Smoothing Spline Analysis Of Variance Research Articles

SMOOTHING SPLINE ANOVA MONITORING PHYSICAL ACTIVITY AND FALL RISK IN COMMUNITY-DWELLING OLDER ADULTS

Abstract Emerging sensing techniques, which are easily transportable, user-friendly, and cost-effective, may reveal new possibilities in monitoring daily objectively measured physical activity (PA) and fall risk appraisal (FRA) identification. We used a Smoothing Spline Analysis of Variance (SS-ANOVA) to profile the daily PA using accelerometer-based device across FRA groups. Using the BTrackS system (static balance assessment) and a short Fall-Efficacy Scale-International, 124 participants (mean age 75, range 60-96, 77% female, 72% no history of falls) were categorized into four different FRA groups: rational (46.8%, low fear of falling (FOF) and normal balance), irrational (17.7%, high FOF and normal balance), incongruent (19.4%, low FOF and poor balance), and congruent (16.1%, high FOF and poor balance). The vector magnitude (VM) and the number of steps were extracted per second from an average 10 (SD=4.89) consecutive days of PA recording. Daily (0-24h) temporal trend was analyzed from 1.7 million records. Groupwise, PA of the congruent group was significantly lower than other three groups, while the rational group had the highest PA based on 95% Bayesian C.I. It is evident that there is a periodic trend in PA; in particular, inactive during night (12-5am), increasing trend in the morning (5am-noon) and peak at noon, moderately decrease in the afternoon (noon-6pm), and significantly decline in the evening. No significant gender differences in PA were found. These results indicate that FOF associated with poor balance contributes to low PA, highlighting the necessity of balance enhancing intervention and cognitive reframing to promote PA in older populations.

Design as Exploration

There are an increasing number of optimal-design paradigms used in architectural design nowadays. In these paradigms, a design task is formulated, or partially formulated, as an optimization problem. Multi-Disciplinary Optimization and Multi-Objective Optimization, as two important optimal-design paradigms, have shown their great potential in improving the performances of complex buildings in recent decades. Nevertheless, current paradigms for ill‑defined conceptual architectural design still lack ways to ensure the achievement of a reliable optimization problem, which hinders reliable design solutions despite the use of advanced optimization algorithms. To address this problem, it is necessary to shift the focus from Optimization Problem Solving to Optimization Problem Formulation. This research particularly focuses on knowledge‑supported, dynamic and interactive Optimization Problem Re-Formulation in order to construct a new Multi‑Objective and Multi-Disciplinary Optimization (MOMDO) method suitable for use in ill‑defined conceptual architectural design. The proposed method consists of two subtype methods: Non‑dynamic, Interactive Re-formulation method (Subtype-I) and Dynamic, Interactive Re‑formulation method (Subtype-II), which can be used to explore design space in a convergent and divergent manner respectively. To support the re-formulation, various kinds of information and knowledge need to be extracted by utilizing different computational techniques, such as advanced sampling algorithms, Self-Organizing Map, Hierarchical Clustering, Smoothing Spline Analysis of Variance, Two-Level Variable Structure and modular programming. Moreover, a software workflow that can provide these computational techniques is developed; it integrates McNeel’s Grasshopper, ESTECO's modeFRONTIER and simulation software tools Daysim, EnergyPlus and Karamba3D. With the support of this software workflow, the proposed method is demonstrated via two case studies concerning the conceptual design of indoor sports halls.

Variation in global and intonational pitch settings among black and white speakers of Southern American English.

This article revisits classic questions about how pitch varies between groups by examining global and intonational pitch differences between black and white speakers from Memphis, Tennessee, using data from read speech to control for stylistic and segmental variables. Results from both mixed-effects regression modeling and smoothing spline analysis of variance find no difference between black and white men in mean F0 and pitch range measures. However, black women produced consistently lower mean F0 than white women. These findings suggest that while pitch patterns in black women's speech remain underexplored in the literature, they may play an important role in shaping attitudes and ideological associations concerning black American speakers in general. Moreover, vocal pitch may be a linguistic variable subject to variation, especially in a context of racialized and gendered linguistic standards.

A Cross-Sectional Age Group Study of Coarticulatory Resistance: The Case of Late-Acquired Voiceless Fricatives in English.

