. The logistic function, in particular, may not be utilized as often because software options remain limited. In this article we show how a specialized version of the logistic function can be modeled using conventional structural equation modeling software. The specialization is a reparameterization of the logistic function whose new parameters correspond to scientifically interesting characteristics of the growth process. In addition to providing an example using simulated data, we show how this nonlinear functional form can be fit using transformed subject-level data obtained through a learning task from an air traffic controller simulation experiment. LISREL syntax for the empirical example is provided.     

Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

This paper uses log-linear models with latent variables (Hagenaars, in Loglinear Models with Latent Variables, 1993) to define a family of cognitive diagnosis models. In doing so, the relationship between many common models is explicitly defined and discussed. In addition, because the log-linear model with latent variables is a general model for cognitive diagnosis, new alternatives to modeling the functional relationship between attribute mastery and the probability of a correct response are discussed.     

An Introduction to Latent Class Growth Analysis and Growth Mixture Modeling

In recent years, there has been a growing interest among researchers in the use of latent class and growth mixture modeling techniques for applications in the social and psychological sciences, in part due to advances in and availability of computer software designed for this purpose (e.g., Mplus and SAS Proc Traj). Latent growth modeling approaches, such as latent class growth analysis (LCGA) and growth mixture modeling (GMM), have been increasingly recognized for their usefulness for identifying homogeneous subpopulations within the larger heterogeneous population and for the identification of meaningful groups or classes of individuals. The purpose of this paper is to provide an overview of LCGA and GMM, compare the different techniques of latent growth modeling, discuss current debates and issues, and provide readers with a practical guide for conducting LCGA and GMM using the Mplus software.     

Abstract: Comparing Semiparametric and Parametric Methods for Modeling Interactions Among Latent Variables

Many approaches have been proposed to estimate interactions among latent variables. These methods often assume a specific functional form for the interaction, such as a bilinear interaction. Theory is seldom specific enough to provide a functional form for an interaction, however, so a more exploratory, diagnostic approach may often be required. Bauer (2005) proposed a semiparametric approach that allows for the estimation of interaction effects of unknown functional form among latent variables. A structural equation mixture model (SEMM) is first fit to the data. Then an approximation of the interaction is obtained by aggregating over the mixing components. A simulation study is used to examine the performance of this semiparametric approach to two parametric approaches: the latent moderated structures approach (Klein & Moosbrugger, 2000) and the unconstrained product-indicator approach (Marsh, Wen, & Hau, 2004). Data were generated from four functional forms: main effects only, quadratic trend, bilinear interaction, and exponential interaction. Estimates of bias and root mean squared error of approximation were calculated by comparing the surface used to generate the data and the model-implied surface constructed from each approach. As expected, the parametric approaches were more efficient than the SEMM. For the main effects model, bias was similar for both the SEMM and parametric approaches. For the bilinear interaction, the parametric approaches provided nearly identical results, although the SEMM approach was slightly more biased. When the parametric approaches assumed a bilinear interaction and the data were generated from a quadratic trend or an exponential interaction, the parametric approaches generated biased estimates of the true surface. The SEMM approach approximated the true data generation surface with a similarly low level of bias for all the nonlinear surfaces. For example, Figure 1 shows the true surface for the bilinear interaction along with the SEMM estimated average surface. The results suggest that the SEMM approach can provide a relatively unbiased approximation to variety of nonlinear relationships among latent variables.     

Disentangling the Effects of Self Leader Perceptions and Ideal Leader Prototypes on Leader Judgments Using Loglinear Modeling With Latent Variables

This study clarifies the relationships among self leader perceptions, ideal leader prototypes, and leader judgments among college students using latent profile analysis (LPA) and log-linear modeling. LPA was used to identify subgroups of individuals with unique patterns of attributes for self and ideal leaders, providing a holistic view of leadership and how multiple attributes work together within individuals. LPA was also used to identify subgroups of individuals with unique patterns of judgments of leader effectiveness. After identification of subgroups (i.e., profiles), log-linear modeling was used to test 1 baseline model and 5 sets of hypothesized associations among self leader profiles, ideal leader profiles, and leader judgment profiles. Results suggest that self leader profiles are related to ideal leader profiles, which in turn are related to leader judgment profiles, but that there is no direct relation between self leader profiles and leader judgment profiles.     

