Nathaniel E. Helwig

Fast and Stable Multiple Smoothing Parameter Selection in Smoothing Spline Analysis of Variance Models With Large Samples

The current parameterization and algorithm used to fit a smoothing spline analysis of variance (SSANOVA) model are computationally expensive, making a generalized additive model (GAM) the preferred method for multivariate smoothing. In this article, we propose an efficient reparameterization of the smoothing parameters in SSANOVA models, and a scalable algorithm for estimating multiple smoothing parameters in SSANOVAs. To validate our approach, we present two simulation studies comparing our reparameterization and algorithm to implementations of SSANOVAs and GAMs that are currently available in R. Our simulation results demonstrate that (a) our scalable SSANOVA algorithm outperforms the currently used SSANOVA algorithm, and (b) SSANOVAs can be a fast and reliable alternative to GAMs. We also provide an example with oceanographic data that demonstrates the practical advantage of our SSANOVA framework. Supplementary materials that are available online can be used to replicate the analyses in this article.

A critique of Tensor Probabilistic Independent Component Analysis: Implications and recommendations for multi-subject fMRI data analysis

Tensor Probabilistic Independent Component Analysis (TPICA) is a popular tool for analyzing multi-subject fMRI data (voxels×time×subjects) because of TPICAs supposed robustness. In this paper, we show that TPICA is not as robust as its authors claim. Specifically, we discuss why TPICAs overall objective is questionable, and we present some flaws related to the iterative nature of the TPICA algorithm. To demonstrate the relevance of these issues, we present a simulation study that compares TPICA versus Parallel Factor Analysis (Parafac) for analyzing simulated multi-subject fMRI data. Our simulation results demonstrate that TPICA produces a systematic bias that increases with the spatial correlation between the true components, and that the quality of the TPICA solution depends on the chosen ICA algorithm and iteration scheme. Thus, TPICA is not robust to small-to-moderate deviations from the models spatial independence assumption. In contrast, Parafac produces unbiased estimates regardless of the spatial correlation between the true components, and Parafac with orthogonality-constrained voxel maps produces smaller biases than TPICA when the true voxel maps are moderately correlated. As a result, Parafac should be preferred for the analysis multi-subject fMRI data where the underlying components may have spatially overlapping voxel activation patterns.

The Special Sign Indeterminacy of the Direct-Fitting Parafac2 Model: Some Implications, Cautions, and Recommendations for Simultaneous Component Analysis

Parafac2 is the most flexible Simultaneous Component Analysis (SCA) model that produces an essentially unique solution. In this paper, we discuss how Parafac2’s special sign indeterminacy affects applications of SCA, and we reveal how an external criterion variable can be used to ensure that estimated Parafac2 weights are meaningfully signed across the levels of the nesting mode. We present an example with real data from clinical psychology that illustrates the importance of Parafac2’s special sign indeterminacy, as well as the effectiveness of our proposed solution. We also discuss the implications of our results for general applications of SCA.

Estimating latent trends in multivariate longitudinal data via Parafac2 with functional and structural constraints

Longitudinal data are inherently multimode in the sense that such data are often collected across multiple modes of variation, for example, time × variables × subjects. In many longitudinal studies, multiple variables are collected to measure some latent construct(s) of interest. In such cases, the goal is to understand temporal trends in the latent variables, as well as individual differences in the trends. Multimode component analysis models provide a powerful framework for discovering latent trends in longitudinal data. However, classic implementations of multimode models do not take into consideration functional information (i.e., the temporal sequence of the collected data) or structural information (i.e., which variables load onto which latent factors) about the study design. In this paper, we reveal how functional and structural constraints can be imposed in multimode models (Parafac and Parafac2) in order to elucidate trends in longitudinal data. As a motivating example, we consider a longitudinal study on per capita alcohol consumption trends conducted from 1970 to 2013 by the U.S. National Institute on Alcohol Abuse and Alcoholism. We demonstrate how functional and structural information about the study design can be incorporated into the Parafac and Parafac2 alternating least squares algorithms to understand temporal and regional trends in three latent constructs: beer consumption, spirits consumption, and wine consumption. Our results reveal that Americans consume more than the recommended amount of alcohol, and total alcohol consumption trends show no signs of decreasing in the last decade.

Efficient estimation of variance components in nonparametric mixed-effects models with large samples

Linear mixed-effects (LME) regression models are a popular approach for analyzing correlated data. Nonparametric extensions of the LME regression model have been proposed, but the heavy computational cost makes these extensions impractical for analyzing large samples. In particular, simultaneous estimation of the variance components and smoothing parameters poses a computational challenge when working with large samples. To overcome this computational burden, we propose a two-stage estimation procedure for fitting nonparametric mixed-effects regression models. Our results reveal that, compared to currently popular approaches, our two-stage approach produces more accurate estimates that can be computed in a fraction of the time.

Smoothing spline analysis of variance models: A new tool for the analysis of cyclic biomechanical data

Cyclic biomechanical data are commonplace in orthopedic, rehabilitation, and sports research, where the goal is to understand and compare biomechanical differences between experimental conditions and/or subject populations. A common approach to analyzing cyclic biomechanical data involves averaging the biomechanical signals across cycle replications, and then comparing mean differences at specific points of the cycle. This pointwise analysis approach ignores the functional nature of the data, which can hinder one׳s ability to find subtle differences between experimental conditions and/or subject populations. To overcome this limitation, we propose using mixed-effects smoothing spline analysis of variance (SSANOVA) to analyze differences in cyclic biomechanical data. The SSANOVA framework makes it possible to decompose the estimated function into the portion that is common across groups (i.e., the average cycle, AC) and the portion that differs across groups (i.e., the contrast cycle, CC). By partitioning the signal in such a manner, we can obtain estimates of the CC differences (CCDs), which are the functions directly describing group differences in the cyclic biomechanical data. Using both simulated and experimental data, we illustrate the benefits of using SSANOVA models to analyze differences in noisy biomechanical (gait) signals collected from multiple locations (joints) of subjects participating in different experimental conditions. Using Bayesian confidence intervals, the SSANOVA results can be used in clinical and research settings to reliably quantify biomechanical differences between experimental conditions and/or subject populations.

