The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.     

Multilevel modeling: current and future applications in personality research

Traditional statistical analyses can be compromised when data are collected from groups or multiple observations are collected from individuals. We present an introduction to multilevel models designed to address dependency in data. We review current use of multilevel modeling in 3 personality journals showing use concentrated in the 2 areas of experience sampling and longitudinal growth. Using an empirical example, we illustrate specification and interpretation of the results of series of models as predictor variables are introduced at Levels 1 and 2. Attention is given to possible trends and cycles in longitudinal data and to different forms of centering. We consider issues that may arise in estimation, model comparison, model evaluation, and data evaluation (outliers), highlighting similarities to and differences from standard regression approaches. Finally, we consider newer developments, including 3-level models, cross-classified models, nonstandard (limited) dependent variables, multilevel structural equation modeling, and nonlinear growth. Multilevel approaches both address traditional problems of dependency in data and provide personality researchers with the opportunity to ask new questions of their data.     

Empirical Bayes Approaches to Multivariate Fuzzy Partitions

In describing high dimensional discrete response data, mathematical and statistical issues arise that require multivariate procedures that are not based on normal distributions, that is, the mathematical representation of high dimensional discrete response data (Event Spaces) requires a representation in lower dimensional parameter spaces consistent with the discrete properties of the Event Space. Mapping discrete responses to latent discrete classes has the limitation of not representing real individual variation within the categories. The use of a fuzzy partition model is proposed which describes individuals in terms of partial membership in multiple latent categories which represents bounded discrete event spaces with significant third and higher order moments. We discuss statistical issues arising in identifying both the deterministic and the stochastic variation of data when applications involve systematic variation due to observed and unobserved variables. We present an empirical Bayes-maximum likelihood estimation scheme for the application of the fuzzy partition models.     

Organization of the narrative components in autobiographical speech of anorexic adolescents: A statistical and non-linear dynamical analysis

Family theories of anorexia nervosa point out that patients’ autobiographic speech may reflect internalized family interactions. Our study characterizes the statistical distribution and temporal organization of the narrative components describing personal relationships in anorexic and control subjects. Semantic components related to personal interactions were encoded from life narratives of 14 adolescent girls with anorexia nervosa (restrictive type) and of 13 matched healthy adolescent girls. Speech analysis was performed using both statistical methods and non-linear time-series analysis. Static indices showed an over-representation of family relations and an under-representation of love relations in anorexic patients. Dynamical indices showed the independence between relational systems in anorexic patients. Dynamical analysis reveals that interactional patterns are internalized through the temporal organization of autobiographical speech. Moreover, these results support the existence of a specific temporal organization in anorexic adolescents’ life narratives which express the internalization of stationary family patterns and indicate relative inability to disengage from active previous relational patterns and to create new ones.     

Functional magnetic resonance imaging: Overview and methods for psychological research

Functional magnetic resonance imaging (fMRI) allows noninvasive imaging of hemodynamic changes related to neural activity. This technique can be used in single-subject designs and can provide millimeter spatial resolution and temporal resolution in the range of 5–10 sec. This paper provides a brief introduction to MRI techniques and their application to functional neuroimaging, focusing on methodological issues that are of particular concern to psychologists, including methods for presenting computerized stimuli to subjects without disrupting the scanner, experimental design issues, and statistical analysis and image processing procedures. To illustrate methodological issues, recent results from a series of studies looking at the topographic organization of visual cortex are presented. General issues concerning limitations in this technique, future directions in its development, its relationship to other neuroimaging techniques, and the role of functional neuroimaging in psychological research are addressed in the Discussion.     

The common fate model for dyadic data: variations of a theoretically important but underutilized model

Studying dyads, very often there is a theoretical construct that has an effect on both members, such as relationship harmony or shared environment. To model such influences, the common fate model (CFM) is often the most appropriate approach. In this article, we address conceptual and statistical issues in the use of the standard CFM and present a series of variations, all of which are estimated by structural equation modeling (SEM). For indistinguishable dyad members (e.g., gay couples), we describe the use of a multilevel SEM method. Throughout the paper, we draw connections to the actor-partner interdependence model (APIM). We also discuss the analysis of hybrid models that combines both the CFM and the APIM. The models are illustrated using data from heterosexual couples.     

“Suspended Animation,” My Mother’s Wife and Cultural Discernment: Considerations for Genetic Research among Immigrants

One of the most difficult contemporary issues facing the bioethics of clinical research is balancing the maintaining of a universality of ethics standards with a sensitivity to cultural issues and differences. The concept of “vulnerability” for research subjects is especially apt for investigating the ethical and cultural issues surrounding the conduct of genetic research among new immigrants to the United States, using the Sudanese Nuer and Dinka tribes, recently settled in the Midwest, as an example. Issues of cultural vulnerability arise for some immigrants, related to relationship to the earth and to kinship issues, that threaten the narrative richness of a subject's life as well as the way she situates herself in the world.     

