scholarly journals Multivariate functional additive mixed models

2021 ◽  
pp. 1471082X2110561
Author(s):  
Alexander Volkmann ◽  
Almond Stöcker ◽  
Fabian Scheipl ◽  
Sonja Greven
Keyword(s):  
Mixed Model ◽  
Principal Component ◽  
Repeated Measurements ◽  
Confidence Bands ◽  
Functional Principal Component Analysis ◽  
Dependency Structure ◽  
Movement Trajectories ◽  
Sports Science ◽  
Covariate Effects ◽  
Functional Additive

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary such as precipitation, temperature and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by, for example, repeated measurements or crossed study designs. Modelling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modelling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.

scholarly journals A functional mixed model for scalar on function regression with application to a functional MRI study

Biostatistics ◽  
2019 ◽  
Author(s):  
Wanying Ma ◽  
Luo Xiao ◽  
Bowen Liu ◽  
Martin A Lindquist
Keyword(s):  
Mixed Model ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Thermal Pain ◽  
Specific Effects ◽  
Functional Principal Component ◽  
Fmri Study ◽  
Subject Specific ◽  
Brain Hemodynamics ◽  
Mri Study

Summary Motivated by a functional magnetic resonance imaging (fMRI) study, we propose a new functional mixed model for scalar on function regression. The model extends the standard scalar on function regression for repeated outcomes by incorporating subject-specific random functional effects. Using functional principal component analysis, the new model can be reformulated as a mixed effects model and thus easily fit. A test is also proposed to assess the existence of the subject-specific random functional effects. We evaluate the performance of the model and test via a simulation study, as well as on data from the motivating fMRI study of thermal pain. The data application indicates significant subject-specific effects of the human brain hemodynamics related to pain and provides insights on how the effects might differ across subjects.

scholarly journals Separation of Chromatographic Co-Eluted Compounds by Clustering and by Functional Data Analysis

Metabolites ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 214
Author(s):  
Aneta Sawikowska ◽  
Anna Piasecka ◽  
Piotr Kachlicki ◽  
Paweł Krajewski
Keyword(s):  
Simulated Data ◽  
Principal Component ◽  
Real Data ◽  
Functional Principal Component Analysis ◽  
Additional Advantage ◽  
Time Alignment ◽  
Peak Separation ◽  
Biological Mixtures ◽  
Overlapping Peaks ◽  
Retention Time Alignment

Peak overlapping is a common problem in chromatography, mainly in the case of complex biological mixtures, i.e., metabolites. Due to the existence of the phenomenon of co-elution of different compounds with similar chromatographic properties, peak separation becomes challenging. In this paper, two computational methods of separating peaks, applied, for the first time, to large chromatographic datasets, are described, compared, and experimentally validated. The methods lead from raw observations to data that can form inputs for statistical analysis. First, in both methods, data are normalized by the mass of sample, the baseline is removed, retention time alignment is conducted, and detection of peaks is performed. Then, in the first method, clustering is used to separate overlapping peaks, whereas in the second method, functional principal component analysis (FPCA) is applied for the same purpose. Simulated data and experimental results are used as examples to present both methods and to compare them. Real data were obtained in a study of metabolomic changes in barley (Hordeum vulgare) leaves under drought stress. The results suggest that both methods are suitable for separation of overlapping peaks, but the additional advantage of the FPCA is the possibility to assess the variability of individual compounds present within the same peaks of different chromatograms.

scholarly journals PSVII-18 Fatty acid composition of the longissimus muscle from Angus and Wagyu sired cattle at the 6th and 12th rib location

2020 ◽  
Vol 98 (Supplement_3) ◽  
pp. 211-212
Author(s):  
Jerad Jaborek ◽  
Francis L Fluharty ◽  
Alejandro E Relling
Keyword(s):  
Fatty Acid ◽  
Mixed Model ◽  
Random Effect ◽  
Repeated Measurements ◽  
Longissimus Muscle ◽  
Trans Isomers ◽  
Fa Composition ◽  
Effect Of Treatment ◽  
Similar Body ◽  
Location Interaction

Abstract The fatty acid (FA) composition of the longissimus muscle (LM) of Angus and Wagyu sired cattle raised to a similar body weight (612 kg) were compared at the 6th and 12th rib locations. Angus sired steers represented T1, cattle from a Wagyu sire selected for growth represented T2, and cattle from a Wagyu sire selected for marbling represented T3. Data were analyzed mixed model with repeated measurements on animal (LM location); the model include the fixed effect of treatment, LM location, and their interaction, and random effect of sex. The percentage of 16:0, 18:1cis9, 18:3, and monounsaturated FA (MUFA) exhibited a treatment*LM location interaction (P ≤ 0.7), where T2 cattle had a greater percentage of 16:0 and a lesser percentage of 18:1cis9, 18:3, and MUFA at the 12th rib vs. 6th rib location compared with T1 and T3 cattle. The percentage of total FA lipid, polyunsaturated FA(PUFA), and PUFA:SFA ratio in the LM were greater (P ≤ 0.02) for T3 cattle compared with T1 and T2 cattle. The percentage of 18:0 was greater (P ≤ 0.01) for T1 cattle compared with T2 and T3 cattle, while T1 cattle had a greater (P ≤ 0.01) percentage of saturated FA (SFA) compared to T3 cattle. The percentage of 18:1cis9, other 18:1cis isomers, 18:2, MUFA, and MUFA:SFA ratio were greater (P ≤ 0.02) for T3 cattle compared with T1 cattle, with T2 cattle being intermediate. The percentage of total FA lipid, 18:0, 18:1 trans isomers, and SFA were greater (P ≤ 0.01) at the 6th rib LM location, while 14:1, 18:cis9, other 18:1 cis isomers, MUFA, MUFA:SFA, and PUFA:SFA ratio were greater (P ≤ 0.02) at the 12th rib LM location

scholarly journals Associations between Google Search Trends for Symptoms and COVID-19 Confirmed and Death Cases in the United States