Gender and Grade Differences in Latent Ability Variables

Scores in ability tests administered to students in grades 4–9 were simultaneously factor-analyzed within twelve gender by grade groups. Gender and grade differences in means and variances were studied for five latent ability factors according to a hierarchical model and compared with means and variances in the observed scores.
Girls had higher means than boys in a general ability factor (G), in a residual general speed factor (Gs') and in a residual factor of numerical facility (N'). Boys were higher in a residual vocabulary factor (V') and most of all in a residual spatial visualization factor (Vz'). Boys had larger variances than girls in N' and Gs'. In general the differences in means and variances were in the same direction for the closest corresponding observed scores, but some striking discrepancies between latent and observed scores were found. As a rule, the discrepancies were due to the complexity of the tests where one factor could compensate for another.
In the discussion it was pointed out that some of the differences found were likely to have changed between the testing in the late 1950s and the present. Nevertheless the demonstration of the divergence between analyses of latent vs. observed scores remains valid.     

潜变量交互效应建模: 告别均值结构

潜变量交互效应建模研究近年来有了长足的发展, 但模型中被认为不可缺少的均值结构往往让实际应用工作者却步。本文首先分析了潜变量交互效应模型中均值结构产生的根源; 然后讨论了指标变换与均值结构的关系; 接着提出了一个均值为零的潜变量交互结构, 所建立的模型不需要均值结构, 却不会改变主效应和交互效应等参数; 最后用模拟例子对无均值结构和有均值结构的两种模型的参数估计进行了比较, 结果符合理论预期, 困扰人们多年的均值结构问题从此可以终结。     

A Latent Growth Curve Modeling Approach to Pooled Interrupted Time Series Analyses

This paper presents a latent variable approach for the estimation of treatment effects within a pooled interrupted time series (ITS) design. Although considered quasi-experimental, the ITS design has been noted as representing one of the strongest alternatives to the randomized experiment, making it highly appropriate for use in documenting the presence of effects that might warrant further evaluation in a large-scale randomized study. Results suggest that the latent variable growth modeling (LGM) is capable of detecting simultaneous differences in both level and slope, and provides tests of significance for these two necessary indicators of an ITS intervention effect. As shown in the analyses, the LGM framework provides a comprehensive and flexible approach to research design and data analysis, making available to a wide audience of researchers an analytical framework for a variety of analyses of growth and developmental processes.     

Modeling Nonlinear Change via Latent Change and Latent Acceleration Frameworks: Examining Velocity and Acceleration of Growth Trajectories

A general equadion is presented, covering all arbitrary values for the true population splits, for obtaining the true population phi, given observed cell frequencies for a selected sample, and true population splits. A nongeneral solution is also offered, based on the use of the G Index. Demonstrations with hypothetical data are given.     

Four Research Designs and a Comprehensive Analysis Strategy for Investigating Common Method Variance with Self-Report Measures Using Latent Variables

Common method variance (CMV) is an ongoing topic of debate and concern in the organizational literature. We present four latent variable confirmatory factor analysis model designs for assessing and controlling for CMV—those for unmeasured latent method constructs, Marker Variables, Measured Cause Variables, as well as a new hybrid design wherein these three types of method latent variables are used concurrently. We then describe a comprehensive analysis strategy that can be used with these four designs and provide a demonstration using the new design, the Hybrid Method Variables Model. In our discussion, we comment on different issues related to implementing these designs and analyses, provide supporting practical guidance, and, finally, advocate for the use of the Hybrid Method Variables Model. Through these means, we hope to promote a more comprehensive and consistent approach to the assessment of CMV in the organizational literature and more extensive use of hybrid models that include multiple types of latent method variables to assess CMV.     