Dynamic properties of successful smiles

Facial expression of emotion is a foundational aspect of social interaction and nonverbal communication. In this study, we use a computer-animated 3D facial tool to investigate how dynamic properties of a smile are perceived. We created smile animations where we systematically manipulated the smile’s angle, extent, dental show, and dynamic symmetry. Then we asked a diverse sample of 802 participants to rate the smiles in terms of their effectiveness, genuineness, pleasantness, and perceived emotional intent. We define a “successful smile” as one that is rated effective, genuine, and pleasant in the colloquial sense of these words. We found that a successful smile can be expressed via a variety of different spatiotemporal trajectories, involving an intricate balance of mouth angle, smile extent, and dental show combined with dynamic symmetry. These findings have broad applications in a variety of areas, such as facial reanimation surgery, rehabilitation, computer graphics, and psychology.

Bootstrap Enhanced Penalized Regression for Variable Selection with Neuroimaging Data

Recent advances in fMRI research highlight the use of multivariate methods for examining whole-brain connectivity. Complementary data-driven methods are needed for determining the subset of predictors related to individual differences. Although commonly used for this purpose, ordinary least squares (OLS) regression may not be ideal due to multi-collinearity and over-fitting issues. Penalized regression is a promising and underutilized alternative to OLS regression. In this paper, we propose a nonparametric bootstrap quantile (QNT) approach for variable selection with neuroimaging data. We use real and simulated data, as well as annotated R code, to demonstrate the benefits of our proposed method. Our results illustrate the practical potential of our proposed bootstrap QNT approach. Our real data example demonstrates how our method can be used to relate individual differences in neural network connectivity with an externalizing personality measure. Also, our simulation results reveal that the QNT method is effective under a variety of data conditions. Penalized regression yields more stable estimates and sparser models than OLS regression in situations with large numbers of highly correlated neural predictors. Our results demonstrate that penalized regression is a promising method for examining associations between neural predictors and clinically relevant traits or behaviors. These findings have important implications for the growing field of functional connectivity research, where multivariate methods produce numerous, highly correlated brain networks.

Influence of proximal trunk borne load on lower limb countermovement joint dynamics

Vertical jumping involves coordinating the temporal sequencing of angular motion, moment, and power across multiple joints. Studying the biomechanical coordination strategies that differentiates loaded from unloaded vertical jumping may better inform training prescription for athletes needing to jump with load. Common multivariate methods (e.g. Principal Components Analysis) cannot quantify coordination in a dataset with more than two modes. This study aimed to identify coordinative factors across four modes of variation using Parallel Factor (Parafac2) analysis, which may differentiate unloaded (body weight [BW]) from loaded (BW + 20% BW) countermovement jump (CMJ). Thirty-one participants performed unloaded and loaded CMJ. Three-dimensional motion capture with force plate analysis was performed. Inverse dynamics was used to quantify sagittal plane joint angle, velocity, moment, and joint power across the ankle, knee, and hip. The four-mode data were as follows: Mode A was jump cycle (101 cycle points), mode B was participant (31 participants by two load), mode C was joint (two sides by three joints), and mode D was variable (angle, velocity, moment, power). Three factors were extracted, which explained 95.1% of the datas variance. Only factors one (P = 0.001) and three (P < 0.001) significantly differentiated loaded from unloaded jumping. The body augmented hip-dominant at the start, and both hip and ankle dominant behaviors at the end of the ascending phase of the CMJ, but kept knee-dominant behavior invariant, when jumping with a 20% BW load. By studying the variation across all data modes, Parafac2 provides a holistic method of studying jumping coordination.

The effect of glenohumeral plane of elevation on supraspinatus subacromial proximity

Shoulder pain is a common clinical problem affecting most individuals in their lifetime. Despite the high prevalence of rotator cuff pathology in these individuals, the pathogenesis of rotator cuff disease remains unclear. Position and motion related mechanisms of rotator cuff disease are often proposed, but poorly understood. The purpose of this study was to determine the impact of systematically altering glenohumeral plane on subacromial proximities across arm elevation as measures of tendon compression risk. Three-dimensional models of the humerus, scapula, coracoacromial ligament, and supraspinatus were reconstructed from MRIs in 20 subjects. Glenohumeral elevation was imposed on the humeral and supraspinatus tendon models for three glenohumeral planes, which were chosen to represent flexion, scapular plane abduction, and abduction based on average values from a previous study of asymptomatic individuals. Subacromial proximity was quantified as the minimum distance between the supraspinatus tendon and coracoacromial arch (acromion and coracoacromial ligament), the surface area of the supraspinatus tendon within 2 mm proximity to the coracoacromial arch, and the volume of intersection between the supraspinatus tendon and coracoacromial arch. The lowest modeled subacromial supraspinatus compression measures occurred during flexion at lower angles of elevation. This finding was consistent across all three measures of subacromial proximity. Knowledge of this range of reduced risk may be useful to inform future studies related to patient education and ergonomic design to prevent the development of shoulder pain and dysfunction.