About

Nathaniel Helwig is an Associate Professor of Psychology at the University of Minnesota's College of Liberal Arts. He holds a PhD in Quantitative Psychology from the University of Illinois, earned in 2013, along with a Master's degree in Psychology and a Master's in Statistics from the same institution, and a Bachelor's degree in Psychology and Mathematics from the University of Miami. His research focuses on advanced statistical methods and their applications in psychology and neuroimaging, including nonparametric regression, permutation tests, multivariate analysis, and smoothing spline analysis of variance models. Helwig has contributed to the development of scalable computational techniques for large samples and has applied these methods to diverse areas such as biomechanics, facial analysis, brain networks, and neuroimaging data. His work emphasizes the use of nonparametric and permutation-based approaches to improve the robustness and interpretability of statistical analyses in psychological and neuroscientific research.

Research topics

• Computer science
• Mathematics
• Psychology
• Statistics
• Econometrics

Selected publications

• Regularized Multilevel Multinomial Regression for Select-All-That-Apply Responses and High-Dimensional Predictors with Applications to Perception of Facial Expressions

  Psychometrika · 2026-04-22

  articleOpen access1st authorCorresponding

  This article develops an analysis pipeline for quantifying and relating mouth shape variation to the emotions perceived from facial expressions. We use open-source data that contains ratings from 802 fairgoers on 27 smile-like expressions. Each rater was given a list of seven emotions (happy, sad, anger, contempt, fear, surprise, and disgust) and asked to select all of the words that best described the facial expression. To develop a generalizable method for quantifying mouth shape variation, we leverage statistical shape analysis techniques to parameterize each mouth's shape in terms of 30 systematically placed landmarks that outline the upper and lower lips. Furthermore, we demonstrate that a three-dimensional representation of these landmark coordinates produces an interpretable feature set that outperforms the original and full-dimensional feature sets in terms of predictive performance. To connect the mouth shape features to the emotion ratings, we develop a nonparametric multinomial regression model that is capable of shrinkage and selection with high-dimensional predictors. Our results demonstrate that the proposed method can produce easily interpretable model predictions that enhance our understanding of the nature in which subtle variations in mouth shape affect the perception of a facial expression.

  PublisherOA PDFDOI

• Robust detection of signed outliers in multivariate data with applications to early identification of risk for autism.

  Psychological Methods · 2025-07-21

  articleOpen accessSenior author

  This article proposes an approach for detecting multivariate outliers that combines robust estimation methods with signed detection information. Our method uses the Mahalanobis distance to quantify each observation's extremeness from the expected value relative to the covariance matrix, and we leverage robust estimation tools, i.e., the minimum covariance determinant, to estimate the mean vector and covariance matrix used in the Mahalanobis distance calculation. Furthermore, we incorporate a signing element into the distance calculation to give researchers greater control over the specific regions of multivariate space that should be prioritized when searching for outliers, which allows for more targeted risk assessment and classification. Lastly, we unify the robust and signed elements into a framework that can be used within bilinear models such as principal components analysis and factor analysis. Using simulated and real data examples, we demonstrate that the proposed approach can result in improved risk assessment and outlier detection, particularly when the sample is contaminated with a moderate-to-large number of outliers that have noteworthy contamination strengths. Overall, our results show that making use of a robust method when assessing multivariate risk leads to more accurate estimates, particularly when combined with relevant signing information. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

  PublisherDOI

• mvout: Robust Multivariate Outlier Detection

  2025-05-30

  datasetOpen accessSenior author

  Detection of multivariate outliers using robust estimates of location and scale. The Minimum Covariance Determinant (MCD) estimator is used to calculate robust estimates of the mean vector and covariance matrix. Outliers are determined based on robust Mahalanobis distances using either an unstructured covariance matrix, a principal components structured covariance matrix, or a factor analysis structured covariance matrix. Includes options for specifying the direction of interest for outlier detection for each variable.

