Finite Mixtures of Hidden Markov Models for Longitudinal Responses Subject to Drop out

Abstract

Drop out is a typical issue in longitudinal studies. When the missingness is non-ignorable, inference based on the observed data only may be biased. This paper is motivated by the Leiden 85+ study, a longitudinal study conducted to analyze the dynamics of cognitive functioning in the elderly. We account for dependence between longitudinal responses from the same subject using time-varying random effects associated with a heterogeneous hidden Markov chain. As several participants in the study drop out prematurely, we introduce a further random effect model to describe the missing data mechanism. The potential dependence between the random effects in the two equations (and, therefore, between the two processes) is introduced through a joint distribution specified via a latent structure approach. The application of the proposal to data from the Leiden 85+ study shows its effectiveness in modeling heterogeneous longitudinal patterns, possibly influenced by the missing data process. Results from a sensitivity analysis show the robustness of the estimates with respect to misspecification of the missing data mechanism. A simulation study provides evidence for the reliability of the inferential conclusions drawn from the analysis of the Leiden 85+ data.     

密集追踪数据分析：模型及其应用

在心理学、教育学和临床医学等领域, 越来越多的研究者开始关注个体内部的行为、心理、临床效果等随时间而产生的动态变化, 重视针对个体的差异化建模。密集追踪是一种在短时间内对个体进行多个时间节点密集追踪测量的方法, 更适合用于研究个体内部心理过程等的动态变化及其作用机制。近年来, 密集追踪成为心理学研究的一大热点, 但许多密集追踪的研究分析仍停留在较为传统的方法。方法学领域已涌现出较多用于密集追踪数据分析的模型方法, 较为主流的模型包括以动态结构方程模型(Dynamic Structural Equation Model, DSEM)为代表的自上而下的建模方法, 以及以组迭代多模型估计(Group Iterative Multiple Model Estimation, GIMME)为代表的自下而上的建模方法。二者均可以方便地对密集追踪数据中的自回归及交叉滞后效应进行建模。     

Incorporating Mobility in Growth Modeling for Multilevel and Longitudinal Item Response Data

Multilevel data often cannot be represented by the strict form of hierarchy typically assumed in multilevel modeling. A common example is the case in which subjects change their group membership in longitudinal studies (e.g., students transfer schools; employees transition between different departments). In this study, cross-classified and multiple membership models for multilevel and longitudinal item response data (CCMM-MLIRD) are developed to incorporate such mobility, focusing on students' school change in large-scale longitudinal studies. Furthermore, we investigate the effect of incorrectly modeling school membership in the analysis of multilevel and longitudinal item response data. Two types of school mobility are described, and corresponding models are specified. Results of the simulation studies suggested that appropriate modeling of the two types of school mobility using the CCMM-MLIRD yielded good recovery of the parameters and improvement over models that did not incorporate mobility properly. In addition, the consequences of incorrectly modeling the school effects on the variance estimates of the random effects and the standard errors of the fixed effects depended upon mobility patterns and model specifications. Two sets of large-scale longitudinal data are analyzed to illustrate applications of the CCMM-MLIRD for each type of school mobility.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

Structural equation models of sexual harassment: longitudinal explorations and cross-sectional generalizations

Sexual harassment and its corresponding outcomes develop and change over time, yet research on this issue has been limited primarily to cross-sectional data. In this article, longitudinal models of harassment were proposed and empirically evaluated via structural equations modeling using data from 217 women who responded to a computerized questionnaire in 1994 and again in 1996. Results indicate that sexual harassment influences both proximal and distal work-related variables (e.g., job satisfaction, work withdrawal, job withdrawal) and psychological outcomes (e.g., life satisfaction, psychological well-being, distress). In addition, a replication of the L. F. Fitzgerald, F. Drasgow, C.L. Hulin, M.J. Gelfand, and V.J. Magley (1997) model of harassment was supported. This research was an initial attempt to develop integrated models of the dynamic effects of sexual harassment over time.     

At the Frontiers of Modeling Intensive Longitudinal Data: Dynamic Structural Equation Models for the Affective Measurements from the COGITO Study

With the growing popularity of intensive longitudinal research, the modeling techniques and software options for such data are also expanding rapidly. Here we use dynamic multilevel modeling, as it is incorporated in the new dynamic structural equation modeling (DSEM) toolbox in Mplus, to analyze the affective data from the COGITO study. These data consist of two samples of over 100 individuals each who were measured for about 100 days. We use composite scores of positive and negative affect and apply a multilevel vector autoregressive model to allow for individual differences in means, autoregressions, and cross-lagged effects. Then we extend the model to include random residual variances and covariance, and finally we investigate whether prior depression affects later depression scores through the random effects of the daily diary measures. We end with discussing several urgent—but mostly unresolved—issues in the area of dynamic multilevel modeling.     

