A Comparison of Methods for Uncovering Sample Heterogeneity: Structural Equation Model Trees and Finite Mixture Models.

Although finite mixture models have received considerable attention, particularly in the social and behavioral sciences, an alternative method for creating homogeneous groups, structural equation model trees (Brandmaier, von Oertzen, McArdle, & Lindenberger, 2013), is a recent development that has received much less application and consideration. It is our aim to compare and contrast these methods for uncovering sample heterogeneity. We illustrate the use of these methods with longitudinal reading achievement data collected as part of the Early Childhood Longitudinal Study-Kindergarten Cohort. We present the use of structural equation model trees as an alternative framework that does not assume the classes are latent and uses observed covariates to derive their structure. We consider these methods as complementary and discuss their respective strengths and limitations for creating homogeneous groups.

Genetic variants specific to aging-related verbal memory: Insights from GWASs in a population-based cohort.

Verbal memory is typically studied using immediate recall (IR) and delayed recall (DR) scores, although DR is dependent on IR capability. Separating these components may be useful for deciphering the genetic variation in age-related memory abilities. This study was conducted to (a) construct individual trajectories in IR and independent aspects of delayed recall, or residualized-DR (rDR), across older adulthood; and (b) identify genetic markers that contribute to four estimated phenotypes: IR and rDR levels and changes after age 60. A cognitively intact sample (N = 20,650 with 125,164 observations) was drawn from the U.S. Health and Retirement Study, a nationally representative study of adults aged 50 and older. Mixed effects regression models were constructed using repeated measures from data collected every two years (1996-2012) to estimate level at age 60 and change in memory post-60 in IR and rDR. Genome-wide association scans (GWAS) were conducted in the genotypic subsample (N = 7,486) using ~1.2 million single nucleotide polymorphisms (SNPs). One SNP (rs2075650) in TOMM40 associated with rDR level at the genome-wide level (p = 5.0x10-08), an effect that replicated in an independent sample from the English Longitudinal Study on Ageing (N = 6,898 with 41,328 observations). Meta-analysis of rDR level confirmed the association (p = 5.0x10-11) and identified two others in TOMM40 (rs71352238 p = 1.0x10-10; rs157582 p = 7.0x10-09), and one in APOE (rs769449 p = 3.1 x10-12). Meta-analysis of IR change identified associations with three of the same SNPs in TOMM40 (rs157582 p = 8.3x10-10; rs71352238 p = 1.9x10-09) and APOE (rs769449 p = 2.2x10-08). Conditional analyses indicate GWAS signals on rDR level were driven by APOE, whereas signals on IR change were driven by TOMM40. Additionally, we found that TOMM40 had effects independent of APOE e4 on both phenotypes. Findings from this first U.S. population-based GWAS study conducted on both age-related immediate and delayed verbal memory merit continued examination in other samples and additional measures of verbal memory.

Theory-guided exploration with structural equation model forests.

Structural equation model (SEM) trees, a combination of SEMs and decision trees, have been proposed as a data-analytic tool for theory-guided exploration of empirical data. With respect to a hypothesized model of multivariate outcomes, such trees recursively find subgroups with similar patterns of observed data. SEM trees allow for the automatic selection of variables that predict differences across individuals in specific theoretical models, for instance, differences in latent factor profiles or developmental trajectories. However, SEM trees are unstable when small variations in the data can result in different trees. As a remedy, SEM forests, which are ensembles of SEM trees based on resamplings of the original dataset, provide increased stability. Because large forests are less suitable for visual inspection and interpretation, aggregate measures provide researchers with hints on how to improve their models: (a) variable importance is based on random permutations of the out-of-bag (OOB) samples of the individual trees and quantifies, for each variable, the average reduction of uncertainty about the model-predicted distribution; and (b) case proximity enables researchers to perform clustering and outlier detection. We provide an overview of SEM forests and illustrate their utility in the context of cross-sectional factor models of intelligence and episodic memory. We discuss benefits and limitations, and provide advice on how and when to use SEM trees and forests in future research. (PsycINFO Database Record

Regularized Structural Equation Modeling.

A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.

On the Mathematical Relationship Between Latent Change Score and Autoregressive Cross-Lagged Factor Approaches: Cautions for Inferring Causal Relationship Between Variables.

The present paper focuses on the relationship between latent change score (LCS) and autoregressive cross-lagged (ARCL) factor models in longitudinal designs. These models originated from different theoretical traditions for different analytic purposes, yet they share similar mathematical forms. In this paper, we elucidate the mathematical relationship between these models and show that the LCS model is reduced to the ARCL model when fixed effects are assumed in the slope factor scores. Additionally, we provide an applied example using height and weight data from a gerontological study. Throughout the example, we emphasize caution in choosing which model (ARCL or LCS) to apply due to the risk of obtaining misleading results concerning the presence and direction of causal precedence between two variables. We suggest approaching model specification not only by comparing estimates and fit indices between the LCS and ARCL models (as well as other models) but also by giving appropriate weight to substantive and theoretical considerations, such as assessing the justifiability of the assumption of random effects in the slope factor scores.

