Regularized Finite Mixture Models for Probability Trajectories

Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse. This work was supported in part by NIAAA grants R37 AA07065 and R01 AA12217 to RAZ.     

随机截距潜在转变分析(RI-LTA)——个案自我转变与个案间差异的分离

传统的潜在转变分析属于单水平分析, 但其同样也可以看作二水平分析。Muthén和Asparouhov就以二水平分析的视角在单水平分析框架内提出了随机截距潜在转变分析(RI-LTA), 其中跨时间点产生的自我转变可以看作在水平1进行分析, 跨时间点不变的个案间差异可以看作在水平2进行分析, 使个案的自我转变和个案间的初始差异分离, 避免了高估保留在初始类别的概率。某研究型大学2016级本科生的追踪调查数据被用于演示使用随机截距潜在转变分析的过程。该方法的最大优势是通过引入随机截距避免了高估保留在本类别的转变概率。未来研究可以运用蒙特卡洛模拟研究探究随机截距潜在转变分析模型的适用性, 也可以用多水平分析的思路为灵感, 探究多水平随机截距潜在转变分析在统计软件中的实现。     

Examining Spirituality Over Time: Latent Growth Curve and Individual Growth Curve Analyses

SUMMARY

Research on spirituality and religiousness has gained growing attention in recent years; however, most studies have used cross-sectional designs. As research on this topic evolves, there has been increasing recognition of the need to examine these constructs and their effects through the use of longitudinal designs. Beyond repeated-measures ANOVA and OLS regression models, what tools are available to examine these constructs over time? The purpose of this paper is to provide an overview of two cutting-edge statistical techniques that will facilitate longitudinal investigations of spirituality and religiousness: latent growth curve analysis using structural equation modeling (SEM) and individual growth curve models. The SEM growth curve approach examines change at the group level, with change over time expressed as a single latent growth factor. In contrast, individual growth curve models consider longitudinal change at the level of the person. While similar results may be obtained using either method, researchers may opt for one over the other due to the strengths and weaknesses associated with these methods. Examples of applications of both approaches to longitudinal studies of spirituality and religiousness are presented and discussed, along with design and data considerations when employing these modeling techniques.     

多阶段混合增长模型的方法及研究现状

多阶段混合增长模型(PGMM)可对发展过程中的阶段性及群体异质性特征进行分析,在能力发展、行为发展及干预、临床心理等研究领域应用广泛。PGMM可在结构方程模型和随机系数模型框架下定义,通常使用基于EM算法的极大似然估计和基于马尔科夫链蒙特卡洛模拟的贝叶斯推断两种方法进行参数估计。样本量、测量时间点数、潜在类别距离等因素对模型及参数估计有显著影响。未来应加强PGMM与其它增长模型的比较研究;在相同或不同的模型框架下研究数据特征、类别属性等对参数估计方法的影响。     

A multivariate reduced-rank growth curve model with unbalanced data

A multivariate reduced-rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model. In addition, the method is more flexible than the traditional growth curve model. For example, response variables do not have to be measured at the same time points, nor the same number of time points. It is also possible to apply various kinds of basis function matrices with different ranks across response variables. It is not necessary to specify an entire set of basis functions in advance. Examples are given for illustration.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We thank Jennifer Stephan for her helpful comments on an earlier version of this paper. We also thank Patrick Curran and Terry Duncan for kindly letting us use the NLSY and substance use data, respectively. The substance use data were provided by Grant DA09548 from the National Institute on Drug Abuse.     

分类精确性指数Entropy在潜剖面分析中的表现:一项蒙特卡罗模拟研究

本研究通过蒙特卡洛模拟考查了分类精确性指数Entropy及其变式受样本量、潜类别数目、类别距离和指标个数及其组合的影响情况。研究结果表明:(1)尽管Entropy值与分类精确性高相关,但其值随类别数、样本量和指标数的变化而变化,很难确定唯一的临界值;(2)其他条件不变的情况下,样本量越大,Entropy的值越小,分类精确性越差;(3)类别距离对分类精确性的影响具有跨样本量和跨类别数的一致性;(4)小样本(N=50~100)的情况下,指标数越多,Entropy的结果越好;(5)在各种条件下Entropy对分类错误率比其它变式更灵敏。     

Multilevel models in developmental psychological research: Rationales and applications

The armoury of statistical techniques has recently been enhanced with the multilevel model for longitudinal data. The present article explains the multilevel model for longitudinal data to the statistically non-sophisticated reader. It shows how the model relates to the five rationales of longitudinal research, as they were put forward by Baltes and Nesselroade (1979). In addition, it shows how the model matches Wohlwill's methodology of developmental functions. To elucidate the model further, three applications are given. The applications pertain to the development of children's sleeping duration during the first 18 months of life, the effects of early hospitalization on the daily frequency of crying, and the developmental relationship between social and solitary play.