Resting-state fMRI (rs-fMRI) is widely used to investigate brain functional connectivity, but the reliability of these measurements remains a key concern for ensuring reproducibility. The distance-based intraclass correlation coefficient (dbICC) generalizes classical ICC to more general data types, making it well-suited for assessing the reliability of measures of functional connectivity. In this study, we applied dbICC to assess the reliability of rs-fMRI data from the Midnight Scanning Club (MSC) dataset, which consists of 10 subjects, each undergoing 10 sessions of 30-minute rs-fMRI scans. The functional connectivity was estimated using Pearson's correlation coefficients between all pairs of brain regions, resulting in a correlation matrix for each session. We compared two distance metrics-the widely used Frobenius metric and the Affine Invariant Riemannian Metric (AIRM) selected to respect the geometry of the space of covariance matrices-to evaluate how the choice of metric affects the reliability of estimating correlation. In addition, we investigated the impact of scan length and time interval between sessions on reliability. Results based on each metric agreed in some respects but disagreed in others, illustrating the impact of choice of metric. We also found that longer scan lengths significantly improve reliability, while the time interval between sessions has less impact.

Curve correlation was recently proposed as a way to measure association between time courses that are noisy and may be observed irregularly and at disparate time points. The crux of the method is basis-function smoothing of the time series, which can effectively mitigate the well-known attenuation problem for correlation estimation with noisy data. This technique is reminiscent of functional data analysis, but treats the observations, rather than the variables, as lying along a continuum. This paper provides an in-depth examination of curve correlation. Whereas in the classical setting the population correlation is the estimand and the sample correlation is its estimate, we show how the curve correlation plays both roles: it may function either as an estimand, since it is not observed directly, and as an estimate of an underlying stochastic process correlation. We contrast curve correlation with the related idea of dynamic correlation, investigate boot-strap and posterior simulation approaches to interval estimation, and derive a formula for the variance of the curve correlations arising from a bivariate Gaussian process. Illustrative examples are provided from accelerometry, meteorology, international development and election outcomes.

The starting point for much of multivariate analysis (MVA) is an $n\times p$ data matrix whose $n$ rows represent observations and whose $p$ columns represent variables. Some multivariate data sets, however, may be best conceptualized not as $n$ discrete $p$-variate observations, but as $p$ curves or functions defined on a common time interval. Here we introduce a framework for extending techniques of multivariate analysis to such settings. The proposed continuous-time multivariate analysis (CTMVA) framework rests on the assumption that the curves can be represented as linear combinations of basis functions such as $B$-splines, as in the Ramsay-Silverman representation of functional data; but whereas functional data analysis extends MVA to the case of observations that are curves rather than vectors -- heuristically, $n\times p$ data with $p$ infinite -- we are instead concerned with what happens when $n$ is infinite. We present continuous-time extensions of the classical MVA methods of covariance and correlation estimation, principal component analysis, Fisher's linear discriminant analysis, and $k$-means clustering. We show that CTMVA can improve on the performance of classical MVA, in particular for correlation estimation and clustering, and can be applied in some settings where classical MVA cannot, including variables observed at disparate time points. CTMVA is illustrated with a novel perspective on a well-known Canadian weather data set, and with applications to data sets involving international development, brain signals, and air quality. The proposed methods are implemented in the publicly available R package \texttt{ctmva}.

The glutamatergic modulator ketamine is associated with changes in sleep, depression, and suicidal ideation (SI). This study sought to evaluate differences in arousal-related sleep metrics between 36 individuals with treatment-resistant major depression (TRD) and 25 healthy volunteers (HVs). It also sought to determine whether ketamine normalizes arousal in individuals with TRD and whether ketamine’s effects on arousal mediate its antidepressant and anti-SI effects. This was a secondary analysis of a biomarker-focused, randomized, double-blind, crossover trial of ketamine (0.5 mg/kg) compared to saline placebo. Polysomnography (PSG) studies were conducted one day before and one day after ketamine/placebo infusions. Sleep arousal was measured using spectral power functions over time including alpha (quiet wakefulness), beta (alert wakefulness), and delta (deep sleep) power, as well as macroarchitecture variables, including wakefulness after sleep onset (WASO), total sleep time (TST), rapid eye movement (REM) latency, and Post-Sleep Onset Sleep Efficiency (PSOSE). At baseline, diagnostic differences in sleep macroarchitecture included lower TST (p = 0.006) and shorter REM latency (p = 0.04) in the TRD versus HV group. Ketamine’s temporal dynamic effects (relative to placebo) in TRD included increased delta power earlier in the night and increased alpha and delta power later in the night. However, there were no significant diagnostic differences in temporal patterns of alpha, beta, or delta power, no ketamine effects on sleep macroarchitecture arousal metrics, and no mediation effects of sleep variables on ketamine’s antidepressant or anti-SI effects. These results highlight the role of sleep-related variables as part of the systemic neurobiological changes initiated after ketamine administration. Clinical Trials Identifier: NCT00088699.