Location,Location, Location: Applying Spatial Statistics to the Relationship Landscape

The desire to understand relationships is a passion shared by professionals in research, clinical, and educational settings. Questionnaires are frequently used in each of these settings for a multitude of purposes—such as screening, assessment, program evaluation, or establishing therapeutic effectiveness. However, clinical issues arise when a couple's answers on questionnaires do not match clinical judgment or lack clinical utility, while statistical problems arise when data from both partners are put into analyses. This article introduces the use of geospatial statistics to analyze couple data plotted on a two‐dimensional “relational map.” Relationship maps can increase assessment sensitivity, track treatment progress, and remove statistical issues typically associated with couple data. This article briefly introduces core assumptions of spatial models, illustrates the use of spatial models in creating a relational landscape of divorce, offers suggestions for the use of relational maps in a clinical setting, and explores future research ideas.     

Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.1978 Psychometric Society Presidential Address.This research has been supported by the Bank of Sweden Tercentenary Foundation under the project entitledStructural Equation Models in the Social Sciences, Karl G. Jöreskog, project director.     

Common functional principal components analysis: a new approach to analyzing human movement data

In many human movement studies angle-time series data on several groups of individuals are measured. Current methods to compare groups include comparisons of the mean value in each group or use multivariate techniques such as principal components analysis and perform tests on the principal component scores. Such methods have been useful, though discard a large amount of information. Functional data analysis (FDA) is an emerging statistical analysis technique in human movement research which treats the angle-time series data as a function rather than a series of discrete measurements. This approach retains all of the information in the data. Functional principal components analysis (FPCA) is an extension of multivariate principal components analysis which examines the variability of a sample of curves and has been used to examine differences in movement patterns of several groups of individuals. Currently the functional principal components (FPCs) for each group are either determined separately (yielding components that are group-specific), or by combining the data for all groups and determining the FPCs of the combined data (yielding components that summarize the entire data set). The group-specific FPCs contain both within and between group variation and issues arise when comparing FPCs across groups when the order of the FPCs alter in each group. The FPCs of the combined data may not adequately describe all groups of individuals and comparisons between groups typically use t-tests of the mean FPC scores in each group. When these differences are statistically non-significant it can be difficult to determine how a particular intervention is affecting movement patterns or how injured subjects differ from controls. In this paper we aim to perform FPCA in a manner allowing sensible comparisons between groups of curves. A statistical technique called common functional principal components analysis (CFPCA) is implemented. CFPCA identifies the common sources of variation evident across groups but allows the order of each component to change for a particular group. This allows for the direct comparison of components across groups. We use our method to analyze a biomechanical data set examining the mechanisms of chronic Achilles tendon injury and the functional effects of orthoses.     

Children's working memory: Its structure and relationship to fluid intelligence

Working memory (WM) has been predominantly studied in adults. The insights provided by these studies have led to the development of competing theories on the structure of WM and conflicting conclusions on how strongly WM components are related to higher order thinking skills such as fluid intelligence. However, it remains unclear whether and to what extent the theories and findings derived from adult data generalize to children. The purpose of the present study is therefore to investigate children's WM (N = 161), who attended classes at the end of kindergarten in Luxembourg. Specifically, we examine different structural models of WM and how its components, as defined in these models, are related to fluid intelligence. Our results indicate that short-term storage capacity primarily explains the relationship between WM and fluid intelligence. Based on these observations we discuss the theoretical and methodological issues that arise when children's WM is investigated.     

Personality over time: Methodological approaches to the study of short-term and long-term development and change

Although theories of personality emphasize the integrative, enduring, and dynamic nature of personality, the current modal research design in personality ignores the dimension of time. We consider a variety of recent methods of longitudinal data analysis to examine both short-term and long-term development and change in personality, including mean-level analyses both across and within individuals across time, variance structures across time, and cycles and dynamic models across time. These different longitudinal analyses can address classic as well as new questions in the study of personality and its development. We discuss the linkages among different longitudinal analyses, measurement issues in temporal data, the spacing of assessments, and the levels of generalization and potential insights afforded by different longitudinal analyses.     

Selecting the “Best” Factor Structure and Moving Measurement Validation Forward: An Illustration

Despite the broad literature base on factor analysis best practices, research seeking to evaluate a measure's psychometric properties frequently fails to consider or follow these recommendations. This leads to incorrect factor structures, numerous and often overly complex competing factor models and, perhaps most harmful, biased model results. Our goal is to demonstrate a practical and actionable process for factor analysis through (a) an overview of six statistical and psychometric issues and approaches to be aware of, investigate, and report when engaging in factor structure validation, along with a flowchart for recommended procedures to understand latent factor structures; (b) demonstrating these issues to provide a summary of the updated Posttraumatic Stress Disorder Checklist (PCL–5) factor models and a rationale for validation; and (c) conducting a comprehensive statistical and psychometric validation of the PCL–5 factor structure to demonstrate all the issues we described earlier. Considering previous research, the PCL–5 was evaluated using a sample of 1,403 U.S. Air Force remotely piloted aircraft operators with high levels of battlefield exposure. Previously proposed PCL–5 factor structures were not supported by the data, but instead a bifactor model is arguably more statistically appropriate.     