Using Classification and Regression Trees (CART) and random forests to analyze attrition: Results from two simulations.

In this article, we describe a recent development in the analysis of attrition: using classification and regression trees (CART) and random forest methods to generate inverse sampling weights. These flexible machine learning techniques have the potential to capture complex nonlinear, interactive selection models, yet to our knowledge, their performance in the missing data analysis context has never been evaluated. To assess the potential benefits of these methods, we compare their performance with commonly employed multiple imputation and complete case techniques in 2 simulations. These initial results suggest that weights computed from pruned CART analyses performed well in terms of both bias and efficiency when compared with other methods. We discuss the implications of these findings for applied researchers.

Ambient air pollution and neurotoxicity on brain structure: Evidence from women's health initiative memory study.

OBJECTIVE: The aim of this study was to examine the putative adverse effects of ambient fine particulate matter (PM2.5 : PM with aerodynamic diameters <2.5µm) on brain volumes in older women. METHODS: We conducted a prospective study of 1,403 community-dwelling older women without dementia enrolled in the Women's Health Initiative Memory Study, 1996-1998. Structural brain magnetic resonance imaging scans were performed at the age of 71-89 years in 2005-2006 to obtain volumetric measures of gray matter (GM) and normal-appearing white matter (WM). Given residential histories and air monitoring data, we used a spatiotemporal model to estimate cumulative PM2.5 exposure in 1999-2006. Multiple linear regression was employed to evaluate the associations between PM2.5 and brain volumes, adjusting for intracranial volumes and potential confounders. RESULTS: Older women with greater PM2.5 exposures had significantly smaller WM, but not GM, volumes, independent of geographical region, demographics, socioeconomic status, lifestyles, and clinical characteristics, including cardiovascular risk factors. For each interquartile increment (3.49µg/m(3) ) of cumulative PM2.5 exposure, the average WM volume (WMV; 95% confidence interval) was 6.23cm(3) (3.72-8.74) smaller in the total brain and 4.47cm(3) (2.27-6.67) lower in the association areas, equivalent to 1 to 2 years of brain aging. The adverse PM2.5 effects on smaller WMVs were present in frontal and temporal lobes and corpus callosum (all p values <0.01). Hippocampal volumes did not differ by PM2.5 exposure. INTERPRETATION: PM2.5 exposure may contribute to WM loss in older women. Future studies are needed to determine whether exposures result in myelination disturbance, disruption of axonal integrity, damages to oligodendrocytes, or other WM neuropathologies.

Four Dietary Items of the School Physical Activity and Nutrition (SPAN) Questionnaire Form a Robust Latent Variable Measuring Healthy Eating Patterns.

OBJECTIVE: Evaluate the factor structure and stability of 4 dietary items (fruit, fruit juice, vegetables, and milk) from the School Physical Activity and Nutrition questionnaire-elementary school version. METHODS: Secondary analysis of intervention data from third graders measured at pre-intervention, post-intervention (10 weeks), and 3-month follow-up. The researchers conducted structural equation modeling invariance analysis to test the stability of the factor structure of the 4 items. RESULTS: Data from 1,147 students. Fit indices revealed good fit for a single factor remaining stable across time (χ(2)/degrees of freedom [DF] = 59.75/59, P = .45), gender (χ(2)/DF = 149.72/128, P = .09), and study groups (χ(2)/DF = 143.04/128, P = .17). CONCLUSIONS AND IMPLICATIONS: A healthy food factor consisting of the 4 items can be used in future data analysis. This offers several advantages in analysis, including the use of latent change scores that are more powerful, more informative, and more easily interpreted than traditional approaches.

Heritability of Health and Aging Limitations on Personally Desired Activities.

The aim of this study is to estimate heritability of incident limitations on personally desired activities within the eighth decade of life. We measured self-rated ability to perform ten personally desired activities in 1606 male veteran twin pairs at baseline and four years later. At follow-up, 33% of the cohort reported more limitations in desired activities. Among twins who completed both assessments, there were no statistically significant differences in incidence rates of limitations as a function of zygosity. Sensitivity tests showed the same for change scores; and that, if cognitive impairment or death are deemed to belong among limitations of desired activities, zygosity contributed 10% to new limitations at follow-up. Maintaining personally desired activities over four years in the eighth decade is not subject to substantial genetic influence. However, if death and cognitive impairment are added to incident limitations, then genetics plays a modest role. In all cases, unique environment is the predominant influence.

