Latent curve analysis

As a method for representing development, latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth. Maximum likelihood parameter estimates and associated asymptotic tests follow directly. These procedures may be viewed as an alternative to standard repeated measures ANOVA and to first-order auto-regressive methods. As formulated, the model encompasses cohort sequential designs and allow for period or practice effects. A numerical illustration using data initially collected by Nesselroade and Baltes is presented.The authors wish to thank John Nesselroade for providing us the data for our illustration and Karen Paul and Connie Tilse for assisting in the data analysis. This research was supported by a grant (No. AG03164) from the National Institute on Aging to the senior author.     

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。     

On growth curves and mixture models

The multilevel model of change and the latent growth model are flexible means to describe all sorts of population heterogeneity with respect to growth and development, including the presence of sub‐populations. The growth mixture model is a natural extension of these models. It comes at hand when information about sub‐populations is missing and researchers nevertheless want to retrieve developmental trajectories from sub‐populations. We argue that researchers have to make rather strong assumptions about the sub‐populations or latent trajectory classes in order to retrieve existing population differences. A simulated example is discussed, showing that a sample of repeated measures drawn from two sub‐populations easily leads to the mistaken inference of three sub‐populations, when assumptions are not met. The merits of methodological advises on this issue are discussed. It is concluded that growth mixture models should be used with understanding, and offer no free way to growth patterns in unknown sub‐populations. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Stability of aggression among adolescents over time: A south African study

In a study spanning 5 years, data were collected on the aggressiveness of over 1,700 male and female subjects. Subjects who were the more aggressive grade 8 (standard 6) pupils at the beginning of the study were discovered to be the more aggressive grade 12 (standard 10) pupils. It is concluded that, whatever its causes, aggression can be viewed as a persistent trait that may be influenced by situational variables but reveals substantial consistency over time. The findings of studies by Huesmann and Eron in the United States as well as Olweus in Scandinavia were thus supported in this South African investigation.     

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.     

Variations in Expected Affect in Young and Middle-Aged Adults

Expected positive and negative affects were measured in three samples of college students and in three samples of middle-aged adults. For each of the samples, negative affect decreased with age. The pattern of the effect was the same for the three samples and for the Expected Balance Scale (Staats, 1987, 1989) and the PANAS (Watson, Clark, & Tellegen, 1988). The higher negative affect in college students, in comparison to that in their middle-aged friends or parents, is contrary to popular stereotypes. This specific and differential decrease in negative affect is not consistent with theories proposing only a general decrement in emotionality with increasing age. An explanation in terms of stress appraisal, coping, and management is suggested.     

On structural models for analyzing change

The recommendation to base the analysis of multi-wave data upon explicit models for change is advocated. Several univariate and multivariate models are described, which emerge from an interaction between the classical test theory and the structural equation modeling approach. The resulting structural models for analyzing change reflect in some of their parameters substantively interesting aspects of intra- and interindividual change in follow-up studies. The models are viewed as an alternative to an ANOVA-based analysis of longitudinal data, and are illustrated on data from a cognitive intervention study of old adults (Bakes et al , 1986). The approach presents a useful means of analyzing change over time, and is applicable for purposes of (latent) growth curve analysis when analysis of variance assumptions are violated (e.g., Schaie & Hertzog, 1982; Morrison, 1976).