As a class, fricatives are more "resistant" to consonant-vowel coarticulation than other English sounds. This study investigates the relative coarticulatory resistance of /θ, s, ʃ/ in child and adult speech to better understand the acquisition of individuated speech sounds. Ten 5-year-old children, seven 8-year-old children, and nine college-age adults produced [əFV] sequences in carrier phrases, where F was /θ/, /s/, or /ʃ/ and V was /æ/, /i/, or /u/. In Experiment 1, coarticulation was perceptually indexed: 65 adults predicted the target stressed vowel based on forward-gated audiovisual speech samples for a subset of four speakers from each age group. In Experiment 2, dynamic spectral measures of the /əFV/ sequences were analyzed using smoothing spline analysis of variance to again test for vowel effects on fricative articulation across age groups. The perceptual results indicated that fricatives blocked vowel-vowel coarticulation across speaker age groups. Contrary to expectation, vowels were most accurately predicted when F was /s/ and not when it was /ʃ/ or /θ/ across age groups. Acoustic results indicated the expected biomechanically motivated /ʃ/ > /s/ > /θ/ coarticulatory resistance hierarchy in adults' speech. By contrast, /ʃ/ > /s/ were similarly influenced by context in 8-year-olds' speech, and the results from 5-year-olds' speech suggested an influence of order of acquisition in that /θ/ was surprisingly resistant to coarticulation. The study results are taken to suggest that a temporal constraint on fricative articulation interacts with biomechanical constraints during development to influence patterns of coarticulation in school-age children's speech.

Estimation and Model Selection for Nonparametric Function-on-Function Regression

Regression models with a functional response and functional covariate have received significant attention recently. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. In this article, we develop a unified framework for estimation and model selection in nonparametric function-on-function regression. We propose a general nonparametric functional regression model with the model space constructed through smoothing spline analysis of variance (SS ANOVA). The proposed model reduces to some of the existing models when selected components in the SS ANOVA decomposition are eliminated. We propose new estimation procedures under either L 1 or L 2 penalty and show that the combination of the SS ANOVA decomposition and L 1 penalty provides powerful tools for model selection and diagnostics. We establish consistency and convergence rates for estimates of the regression function and each component in its decomposition under both the L 1 and L 2 penalties. Simulation studies and real examples show that the proposed methods perform well. Technical details and additional simulation results are available in online supplementary materials.

Normative cervical spine kinematics of a circumduction task

Neck pain is a prevalent condition and clinical examination techniques are limited and unable to assess out-of-plane motion. Recent works investigating cervical kinematics during neck circumduction (NC), a dynamic 3D task, has shown the ability to discern those with and without neck pain. The purposes of this study were to establish 1) confidence and prediction intervals of head-to-torso kinematics during NC in a healthy cohort, 2) a baseline summative metric to quantify the duration and magnitude of deviations outside the prediction interval, and 3) the reliability of NC. Thirty-nine participants (25.6 ± 6.3 years, 19F/20M) without neck pain completed left and right NC. A two-way smoothing spline analysis of variance was utilized to determine the mean-fitted values and 90% confidence and prediction intervals for NC. A standardized effect size was calculated and aggregated across all axes (Delta RMSD aggregate), as a summative metric of motion quality. Confidence and prediction intervals were comparable for left and right NC and demonstrated excellent reliability. The average sum of the Delta RMSD aggregate was 2.76 ± 0.55 for left NC and 2.74 ± 0.63 for right NC. The results of this study demonstrate the feasibility of utilizing normative intervals of a NC task to assess head-to-torso kinematics.

Hierarchical Total Variations and Doubly Penalized ANOVA Modeling for Multivariate Nonparametric Regression

For multivariate nonparametric regression, functional analysis of variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main effects, two-way interactions, etc. Such an approach has been pursued explicitly in smoothing spline ANOVA modeling and implicitly in various greedy methods such as MARS. We develop a new method for functional ANOVA modeling, based on doubly penalized estimation using total-variation and empirical-norm penalties, to achieve sparse selection of component functions and their basis functions. For this purpose, we formulate a new class of hierarchical total variations, which measures total variations at different levels including main effects and multi-way interactions, possibly after some order of differentiation. Furthermore, we derive suitable basis functions for multivariate splines such that the hierarchical total variation can be represented as a regular Lasso penalty, and hence we extend a previous backfitting algorithm to handle doubly penalized estimation for ANOVA modeling. We present extensive numerical experiments on simulations and real data to compare our method with existing methods including MARS, tree boosting, and random forest. The results are very encouraging and demonstrate notable gains from our method in prediction or classification accuracy and simplicity of the fitted functions. Supplementary materials for this article are available online.