Frequency of Interpersonal Trauma Types,Avoidant Attachment,Self-Compassion,and Interpersonal Competence: A Model of Persisting Posttraumatic Symptoms

Given limited knowledge about how psychosocial factors interact to modulate posttraumatic stress symptoms, this study evaluated an integrative model proposing that experiencing more interpersonal trauma types (e.g., abuse, assault, rape, etc.) leads to greater avoidant attachment and lower self-compassion, which limits the development and use of effective interpersonal skills. In turn, lower levels of self-compassion and interpersonal competence perpetuate posttraumatic symptoms. Anonymous trauma-experienced adults (n = 132) completed self-report measures in an online study hyperlinked on trauma support websites. Data were subjected to confirmatory factor analysis and structural equation modeling, which provided support for the hypothesized model. Specifically, higher frequency of interpersonal trauma types experienced was linked to higher avoidant attachment and lower self-compassion, which in turn were associated with lower interpersonal competence, which correlated with greater posttraumatic stress symptoms. Although cross-sectional data cannot address directionality of associations, this study’s findings emphasize the potential utility of future longitudinal research designed to examine possible causal relationships among these specific psychosocial factors. For example, study findings suggest that those who experience more types of interpersonal trauma and who are characterized by avoidant attachment and lower self-compassion and interpersonal competence may be the most susceptible to experiencing severe posttraumatic symptoms. However, findings also suggest that efforts to increase self-compassion and interpersonal skills may help reduce symptoms.     

The Relation of Social Capital to Child Psychosocial Adjustment Difficulties: The Role of Positive Parenting and Neighborhood Dangerousness

Substantial research attention has focused on the psychosocial adjustment problems of children and adolescents residing in disadvantaged neighborhoods. However, less attention has been directed to neighborhood factors within disadvantaged neighborhoods that may facilitate child psychosocial adjustment. An expanded model, assessing how social capital, neighborhood dangerousness, and positive parenting relate to child psychosocial adjustment difficulties, was estimated using structural equation modeling (Lisrel 8.3). Participants included 130 African American mothers and their children (mean age = 12.9 years) residing in inner city New Orleans, LA. The model examined 3 avenues through which social capital (e.g., support, neighborhood cohesion) may relate to fewer child psychosocial adjustment difficulties: a direct relation; through its relation to positive parenting; and through its relation to neighborhood dangerousness. Results indicate that social capital related to child psychosocial adjustment difficulties through positive parenting and neighborhood dangerousness, but not directly. Overall, the proposed model fit the observed data reasonably well. The results suggest that social capital in disadvantaged neighborhoods is important in indirectly facilitating child psychosocial adjustment and should be incorporated into assessment and intervention practices.     

The Multigroup Multilevel Categorical Latent Growth Curve Models

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup multilevel framework and allowed for autoregressive residuals. The parameter in the new model can be estimated using the computer program WinBUGS, which adopts Markov Chain Monte Carlo algorithms. Two simulation studies were conducted. An empirical example was raised and established based on models generated by the results of empirical data, which have been fitted and compared.     

A Psychosocial Resource Impairment Model Explaining Partner Violence and Distress: Moderating Role of Income

This study examines the role of income in a psychosocial resource impairment model that explains partner violence and distress. Using data from a nationally representative sample, we test whether psychosocial resources of social support and self-esteem operate differently in four income groups (poor, “working”-poor, middle and upper-income). Structural equation modeling shows that among women considered working-poor, low self-esteem is relevant for the process through which violence becomes linked to distress. Women of upper-income appear distinct with negative interactions serving as sole mediator of violence and distress. Other findings indicate impaired support may mediate the violence and distress relation for women, regardless of income. Overall, income partially moderates the impact of partner violence on distress, suggesting social contexts should be considered when examining the effects of violence.     