The main diagnostic criteria for major depressive disorder (MDD) are consistent experiences of high levels of negative emotions and low levels of positive emotions. Therefore, modification of these emotions is essential in the treatment of MDD. In the current study, we harnessed a computational approach to explore whether experiencing negative emotions during psychological treatment is related to subsequent changes in these emotions. Facial expressions were automatically extracted from 175 sessions of 58 patients with MDD. Within sessions, a U-shaped trajectory of change in valence was observed in which patients expressed an increase in negative emotions in the middle of the session. Between sessions, a consistent increase in valence was observed. A trajectory of within-sessions decrease followed by an increase in valence was positively associated with greater perceived positive emotions and subsequent decreases in depressive symptoms. These findings highlight the importance of targeting negative emotions during treatment to achieve more favorable outcomes.

In many psychological studies, in particular those conducted by experience sampling, mental states are measured repeatedly for each participant. Such a design allows for regression models that separate between- from within-person, or trait-like from state-like, components of association between two variables. But these models are typically designed for continuous variables, whereas mental state variables are most often measured on an ordinal scale. In this paper we develop a model for disaggregating between- from within-person effects of one ordinal variable on another. As in standard ordinal regression, our model posits a continuous latent response whose value determines the observed response. We allow the latent response to depend nonlinearly on the trait and state variables, but impose a novel penalty that shrinks the fit towards a linear model on the latent scale. A simulation study shows that this penalization approach is effective at finding a middle ground between an overly restrictive linear model and an overfitted nonlinear model. The proposed method is illustrated with an application to data from the experience sampling study of Baumeister et al. (2020, Personality and Social Psychology Bulletin, 46, 1631).

The intraclass correlation coefficient (ICC) is a classical index of measurement reliability. With the advent of new and complex types of data for which the ICC is not defined, there is a need for new ways to assess reliability. To meet this need, we propose a new distance-based ICC (dbICC), defined in terms of arbitrary distances among observations. We introduce a bias correction to improve the coverage of bootstrap confidence intervals for the dbICC, and demonstrate its efficacy via simulation. We illustrate the proposed method by analyzing the test-retest reliability of brain connectivity matrices derived from a set of repeated functional magnetic resonance imaging scans. The Spearman-Brown formula, which shows how more intensive measurement increases reliability, is extended to encompass the dbICC.

Time is among the most important yet mysterious aspects of experience. We investigated everyday mental time travel, especially into the future. Two community samples, contacted at random points for 3 (Study 1; 6,686 reports) and 14 days (Study 2; 2,361 reports), reported on their most recent thought. Both studies found that thoughts about the present were frequent, thoughts about the future also were common, whereas thoughts about the past were rare. Thoughts about the present were on average highly happy and pleasant but low in meaningfulness. Pragmatic prospection (thoughts preparing for action) was evident in thoughts about planning and goals. Thoughts with no time aspect were lower in sociality and experiential richness. Thoughts about the past were relatively unpleasant and involuntary. Subjective experiences of thinking about past and future often were similar—while both differed from present focus, consistent with views that memory and prospection use similar mental structures.

We propose a novel approach to the analysis of synchronized three-dimensional motion in dyads. Motion recorded at high time resolution, as with a gaming device, is preprocessed in each of the three spatial dimensions by spline smoothing. Synchrony is then defined, at each time point, as the cosine between the two individuals' estimated velocity vectors. The approach is extended to allow a time lag, allowing for the analysis of leader-follower dynamics. Mean square cosine over the time range is proposed as a scalar summary of dyadic synchrony, and this measure is found to be positively associated with cognitive empathy.

Functional principal component analysis for sparse longitudinal data usually proceeds by first smoothing the covariance surface, and then obtaining an eigendecomposition of the associated covariance operator. Here we consider the use of penalized tensor product splines for the initial smoothing step. Drawing on a result regarding finite-rank symmetric integral operators, we derive an explicit spline representation of the estimated eigenfunctions, and show that the effect of penalization can be notably disparate for alternative approaches to tensor product smoothing. The latter phenomenon is illustrated with two data sets derived from magnetic resonance imaging of the human brain.