Kernel Ordinary Differential Equations

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations. We do not assume the functional forms in ODE to be known, or restrict them to be linear or additive, and we allow pairwise interactions. We perform sparse estimation to select individual functionals, and construct confidence intervals for the estimated signal trajectories. We establish the estimation optimality and selection consistency of kernel ODE under both the low-dimensional and high-dimensional settings, where the number of unknown functionals can be smaller or larger than the sample size. Our proposal builds upon the smoothing spline analysis of variance (SS-ANOVA) framework, but tackles several important problems that are not yet fully addressed, and thus extends the scope of existing SS-ANOVA as well. We demonstrate the efficacy of our method through numerous ODE examples.

Construction of Design Guidelines for Optimal Automotive Frame Shape Based on Statistical Approach and Mechanical Analysis

A body frame composed of thin sheet metal is a crucial structure that determines the safety performance of a vehicle. Designing a correct weight and high-performance automotive body is an emerging engineering problem. To improve the performance of the automotive frame, we attempt to reconstruct its design criteria based on statistical and mechanical approaches. At first, a fundamental study on the frame strength is conducted and a cross-sectional shape optimization problem is developed for designing the cross-sectional shape of an automobile frame having a very high mass efficiency for strength. Shape optimization is carried out using the nonlinear finite element method and a meta-modeling-based genetic algorithm. Data analysis of the obtained set of optimal results is performed to identify the dominant design variables by employing the smoothing spline analysis of variance, the principal component analysis, and the self-organizing map technique. The relationship between the cross-sectional shape and the objective function is also analyzed by hierarchical clustering. A design guideline is obtained from these statistical approach results. A comparison between the statistically obtained design guideline and the conventional one based on the designers’ experience is performed based on mechanical interpretation of the optimal cross-sectional frame. Finally, a mechanically reasonable new general-purpose design guideline is proposed for the cross-sectional shape of the automotive frame.

Spectrally Sparse Nonparametric Regression via Elastic Net Regularized Smoothers

Nonparametric regression frameworks, such as generalized additive models (GAMs) and smoothing spline analysis of variance (SSANOVA) models, extend the generalized linear model (GLM) by allowing for unknown functional relationships between an exponential family response variable and a collection of predictor variables. The unknown functional relationships are typically estimated using penalized likelihood estimation, which adds a roughness penalty to the (negative) log-likelihood function. In this article, I propose a spectral parameterization of a smoothing spline, which allows for an efficient application of Elastic Net regression to smooth and select eigenvectors of a kernel matrix. The classic (ridge regression) solution for a smoothing spline is a special case of the proposed kernel eigenvector smoothing and selection operator. Extensions for tensor product smoothers are developed for both the GAM and SSANOVA frameworks. Using simulated and real data examples, I demonstrate that the proposed approach offers practical and computational gains over typical approaches for fitting GAMs, SSANOVA models, and Elastic Net penalized GLMs. Supplementary materials for this article are available online.

Statistical regularization for trend detection: an integrated approach for detecting long-term trends from sparse tropospheric ozone profiles

Abstract. Detecting a tropospheric ozone trend from sparsely sampled ozonesonde profiles (typically once per week) is challenging due to the short-lived anomalies in the time series resulting from ozone's high temporal variability. To enhance trend detection, we have developed a sophisticated statistical approach that utilizes a geoadditive model to assess ozone variability across a time series of vertical profiles. Treating the profile time series as a set of individual time series on discrete pressure surfaces, a class of smoothing spline ANOVA (analysis of variance) models is used for the purpose of jointly modeling multiple correlated time series (on separate pressure surfaces) by their associated seasonal and interannual variabilities. This integrated fit method filters out the unstructured variation through a statistical regularization (i.e., a roughness penalty) by taking advantage of the additional correlated data points available on the pressure surfaces above and below the surface of interest. We have applied this technique to the trend analysis of the vertically correlated time series of tropospheric ozone observations from (1) IAGOS (In-service Aircraft for a Global Observing System) commercial aircraft profiles above Europe and China throughout 1994–2017 and (2) NOAA GML's (Global Monitoring Laboratory) ozonesonde records at Hilo, Hawaii, (1982–2018) and Trinidad Head, California (1998–2018). We illustrate the ability of this technique to detect a consistent trend estimate and its effectiveness in reducing the associated uncertainty in the profile data due to the low sampling frequency. We also conducted a sensitivity analysis of frequent IAGOS profiles above Europe (approximately 120 profiles per month) to determine how many profiles in a month are required for reliable long-term trend detection. When ignoring the vertical correlation, we found that a typical sampling strategy (i.e. four profiles per month) might result in 7 % of sampled trends falling outside the 2σ uncertainty interval derived from the full dataset with an associated 10 % of mean absolute percentage error. Based on a series of sensitivity studies, we determined optimal sampling frequencies for (1) basic trend detection and (2) accurate quantification of the trend. When applying the integrated fit method, we find that a typical sampling frequency of four profiles per month is adequate for basic trend detection; however, accurate quantification of the trend requires 14 profiles per month. Accurate trend quantification can be achieved with only 10 profiles per month if a regular sampling frequency is applied. In contrast, the standard separated fit method, which ignores the vertical correlation between pressure surfaces, requires 8 profiles per month for basic trend detection and 18 profiles per month for accurate trend quantification. While our method improves trend detection from sparse datasets, the key to substantially reducing the uncertainty is to increase the sampling frequency.