Selecting a linear mixed model for longitudinal data: repeated measures analysis of variance, covariance pattern model, and growth curve approaches

With increasing popularity, growth curve modeling is more and more often considered as the 1st choice for analyzing longitudinal data. Although the growth curve approach is often a good choice, other modeling strategies may more directly answer questions of interest. It is common to see researchers fit growth curve models without considering alterative modeling strategies. In this article we compare 3 approaches for analyzing longitudinal data: repeated measures analysis of variance, covariance pattern models, and growth curve models. As all are members of the general linear mixed model family, they represent somewhat different assumptions about the way individuals change. These assumptions result in different patterns of covariation among the residuals around the fixed effects. In this article, we first indicate the kinds of data that are appropriately modeled by each and use real data examples to demonstrate possible problems associated with the blanket selection of the growth curve model. We then present a simulation that indicates the utility of Akaike information criterion and Bayesian information criterion in the selection of a proper residual covariance structure. The results cast doubt on the popular practice of automatically using growth curve modeling for longitudinal data without comparing the fit of different models. Finally, we provide some practical advice for assessing mean changes in the presence of correlated data.     

Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling

R. M. Baron and D. A. Kenny (1986; see record 1987-13085-001) provided clarion conceptual and methodological guidelines for testing mediational models with cross-sectional data. Graduating from cross-sectional to longitudinal designs enables researchers to make more rigorous inferences about the causal relations implied by such models. In this transition, misconceptions and erroneous assumptions are the norm. First, we describe some of the questions that arise (and misconceptions that sometimes emerge) in longitudinal tests of mediational models. We also provide a collection of tips for structural equation modeling (SEM) of mediational processes. Finally, we suggest a series of 5 steps when using SEM to test mediational processes in longitudinal designs: testing the measurement model, testing for added components, testing for omitted paths, testing the stationarity assumption, and estimating the mediational effects.     

Determining career orientations in women from different social-class backgrounds

This study examines career orientations in women from high- and low-socioeconomic status backgrounds, using a longitudinal data set collected over a period of 10 years, from 1973 to 1982. When first contacted, respondents were 18 years of age. The final data collection in 1982 resulted in a sample of some 1300 women. The longitudinal data were analyzed using LISREL structural equation modeling and were guided by a theoretical framework developed by Krumboltz (1981) which focuses on the process of decision-making. Results from the study indicated that there were effects of social-class background in the development of women's career orientations, over the secondary school-early career development stage. Group differences in determinants of orientation were found for political attitudes, occupational interests, senior school achievement, and professional attainment. Differences were also found in the influence of motivational tendencies and work satisfaction on model variables for the two groups of women. The benefit of the decision-making theoretical framework and its further development for use in studies of career development generally are discussed.     

Concurrent and longitudinal effects of ethnic identity and experiences of discrimination on psychosocial adjustment of Navajo adolescents

In this study, we examined concurrent and longitudinal relations among Navajo adolescents' ethnic identity, experiences of discrimination, and psychosocial outcomes (i.e., self-esteem, substance use, and social functioning). At Time 1, 137 Navajo adolescents (67 male, 70 female), primarily in Grades 9 and 10, completed a written survey assessing ethnic identity, discrimination experiences, and a range of internalizing and externalizing behaviors. Two years later, 92 participants completed the same survey again. Ethnic and cultural identification was assessed via the Multiethnic Ethnic Identity Measure (MEIM; Phinney, 1992) and the Orthogonal Cultural Identification Scale (OCIS; Oetting & Beauvais, 1990). At Time 1, MEIM Affirmation and Belonging, MEIM Exploration, and OCIS White American identification all demonstrated strong, positive associations with adaptive functioning for male and female adolescents, whereas discrimination experiences were linked to lower self-esteem and social functioning for male adolescents. By Time 2, fewer significant concurrent associations between ethnic identity and psychosocial functioning scores remained, and discrimination experiences emerged as the most consistent correlate of poorer psychosocial functioning for male adolescents. Controlling for Time 1 psychosocial functioning, relatively few direct effects of ethnic and cultural identification variables predicted psychosocial functioning longitudinally, but discrimination experiences demonstrated strong and consistent longitudinal links with boys' substance use. Finally, interaction effects assessing the moderating influence of ethnic and cultural identification on negative links between discrimination and psychosocial functioning suggested that embeddedness in and connection to Navajo culture and, in some cases, connection to White American culture, served as a buffer to the negative effects of discrimination experiences.     