Rationale and Applications of Survival Tree and Survival Ensemble Methods.

Classification and Regression Trees (CART), and their successors-bagging and random forests, are statistical learning tools that are receiving increasing attention. However, due to characteristics of censored data collection, standard CART algorithms are not immediately transferable to the context of survival analysis. Questions about the occurrence and timing of events arise throughout psychological and behavioral sciences, especially in longitudinal studies. The prediction power and other key features of tree-based methods are promising in studies where an event occurrence is the outcome of interest. This article reviews existing tree algorithms designed specifically for censored responses as well as recently developed survival ensemble methods, and introduces available computer software. Through simulations and a practical example, merits and limitations of these methods are discussed. Suggestions are provided for practical use.

Nutrition self-efficacy is unidirectionally related to outcome expectations in children.

OBJECTIVE: To clarify the underlying relationship between nutrition self-efficacy and outcome expectations because the direction of the relationship (unidirectional vs bidirectional) is debated in the literature. METHODS: Secondary data analysis of a 10-week, 10-lesson school-based nutrition education intervention among 3rd grade students (N = 952). Nutrition self-efficacy (7 items) and nutrition outcome expectations (9 items) were measured through student self-report at intervention pre- (time 1) and post- (time 2) assessments. A series of two time point, multi-group cross-lagged bivariate change score models were used to determine the direction of the relationship. RESULTS: A cross lag from nutrition self-efficacy at time 1 predicting changes in nutrition outcome expectations at time 2 significantly improved the fit of the model (Model 3), whereas a cross lag from nutrition outcome expectations at time 1 to changes in nutrition self-efficacy at time 2 only slightly improved the fit of the model (Model 2). Furthermore, adding both cross lags (Model 4) did not improve model fit compared to the model with only the self-efficacy cross lag (Model 3). Lastly, the nutrition outcome expectations cross lag did not significantly predict changes in nutrition self-efficacy in any of the models. CONCLUSIONS: Data suggest that there is a unidirectional relationship between nutrition self-efficacy and outcome expectations, in which self-efficacy predicts outcome expectations. Therefore, theory-based nutrition interventions may consider focusing more resources on changing self-efficacy because it may also lead to changes in outcome expectations as well.

Measurement Invariance of Cognitive Abilities Across Ethnicity, Gender, and Time Among Older Americans.

OBJECTIVES: The aim of this research was to test the invariance of the cognitive variables in the Health and Retirement Study/Asset Health Dynamics Among the Oldest Old studies (HRS/AHEAD) across ethnicity, gender, and time. METHOD: Analyses were conducted using a selected subsample of the HRS/AHEAD data set. The cognitive performance tests measuring episodic memory and mental status were used, and invariance of a two-factor structure was tested using confirmatory factor analyses and multilevel modeling for longitudinal data. RESULTS: Results provided some support for "strict" factorial invariance of the episodic memory and mental status measures across ethnicity and gender. Further support of weak ("metric") measurement invariance was found across time. DISCUSSION: Results of the research further our understanding of invariance of the HRS/AHEAD cognitive ability measures. Further implications are discussed.

Loehlin's original models and model contributions.

This is a short story about John C. Loehlin who is now at the University of Texas at Austin, dealing with his original simulation models and developments, which led to his current latent variable models. This talk was initially presented at a special meeting for John before the BGA in Rhode Island, and I was very pleased to contribute. It probably goes without saying, but John helped create this important society, has been a key contributor to this journal for several decades, and he deserves a lot for this leadership.

A Brief Report on the Factor Structure of the Cognitive Measures in the HRS/AHEAD Studies.

Using cognitive data from the Health and Retirement Study and Asset Health Dynamics Among the Oldest Old studies that were collected between 1992 and 2004, McArdle and colleagues (2007) found that a two-factor model (episodic memory and mental status) fit better than a one-factor model. The question that was addressed in the present study was whether these results would replicate in newer cohorts of data, collected between 2006 and 2010. We also tested age, education, and gender as predictors of the identified factors. Results confirm that a two-factor structure fits better than the single-factor model in the newer cohorts. Differential predictors were also observed.

Cohort profile: the Hawai'i Family Study of Cognition.

Intergenerational longitudinal studies over the lifespan provide valuable information for understanding the contexts and dynamic relations among cognition, family and health in adults and the elderly. The Hawai'i Family Study of Cognition (HFSC), initiated in the early 1970s, included a cohort of over 6500 individuals representing over 1800 families of parents and their offspring. The HFSC gathered data on cognitive, personality, biological and other psychosocial variables, and provided novel information on the nature of cognitive abilities, especially on family issues. Some families were reassessed with short-term retesting in the 1970s. A select sample of offspring and their siblings and spouses were re-measured in the 1980s. Decades later, a 40-year follow-up of the original HFSC cohort was facilitated by the availability of contemporary tracking and tracing methods and internet-based testing. A subgroup of the original HFSC participants was re-contacted and retested on contemporary cognitive as well as socio-demographic and health measures. In this paper, we describe the original HFSC cohort and the design and methodology of the re-contact and retest studies of the HFSC, plans for expanding the re-contact and retesting, as well as directions for future research and collaborations. The Principal Investigator may be contacted for more information regarding the application, review and approval process for data access requests from qualified individuals outside the project.