Bayesian Semiparametric Structural Equation Models with Latent Variables

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identifiability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and efficient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.     

The Latent Structure of Substance Use Among American Indian Adolescents: An Example Using Categorical Variables

Researchers frequently have only categorical data to analyze and cannot, for theoretical or methodological reasons, assume that the observed variables are discrete representations of an underlying continuous variable. We present latent class analysis as an alternative method of measuring latent variables in these circumstances. Latent class analysis does not require the assumptions of factor analyses about the nature of manifest and latent variables, but does allow the use of more precise model selection than techniques such as cluster analysis. We modeled the lifetime substance use of American Indian youth. The latent class model of American Indian teenagers' substance use had four classes: Abstaining, Predominantly Alcohol, Predominantly Alcohol and Marijuana, and Plural Substance. We then demonstrated the usefulness of this latent variable by using it to differentiate levels of several variables in a manner consistent with Social Cognitive Theory.     

初中留守儿童的学业自我效能与学校适应:潜变量增长模型分析

为考察初中留守儿童学校适应的发展趋势,以及学业自我效能的变化趋势对其的影响,对142名被试进行2年4次追踪测试。结果发现:(1)初中留守儿童学校适应在2年内未出现显著下降,但起始水平和发展速度均存在显著的个体差异;(2)控制性别、社会经济地位的效应后,学业自我效能的初始水平对学校适应的初始水平具有正向影响,但对其发展速度没有影响;(3)学业自我效能的发展速度可正向预测学校适应的发展速度。     

Assessing the reliability of Curriculum-Based Measurement: an application of Latent Growth Modeling

The purpose of this study was to demonstrate the use of Latent Growth Modeling (LGM) as a method for estimating reliability of Curriculum-Based Measurement (CBM) progress-monitoring data. The LGM approach permits the error associated with each measure to differ at each time point, thus providing an alternative method for examining of the reliability of CBM reading aloud data over repeated measurements. The analysis revealed that the reliability of CBM data was not a fixed property of the measure, but it changed with time. The study demonstrates the need to consider reliability in new ways with respect to the use of CBM data as repeated measures.     

儿童社交淡漠与学业成绩的发展轨迹：基于潜变量增长模型

采用同伴提名和教师评价对535名小学3~4年级儿童社交淡漠与学业成绩的发展进行了三次追踪研究,通过平行潜变量增长模型考察社交淡漠与学业成绩的发展轨迹及其相互作用模式。结果发现：（1）儿童社交淡漠和学业成绩在三年中较为稳定,三年中社交淡漠与学业成绩均呈负相关;（2）儿童学业成绩的初始水平可以负向预测社交淡漠的发展速度。该结果揭示学业成绩可能是儿童社交淡漠发展过程的重要保护因素,为儿童社会行为的健康发展提供了新的实证依据。     

Measuring Patterns of Change in Personality Assessments: An Annotated Application of Latent Growth Curve Modeling

Latent growth curve (LGC) modeling within the framework of structural equation modeling (SEM) is now highly regarded as one of the most powerful and informative approaches to the analysis of longitudinal data (see, e.g., Curran &; Hussong, 2003 Curran, P. J. and Hussong, A. M. 2003. The use of latent trajectory models in psychopathology research. Journal of Abnormal Psychology, 112: 526–544. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Whereas LGC modeling enables researchers to test for differences in developmental trajectories across time, conventional repeated measures analyses do not provide this opportunity. Nonetheless, a review of studies reported in most psychology journals reveals scant application of this methodological approach. One possible explanation for this limited use of LGC modeling is a lack of knowledge related to its application. The intent of this article, then, is to address this deficiency by presenting an annotated application of LGC modeling to health psychology data. Based on a sample of 405 Hong Kong Chinese women who recently underwent breast cancer surgery, we walk the readers through SEM modeling procedures that test for differences in both the initial status and rate of change in Psychological Morbidity and Social Adjustment at 1, 4, and 8 months postsurgery. We interpret findings from both a methodological and a substantive perspective.