Modular regression - a Lego system for building structured additive distributional regression models with tensor product interactions

Semiparametric regression models offer considerable flexibility concerning the specification of additive regression predictors including effects as diverse as nonlinear effects of continuous covariates, spatial effects, random effects, or varying coefficients. Recently, such flexible model predictors have been combined with the possibility to go beyond pure mean-based analyses by specifying regression predictors on potentially all parameters of the response distribution in a distributional regression framework. In this paper, we discuss a generic concept for defining interaction effects in such semiparametric distributional regression models based on tensor products of main effects. These interactions can be assigned anisotropic penalties, i.e. different amounts of smoothness will be associated with the interacting covariates. We investigate identifiability and the decomposition of interactions into main effects and pure interaction effects (similar as in a smoothing spline analysis of variance) to facilitate a modular model building process. The decomposition is based on orthogonality in function spaces which allows for considerable flexibility in setting up the effect decomposition. Inference is based on Markov chain Monte Carlo simulations with iteratively weighted least squares proposals under constraints to ensure identifiability and effect decomposition. One important aspect is therefore to maintain sparse matrix structures of the tensor product also in identifiable, decomposed model formulations. The performance of modular regression is verified in a simulation on decomposed interaction surfaces of two continuous covariates and two applications on the construction of spatio-temporal interactions for the analysis of precipitation on the one hand and functional random effects for analysing house prices on the other hand.

Nasal coarticulation in Bininj Kunwok: An aerodynamic analysis

Bininj Kunwok (BKw), a language spoken in Northern Australia, restricts the degree of anticipatory nasalization, as suggested by previous aerodynamic and acoustic analyses (Butcher 1999). The current study uses aerodynamic measurements of speech to investigate patterns of nasalization and nasal articulation in Bininj Kunwok to compare with Australian languages more generally. The role of nasal coarticulation in ensuring language compre-hensibility a key question in phonetics research today is explored. Nasal aerodynamics is measured in intervocalic, word-medial nasals in the speech of five female speakers of BKw and data are analyzed using Smoothing Spline Analysis of Variance (SSANOVA) and Functional Data Analysis averaging techniques. Results show that in a VNV sequence there is very little anticipatory vowel nasalization with no restriction on carryover nasalization for a following vowel. The maximum peak nasal flow is delayed until the oral release of a nasal for coronal articulations, indicating a delayed velum opening gesture. Patterns of anticipatory nasalization appears similar to nasal airflow in French non-nasalized vowels in oral vowel plus nasal environments (Delvaux et al. 2008). Findings show that Bininj Kunwok speakers use language specific strategies in order to limit anticipatory nasalization, enhancing place of articulation cues at a site of intonational prominence which also is also the location of the majority of place of articulation contrasts within the language. Patterns of airflow suggest enhancement and coarticulatory resistance in prosodically prominent VN and VNC sequences which we interpret as evidence of speakers maintaining a phonological contrast to enhance place of articulation cues.