The problem of dividing an estate among creditors, when their claims total more than the value of the estate, was posed in the Talmud and has been analyzed in the game theory literature. Here, we reveal a close connection between schemes for estate division and linear regression solution paths obtained by least angle regression or by the lasso. We focus primarily on the division scheme known as constrained equal awards, but also consider a more complex approach described by Aumann and Maschler. Supplementary materials for this article are available online.

In the fields of neuroimaging and genetics, a key goal is testing the association of a single outcome with a very high-dimensional imaging or genetic variable. Often, summary measures of the high-dimensional variable are created to sequentially test and localize the association with the outcome. In some cases, the associations between the outcome and summary measures are significant, but subsequent tests used to localize differences are underpowered and do not identify regions associated with the outcome. Here, we propose a generalization of Rao's score test based on projecting the score statistic onto a linear subspace of a high-dimensional parameter space. The approach provides a way to localize signal in the high-dimensional space by projecting the scores to the subspace where the score test was performed. This allows for inference in the high-dimensional space to be performed on the same degrees of freedom as the score test, effectively reducing the number of comparisons. Simulation results demonstrate the test has competitive power relative to others commonly used. We illustrate the method by analyzing a subset of the Alzheimer's Disease Neuroimaging Initiative dataset. Results suggest cortical thinning of the frontal and temporal lobes may be a useful biological marker of Alzheimer's disease risk.

Motivated by studies of the development of the human cerebral cortex, we consider the estimation of a mean growth trajectory and the relative merits of cross-sectional and longitudinal data for that task. We define a class of relative efficiencies that compare function estimates in terms of aggregate variance of a parametric function estimate. These generalize the classical design effect for estimating a scalar with cross-sectional versus longitudinal data, and are shown to be bounded above by it in certain cases. Turning to nonparametric function estimation, we find that longitudinal fits may tend to have higher aggregate variance than cross-sectional ones, but that this may occur because the former have higher effective degrees of freedom reflecting greater sensitivity to subtle features of the estimand. These ideas are illustrated with cortical thickness data from a longitudinal neuroimaging study.

Many modern neuroimaging studies acquire large spatial images of the brain observed sequentially over time. Such data are often stored in the forms of matrices. To model these matrix-variate data we introduce a class of separable processes using explicit latent process modeling. To account for the size and two-way structure of the data, we extend principal component analysis to achieve dimensionality reduction at the individual level. We introduce necessary identifiability conditions for each model and develop scalable estimation procedures. The method is motivated by and applied to a functional magnetic resonance imaging study designed to analyze the relationship between pain and brain activity.

We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise influence matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor. This procedure adapts to varying complexity of the nonlinear model at different locations along the function, and thereby achieves better performance than competing tensor product smoothers in an analysis of the development of white matter microstructure in the brain.

BACKGROUND:Social anxiety disorder (SAD) typically onsets in adolescence and is associated with multiple impairments. Despite promising clinical interventions, most socially anxious adolescents remain untreated. To address this clinical neglect, we developed a school-based, 12-week group intervention for youth with SAD, Skills for Academic and Social Success (SASS). When implemented by psychologists, SASS has been found effective. To promote dissemination and optimize treatment access, we tested whether school counselors could be effective treatment providers.METHOD:We randomized 138, ninth through 11th graders with SAD to one of three conditions: (a) SASS delivered by school counselors (C-SASS), (b) SASS delivered by psychologists (P-SASS), or (c) a control condition, Skills for Life (SFL), a nonspecific counseling program. Blind, independent, evaluations were conducted with parents and adolescents at baseline, post-intervention, and 5 months beyond treatment completion. We hypothesized that C-SASS and P-SASS would be superior to the control, immediately after treatment and at follow-up. No prediction was made about the relative efficacy of C-SASS and P-SASS.RESULTS:Compared to controls, adolescents treated with C-SASS or P-SASS experienced significantly greater improvement and reductions of anxiety at the end of treatment and follow-up. There were no significant differences between SASS delivered by school counselors and psychologists.CONCLUSION:With training, school counselors are effective treatment providers to adolescents with social anxiety, yielding benefits comparable to those obtained by specialized psychologists. Questions remain regarding means to maintain counselors' practice standards without external support.

Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.