  PublisherOA PDFDOI

• Dynamic Facial Health Predicts Psychological First Impressions with Applications to Tailored Treatments for Facial Paralysis

  Journal of Personalized Medicine · 2025-11-02

  articleOpen access1st authorCorresponding

  Background: Past studies demonstrate that certain facial features systematically affect first impressions of psychological traits. However, no previous studies have examined how individual differences in facial health affect first impressions of psychological traits. Methods: In this study, we asked a large sample of fairgoers to give their first impressions of psychological traits in response to viewing videos of unilateral facial paralysis patients with varying degrees of facial functioning. Then, we used linear mixed-effects regression models to understand how individual differences in facial health predict first impressions. Results: Our results replicate previous findings regarding first impressions of faces, such as the attractiveness halo effect, as well as age (maturity) and gender (masculinity) effects. More importantly, our results reveal that facial health, as measured by a clinician-graded scale, is a significant predictor of first impressions. Specifically, we found that individuals with better dynamic facial health (as assessed by clinicians) were perceived to be more competent and more affiliative, but not more dominant, than individuals with lower levels of dynamic facial functioning. Conclusions: Our results have important implications for personalized medicine via the development and refinement of individually tailored therapies to improve facial reanimation surgery outcomes.

  PublisherOA PDFDOI

• Resting-State Functional Connectivity Predicts Attention Problems in Children: Evidence from the ABCD Study

  NeuroSci · 2024-10-12 · 3 citations

  articleOpen accessSenior authorCorresponding

  Attention deficit/hyperactivity disorder (ADHD) is a common neurodevelopmental disorder, and numerous functional and structural differences have been identified in the brains of individuals with ADHD compared to controls. This study uses data from the baseline sample of the large, epidemiologically informed Adolescent Brain Cognitive Development Study of children aged 9–10 years old (N = 7979). Cross-validated Poisson elastic net regression models were used to predict a dimensional measure of ADHD symptomatology from within- and between-network resting-state correlations and several known risk factors, such as biological sex, socioeconomic status, and parental history of problematic alcohol and drug use. We found parental history of drug use and biological sex to be the most important predictors of attention problems. The connection between the default mode network and the dorsal attention network was the only brain network identified as important for predicting attention problems. Specifically, we found that reduced magnitudes of the anticorrelation between the default mode and dorsal attention networks relate to increased attention problems in children. Our findings complement and extend recent studies that have connected individual differences in structural and task-based fMRI to ADHD symptomatology and individual differences in resting-state fMRI to ADHD diagnoses.

  PublisherOA PDFDOI

• gammi: Generalized Additive Mixed Model Interface

  2024-09-15

  datasetOpen access1st authorCorresponding

  An interface for fitting generalized additive models (GAMs) and generalized additive mixed models (GAMMs) using the 'lme4' package as the computational engine, as described in Helwig (2024) &lt;<a href="https://doi.org/10.3390%2Fstats7010003" target="_top">doi:10.3390/stats7010003</a>&gt;. Supports default and formula methods for model specification, additive and tensor product splines for capturing nonlinear effects, and automatic determination of spline type based on the class of each predictor. Includes an S3 plot method for visualizing the (nonlinear) model terms, an S3 predict method for forming predictions from a fit model, and an S3 summary method for conducting significance testing using the Bayesian interpretation of a smoothing spline.

  PublisherOA PDFDOI

• Precise Tensor Product Smoothing via Spectral Splines

  Stats · 2024-01-10 · 3 citations

  articleOpen access1st authorCorresponding

  Tensor product smoothers are frequently used to include interaction effects in multiple nonparametric regression models. Current implementations of tensor product smoothers either require using approximate penalties, such as those typically used in generalized additive models, or costly parameterizations, such as those used in smoothing spline analysis of variance models. In this paper, I propose a computationally efficient and theoretically precise approach for tensor product smoothing. Specifically, I propose a spectral representation of a univariate smoothing spline basis, and I develop an efficient approach for building tensor product smooths from marginal spectral spline representations. The developed theory suggests that current tensor product smoothing methods could be improved by incorporating the proposed tensor product spectral smoothers. Simulation results demonstrate that the proposed approach can outperform popular tensor product smoothing implementations, which supports the theoretical results developed in the paper.