An SS ANOVA (Smoothing Spline Analysis of Variance) study of high tone lowering in Tsua

This article examines the acoustic phonetic properties of consonant-tone interaction in the Khoisan language, Tsua, using speech production data from original field research in Botswana. The Tsua tonal melodies with Fundamental Frequency (F0) shapes having the most extreme excursions are the result of a rare consonant-tone interaction pattern with depressor types found in both African and East Asian tone languages. The Tsua depressor types are voiced obstruents, aspirated obstruents and the glottal fricative /h/. Statistical analysis via Smoothing Spline Analysis of Variance (SS ANOVA) reveals two striking generalisations: (i) only root-initial High tones followed by a non-High tone are depressed; and (ii) the overall shapes of the F0 curves are more important for tone melody identification than whether they are produced at a slightly higher or lower Hertz value, even if the difference is statistically significant. The first finding reflects the context-dependent nature of Tsua tonal depression. The second stands in contrast to studies of other tone systems that suggest the relative Hertz differential between adjacent tones is more important for identification. These findings expand our knowledge of tonal phonetics by showing what is possible in a typologically rare tone system, and highlight the importance of statistical methods in phonetic fieldwork.

Sensitivity analysis of the dynamic response of an electronic fuel injector regarding fuel properties and operating conditions

The sensitivity of fuel properties to the dynamic response (needle valve opening/closing delay and needle valve opening/closing time) of a electronic fuel injector was investigated. The fuel properties in different operating conditions were varied individually in bulk modulus, density and viscosity. Firstly, an electronic fuel injector model was built and validated by injection rate and injection mass at three different rail pressures and three different activation times. Secondly, a DOE (design of experiment) model was built and the Uniform Latin Hypercube (ULH) design method was applied to study the influences of the fuel properties on the injector dynamic response from a statistical point of view. The effects of the fuel properties were compared by using a SS-ANOVA (smoothing spline analysis of variance) method at both a low and a high rail pressure. The bulk modulus was found to play a dominant role in influencing the valve opening/closing delay at the low rail pressure. However, at the high rail pressure, the effects of the viscosity are prominent, while the effects of the bulk modulus and the density are negligible. Additionally, how these fuel properties affect the dynamic response were reported by RSM (Response Surface Method) function charts, and the details of the pressure differences and needle valve movements were also disclosed.

Bayes Factors for Smoothing Spline ANOVA

This paper describes an approach for variable selection and hypothesis testing in semiparametric additive models using Bayes factors in smoothing spline analysis of variance (SSANOVA) models. Effects can be linear or nonparametric (i.e., smooth or interactions between selected linear and smooth effects). To evaluate the importance of each term in the model, we develop Bayes factors for both linear and nonparametric terms. We compute approximate Bayes factors by Monte Carlo and Laplace integration. These Bayes factors can be computed to compare any two sub-models including one model nested in another. This permits formal tests of any portion or simultaneous portions of an SSANOVA model. We demonstrate this approach with an example.

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.

Complete tonal neutralization in Taiwan southern Min

This study reported the result of a production experiment on the tonal neutralization of context unchecked 21 tone and checked 21 tone with a glottal stop coda in Taiwan Southern Min, which are said to be realized the same as a high falling sandhi tone 51 on surface when occurring in context positions. Speakers of two age groups, younger and older, were recruited for the production experiments to examine whether the neutralization is complete. The comparison between the f0 contours was conducted with smoothing spline analysis of variance, and it showed a case of complete neutralization for both age groups, where the two f0 contours were simply overlapped. As reported by linear mixed effects modeling, the durations of the target syllables with underlying checked and unchecked 21 tones were not significantly different from each other.

Analyzing spatiotemporal trends in social media data via smoothing spline analysis of variance

Social media have become an integral part of life for many individuals, and social media websites generate incredible amounts of data on a variety of societal topics. Furthermore, some social media posts contain geolocation information, so social media data can be viewed as a spatiotemporal phenomenon. To understand spatiotemporal trends in ultra-large sample social media data, we propose a novel application of the Smoothing Spline Analysis of Variance (SSANOVA) framework, which is a nonparametric approach capable of discovering latent functional relationships in noisy data. Unlike currently available approaches, our proposed SSANOVA framework (a) makes few assumptions about the nature of the spatiotemporal trend, (b) provides a mean of assessing the uncertainty of the estimated spatiotemporal trend, and (c) is scalable to analyze massive samples of social media data. To demonstrate the potential of our approach, we model the daily spatiotemporal Twitter trend in the United States. Our results reveal that the proposed SSANOVA approach can provide accurate and informative estimates of spatiotemporal social media trends, as well as useful information about the precision of the estimated spatiotemporal trends.

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.