2021 ◽  
Vol 18 (9) ◽  
pp. 4560
Author(s):  
Mostafa Abbas ◽  
Thomas B. Morland ◽  
Eric S. Hall ◽  
Yasser EL-Manzalawy
Keyword(s):  
Functional Data ◽  
Time Series Data ◽  
Principal Component ◽  
State Level ◽  
The United States ◽  
Functional Principal Component Analysis ◽  
Series Data ◽  
Dynamic Correlation ◽  
The Us ◽  
Google Search

We utilize functional data analysis techniques to investigate patterns of COVID-19 positivity and mortality in the US and their associations with Google search trends for COVID-19-related symptoms. Specifically, we represent state-level time series data for COVID-19 and Google search trends for symptoms as smoothed functional curves. Given these functional data, we explore the modes of variation in the data using functional principal component analysis (FPCA). We also apply functional clustering analysis to identify patterns of COVID-19 confirmed case and death trajectories across the US. Moreover, we quantify the associations between Google COVID-19 search trends for symptoms and COVID-19 confirmed case and death trajectories using dynamic correlation. Finally, we examine the dynamics of correlations for the top nine Google search trends of symptoms commonly associated with COVID-19 confirmed case and death trajectories. Our results reveal and characterize distinct patterns for COVID-19 spread and mortality across the US. The dynamics of these correlations suggest the feasibility of using Google queries to forecast COVID-19 cases and mortality for up to three weeks in advance. Our results and analysis framework set the stage for the development of predictive models for forecasting COVID-19 confirmed cases and deaths using historical data and Google search trends for nine symptoms associated with both outcomes.

scholarly journals Functional ANOVA approaches for detecting changes in air pollution during the COVID-19 pandemic

2021 ◽  
Author(s):  
Christian Acal ◽  
Ana M. Aguilera ◽  
Annalina Sarra ◽  
Adelia Evangelista ◽  
Tonio Di Battista ◽  
...  
Keyword(s):  
Air Pollution ◽  
Air Quality ◽  
Functional Data ◽  
Central Italy ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Area Of Interest ◽  
Pm 10 ◽  
The Impact ◽  
Monitoring Stations

AbstractFaced with novel coronavirus outbreak, the most hard-hit countries adopted a lockdown strategy to contrast the spread of virus. Many studies have already documented that the COVID-19 control actions have resulted in improved air quality locally and around the world. Following these lines of research, we focus on air quality changes in the urban territory of Chieti-Pescara (Central Italy), identified as an area of criticality in terms of air pollution. Concentrations of $$\hbox {NO}_{{2}}$$ NO 2 , $$\hbox {PM}_{{10}}$$ PM 10 , $$\hbox {PM}_{2.5}$$ PM 2.5 and benzene are used to evaluate air pollution changes in this Region. Data were measured by several monitoring stations over two specific periods: from 1st February to 10 th March 2020 (before lockdown period) and from 11st March 2020 to 18 th April 2020 (during lockdown period). The impact of lockdown on air quality is assessed through functional data analysis. Our work makes an important contribution to the analysis of variance for functional data (FANOVA). Specifically, a novel approach based on multivariate functional principal component analysis is introduced to tackle the multivariate FANOVA problem for independent measures, which is reduced to test multivariate homogeneity on the vectors of the most explicative principal components scores. Results of the present study suggest that the level of each pollutant changed during the confinement. Additionally, the differences in the mean functions of all pollutants according to the location and type of monitoring stations (background vs traffic), are ascribable to the $$\hbox {PM}_{{10}}$$ PM 10 and benzene concentrations for pre-lockdown and during-lockdown tenure, respectively. FANOVA has proven to be beneficial to monitoring the evolution of air quality in both periods of time. This can help environmental protection agencies in drawing a more holistic picture of air quality status in the area of interest.

Assessing bias, precision, and agreement in method comparison studies

2019 ◽  
Vol 29 (3) ◽  
pp. 778-796 ◽  
Author(s):  
Patrick Taffé
Keyword(s):  
Measurement Method ◽  
Method Comparison ◽  
Estimation Procedure ◽  
Measurement Methods ◽  
Repeated Measurements ◽  
Confidence Bands ◽  
The Other ◽  
Reference Standard ◽  
Simultaneous Confidence Bands ◽  
Index Of Agreement

Recently, a new estimation procedure has been developed to assess bias and precision of a new measurement method, relative to a reference standard. However, the author did not develop confidence bands around the bias and standard deviation curves. Therefore, the goal in this paper is to extend this methodology in several important directions. First, by developing simultaneous confidence bands for the various parameters estimated to allow formal comparisons between different measurement methods. Second, by proposing a new index of agreement. Third, by providing a series of new graphs to help the investigator to assess bias, precision, and agreement between the two measurement methods. The methodology requires repeated measurements on each individual for at least one of the two measurement methods. It works very well to estimate the differential and proportional biases, even with as few as two to three measurements by one of the two methods and only one by the other. The repeated measurements need not come from the reference standard but from either measurement methods. This is a great advantage as it may sometimes be more feasible to gather repeated measurements with the new measurement method.

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