  PublisherOA PDFDOI

• Versatile Descent Algorithms for Group Regularization and Variable Selection in Generalized Linear Models

  Journal of Computational and Graphical Statistics · 2024-05-31 · 4 citations

  articleOpen access1st authorCorresponding

  This paper proposes an adaptively bounded gradient descent (ABGD) algorithm for group elastic net penalized regression. Unlike previously proposed algorithms, the proposed algorithm adaptively bounds the Fisher information matrix, which results in a flexible and stable computational framework. In particular, the proposed algorithm (i) does not require orthogonalization of the predictors, and (ii) can be easily applied to any combination of exponential family response distribution and link function. The proposed algorithm is implemented in the grpnet R package (available from CRAN), which implements the approach for common response distributions (Gaussian, binomial, and Poisson), as well as several response distributions not previously considered in the group penalization literature (i.e., multinomial, negative binomial, gamma, and inverse Gaussian). Simulated and real data examples demonstrate that the proposed algorithm is as or more efficient than existing methods for Gaussian, binomial, and Poisson distributions. Furthermore, using two genomic examples, I demonstrate how the proposed algorithm can be applied to high-dimensional multinomial regression problems with grouped predictors. R code to reproduce the results is included as supplementary materials.

  PublisherOA PDFDOI

• Self-selected diets: Exploring the factors driving food choices and satisfaction with dietary variety among independent adults

  Food Quality and Preference · 2024-03-05 · 5 citations

  article
  PublisherDOI

• grpnet: Group Elastic Net Regularized GLMs and GAMs

  2023-07-13 · 3 citations

  datasetOpen access1st authorCorresponding

  Efficient algorithms for fitting generalized linear and additive models with group elastic net penalties as described in Helwig (2025) &lt;<a href="https://doi.org/10.1080%2F10618600.2024.2362232" target="_top">doi:10.1080/10618600.2024.2362232</a>&gt;. Implements group LASSO, group MCP, and group SCAD with an optional group ridge penalty. Computes the regularization path for linear regression (gaussian), multivariate regression (multigaussian), smoothed support vector machines (svm1), squared support vector machines (svm2), logistic regression (binomial), multinomial logistic regression (multinomial), log-linear count regression (poisson and negative.binomial), and log-linear continuous regression (gamma and inverse gaussian). Supports default and formula methods for model specification, k-fold cross-validation for tuning the regularization parameters, and nonparametric regression via tensor product reproducing kernel (smoothing spline) basis function expansion.

  PublisherOA PDFDOI

Frequent coauthors

• Sofía Lyford-Pike

  University of Minnesota

  11 shared

• Stephen J. Guy

  11 shared

• Nick Sohre

  University of Minnesota System

  10 shared

• Tessa A. Hadlock

  Harvard University

  9 shared

• Ping Ma

  Xinjiang University

  7 shared

• Karen B. Schloss

  6 shared

• Mark R. Ruprecht

  University of Minnesota

  5 shared

• Sungjin Hong

  4 shared

Education

• PhD, Quantitative Psychology

  University of Illinois System

  2013

• MS, Statistics

  University of Illinois System

  2010

• BS, Psychology + Mathematics

  University of Miami

  2007

Awards & honors

• Distinguished Dissertation Award, American Psychological Ass…
• Student Paper Competition Winner, American Statistical Assoc…
• Nancy Hirschberg Award (for outstanding original research or…
• Woodrow Fellowship (for outstanding original research or sch…
• Outstanding Quantitative Psychology Doctoral Student, Depart…