Cross-Sectional Analysis of Longitudinal Mediation Processes

Statistical mediation analysis can help to identify and explain the mechanisms behind psychological processes. Examining a set of variables for mediation effects is a ubiquitous process in the social sciences literature; however, despite evidence suggesting that cross-sectional data can misrepresent the mediation of longitudinal processes, cross-sectional analyses continue to be used in this manner. Alternative longitudinal mediation models, including those rooted in a structural equation modeling framework (cross-lagged panel, latent growth curve, and latent difference score models) are currently available and may provide a better representation of mediation processes for longitudinal data. The purpose of this paper is twofold: first, we provide a comparison of cross-sectional and longitudinal mediation models; second, we advocate using models to evaluate mediation effects that capture the temporal sequence of the process under study. Two separate empirical examples are presented to illustrate differences in the conclusions drawn from cross-sectional and longitudinal mediation analyses. Findings from these examples yielded substantial differences in interpretations between the cross-sectional and longitudinal mediation models considered here. Based on these observations, researchers should use caution when attempting to use cross-sectional data in place of longitudinal data for mediation analyses.     

Development of conscientiousness in childhood and adolescence: Typical trajectories and associations with academic,health, and relationship changes

Conscientiousness is related to a range of important life outcomes, so it is important to understand its development early in life. We examined how conscientiousness changes from late childhood through middle adolescence and what other psychosocial changes it co-occurs with. We developed and validated a conscientiousness scale for use in existing data. Then in a longitudinal study of participants at ages 10, 13, and 16 (N = 90 at Time 1) we used growth curve modeling to examine how conscientiousness co-develops with academic, health, and relationship functioning. Mean levels of conscientiousness decreased from 10 to 13 and then increased to age 16. The later increase was stronger among females. Changes in conscientiousness were associated with adaptive changes in other variables.     

大学新生主观社会地位与抑郁的变化轨迹:一项多元潜变量增长模型分析

采用整群取样的方法在全国按东部、中部和西部共抽取了7所高校的1983名新生,进行了历时四个月的四次追踪测试。使用潜变量增长模型建模,分别考察了新生主观社会地位和抑郁的变化轨迹,并就两者间的变化关系进行了分析。结果发现新生入学后四个月内：（1）主观社会地位呈阶段化线性增长,其起始水平和第一阶段的增长速度存在显著个体间差异;（2）抑郁呈二次方增长,其起始水平和增长速度存在显著个体间差异;（3）入学后主观社会地位的下滑速度能有效预测新生抑郁水平的上升速度。研究基于情绪压制理论,对主观社会地位与抑郁间的变化关系进行了分析。     

MEDIATING ROLE OF MATERNAL SENSITIVITY: ENHANCING LANGUAGE DEVELOPMENT IN AT‐RISK FAMILIES

Home‐visiting programs have gained increasing importance in family‐centered prevention and intervention. However, few studies have examined the mechanisms underlying early intervention treatment effects. The goal of this study is to analyze the mediating role of maternal sensitivity in enhancing language development with the home‐visiting program Parents as Teachers (PAT). Data were collected and analyzed within the ongoing, long‐term ZEPPELIN study, a randomized controlled trial with 251 participating at‐risk families. Via longitudinal mediation analysis, we examined whether effects of the PAT on receptive and expressive language outcomes at 24 and 36 months were mediated by maternal sensitivity at 12 months. Within a moderated mediation framework, we investigated whether the level of family psychosocial stress affects this mediation. Results showed that intervention effects on language outcomes are mediated by maternal sensitivity—weakly and through specific pathways. Moderation and moderated mediation analyses indicated that effects of the PAT and also specific mediation effects increase with the level of psychosocial stress. Implications of the results for practice are discussed.     

Social support, sense of community in school, and self-efficacy as resources during early adolescence: an integrative model

Influences of different sources of social support (from parents and friends), school sense of community, and self-efficacy on psychosocial well being (as measured by self-reported life satisfaction and psychological symptoms) in early adolescence were investigated in an integrative model. The model was tested using structural equation modeling. Multi-group comparisons were used to estimate differences between sex and age groups. The survey sample was composed of 7,097 students in Northern Italy (51.4% male) divided into three age cohorts (equivalent to 6th, 8th, and 10th grades with median ages of 11, 13, and 15). Findings obtained using SEM were consistent with self-efficacy and school sense of community mediating effects of social support on psychosocial adjustment. The multi-group comparison indicates a need for more complex developmental models and more research on how changing forms of support interact with each other as their effects also change during this important stage of the life. Implications for primary prevention and cross-cultural comparisons are discussed.