Successful emotion regulation skills application predicts subsequent reduction of symptom severity during treatment of major depressive disorder.

OBJECTIVE: Deficits in emotion regulation (ER) skills are considered a putative maintaining factor for major depressive disorder (MDD) and hence a promising target in the treatment of MDD. However, to date, the association between the successful application of arguably adaptive ER skills and changes in depressive symptom severity (DSS) has yet to be investigated over the course of treatment. Thus, the primary aim of this study was to clarify reciprocal prospective associations between successful ER skills application and DSS over the course of inpatient cognitive behavioral therapy for MDD. Additionally, we explored whether such associations would differ across specific ER skills. METHOD: We assessed successful ER skills application and DSS 4 times during the first 3 weeks of treatment in 152 inpatients (62.5% women, average age 45.6 years) meeting criteria for MDD. We first tested whether successful skills application and depression were cross-sectionally associated by computing Pearson's correlations. Then, we utilized latent curve modeling to test whether changes in successful skills application were negatively associated with changes in DSS during treatment. Finally, we used latent change score models to clarify whether successful skills application would predict subsequent reduction of DSS. RESULTS: Cross-sectionally, successful ER skills application was associated with lower levels of DSS at all assessment times, and an increase of successful skills application during treatment was associated with a decrease of DSS. Moreover, successful overall ER skills application predicted subsequent changes in DSS (but not vice versa). Finally, strength of associations between successful application and DSS differed across specific ER skills. Among a broad range of potentially adaptive skills, only the abilities to tolerate negative emotions and to actively modify undesired emotions were significantly associated with subsequent improvement in DSS. CONCLUSIONS: Systematically enhancing health-relevant ER skills with specific interventions may help reduce DSS in patients suffering from MDD.

Fighting for Intelligence: A Brief Overview of the Academic Work of John L. Horn.

John L. Horn (1928-2006) was a pioneer in multivariate thinking and the application of multivariate methods to research on intelligence and personality. His key works on individual differences in the methodological areas of factor analysis and the substantive areas of cognition are reviewed here. John was also our mentor, teacher, colleague, and friend. We overview John Horn's main contributions to the field of intelligence by highlighting 3 issues about his methods of factor analysis and 3 of his substantive debates about intelligence. We first focus on Horn's methodological demonstrations describing (a) the many uses of simulated random variables in exploratory factor analysis; (b) the exploratory uses of confirmatory factor analysis; and (c) the key differences between states, traits, and trait-changes. On a substantive basis, John believed that there were important individual differences among people in terms of cognition and personality. These sentiments led to his intellectual battles about (d) Spearman's g theory of a unitary intelligence, (e) Guilford's multifaceted model of intelligence, and (f) the Schaie and Baltes approach to defining the lack of decline of intelligence earlier in the life span. We conclude with a summary of John Horn's unique approaches to dealing with common issues.

Structural equation model trees.

In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model.

The Project TALENT Twin and Sibling Study.

Project TALENT is a US national longitudinal study of about 377,000 individuals born in 1942-1946, first assessed in 1960. Students in about 1,200 schools participated in a 2-day battery covering aptitudes, abilities, interests, and individual and family characteristics (Flanagan, 1962; www.projectTALENT.org). Follow-up assessments 1, 5, and 11 years later assessed educational and occupational outcomes. The sample includes approximately 92,000 siblings from 40,000 families, including 2,500 twin pairs and 1,200 other siblings of twins. Until recently, almost no behavior genetic research has been conducted with the sample. In the original data collection information was not collected with the intent to link family members. Recently, we developed algorithms using names, addresses, birthdates, and information about family structure to link siblings and identify twins. We are testing several methods to determine zygosity, including use of yearbook photographs. In this paper, we summarize the design and measures in Project TALENT, describe the Twin and Sibling sample, and present our twin-sib-classmate model. In most twin and family designs, the 'shared environment' includes factors specific to the family combined with between-family differences associated with macro-level variables such as socioeconomic status. The school-based sampling design used in Project TALENT provides a unique opportunity to partition the shared environment into variation shared by siblings, specific to twins, and associated with school- and community-level factors. The availability of many measured characteristics on the family, schools, and neighborhoods enhances the ability to study the impact of specific factors on behavioral variation.