Using Latent Class Analysis to Model Temperament Types

Mixture models are appropriate for data that arise from a set of qualitatively different subpopulations. In this study, latent class analysis was applied to observational data from a laboratory assessment of infant temperament at four months of age. The EM algorithm was used to fit the models, and the Bayesian method of posterior predictive checks was used for model selection. Results show at least three types of infant temperament, with patterns consistent with those identified by previous researchers who classified the infants using a theoretically based system. Multiple imputation of group memberships is proposed as an alternative to assigning subjects to the latent class with maximum posterior probability in order to reflect variance due to uncertainty in the parameter estimation. Latent class membership at four months of age predicted longitudinal outcomes at four years of age. The example illustrates issues relevant to all mixture models, including estimation, multi-modality, model selection, and comparisons based on the latent group indicators.     

Engagement in Activities Is Associated With Affective Arousal in Alzheimer's Caregivers: A Preliminary Examination of the Temporal Relations Between Activity and Affect

The primary purpose of this study was to examine the synchronous and temporal relations between engagement in activities and the two primary dimensions of affect—namely, positive and negative affect—using an intensive time-series design called concomitant time series analysis (CTSA). Twenty-four dementia caregivers completed 56 diary measures (4 times per day for 2 weeks) assessing their experience of positive and negative affect as well as engagement in a variety of activities. Total number of activities was significantly correlated with positive affect (r = .40), but not negative affect (r = -.12). Obtained pleasure from activities was significantly correlated with both positive (r = .42) and negative affect (r = - .17). These results may help further develop behavioral models of depression by suggesting that behavioral or self-reinforcing activities are associated primarily (or more saliently) with one's experience of positive affect. Future research examining the effect of behavioral interventions on both positive and negative affect is suggested, as is the examination of factors that may be more strongly associated with negative affect.     

Multilevel analysis of matching behavior

Multilevel modeling has been considered a promising statistical tool in the field of the experimental analysis of behavior and may serve as a convenient statistical analysis for matching behavior because it structures data in groups (or levels) to account simultaneously for the within‐subject and between‐subject variances. Heretofore, researchers have sometimes pooled data erroneously from different subjects in a single analysis by using average ratios, average response and reinforcer rates, aggregation of subjects, etc. Unfortunately, this leads to loss of information and biased estimations, which can severely undermine generalization of the results. Instead, a multilevel approach is advocated to combine several subjects' matching behavior. A reanalysis of previous data on matching behavior is provided to illustrate the method and point out its advantages. It illustrates that multilevel regression leads to better estimations, is more convenient, and offers more behavioral information. We hope this paper will encourage the use of multilevel modeling in the statistical practices of behavior analysts.     

SPSS and SAS programs for addressing interdependence and basic levels-of-analysis issues in psychological data.

Levels-of-analysis issues arise whenever individual-level data are collected from more than one person from the same dyad, family, classroom, work group, or other interaction unit. Interdependence in data from individuals in the same interaction units also violates the independence-of-observations assumption that underlies commonly used statistical tests. This article describes the data analysis challenges that are presented by these issues and presents SPSS and SAS programs for conducting appropriate analyses. The programs conduct the within-and-between-analyses described by Dansereau, Alutto, and Yammarino (1984) and the dyad-level analyses described by Gonzalez and Griffin (1999) and Griffin and Gonzalez (1995). Contrasts with general multilevel modeling procedures are then discussed.     

SPSS and SAS programs for addressing interdependence and basic levels-of-analysis issues in psychological data

Levels-of-analysis issues arise whenever individual-level data are collected from more than one person from the same dyad, family, classroom, work group, or other interaction unit. Interdependence in data from individuals in the same interaction units also violates the independence-of-observations assumption that underlies commonly used statistical tests. This article describes the data analysis challenges that are presented by these issues and presents SPSS and SAS programs for conducting appropriate analyses. The programs conduct the within- and-between-analyses described by Dansereau, Alutto, and Yammarino (1984) and the dyad-level analyses describedby Gonzalez and Griffin (1999) and Griffin and Gonzalez (1995). Contrasts with general multilevel modeling procedures are then discussed.     

A Latent Gaussian process model for analysing intensive longitudinal data

Intensive longitudinal studies are becoming progressively more prevalent across many social science areas, and especially in psychology. New technologies such as smart-phones, fitness trackers, and the Internet of Things make it much easier than in the past to collect data for intensive longitudinal studies, providing an opportunity to look deep into the underlying characteristics of individuals under a high temporal resolution. In this paper we introduce a new modelling framework for latent curve analysis that is more suitable for the analysis of intensive longitudinal data than existing latent curve models. Specifically, through the modelling of an individual-specific continuous-time latent process, some unique features of intensive longitudinal data are better captured, including intensive measurements in time and unequally spaced time points of observations. Technically, the continuous-time latent process is modelled by a Gaussian process model. This model can be regarded as a semi-parametric extension of the classical latent curve models and falls under the framework of structural equation modelling. Procedures for parameter estimation and statistical inference are provided under an empirical Bayes framework and evaluated by simulation studies. We illustrate the use of the proposed model though the analysis of an ecological momentary assessment data set.