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NASA NTRS2017

Lessons from Astrobiological Planetary Analogue Exploration in Iceland: Biomarker Assay Performance and Downselection

Understanding the sensitivity of biomarker assays to the local physicochemical environment, and the underlying spatial distribution of the target biomarkers in 'homogeneous' environments, can increase mission science return. We have conducted four expeditions to Icelandic Mars analogue sites in which an increasingly refined battery of physicochemical measurements and biomarker assays were performed, staggered with scouting of further sites. Completed expeditions took place in 2012 (location scouting and field assay use testing), 2013 (sampling of two major sites with three assays and observational physicochemical measurements), 2015 (repeat sampling of prior sites and one new site, scouting of new sites, three assays and three instruments), and 2016 (preliminary sampling of new sites with analysis of returned samples). Target sites were geologically recent basaltic lava flows, and sample loci were arranged in hierarchically nested grids at 10 cm, 1 m, 10 m, 100 m, and >1 km order scales, subject to field constraints. Assays were intended to represent a diversity of potential biomarker types (cell counting via nucleic acid staining and fluorescence microscopy, ATP quantification via luciferase luminescence, and relative DNA quantification with simple domain-level primers) rather a specific mission science target, and were selected to reduce laboratory overhead, require limited consumables, and allow rapid turnaround. All analytical work was performed in situ or in a field laboratory within a day's travel of the field sites unless otherwise noted. We have demonstrated the feasibility of performing ATP quantification and qPCR analysis in a field-based laboratory with single-day turnaround. The ATP assay was generally robust and reliable and required minimal field equipment and training to produce a large amount of useful data. DNA was successfully extracted from all samples, but the serial-batch nature of qPCR significantly limited the number of primers (hence classifications) and replicates that could be run in a single day. Fluorescence microscopy did not prove feasible under the same constraints, primarily due to the large number of person-hours required to view, analyze, and record results from the images; however, this could be mitigated with higher-quality imaging instruments and appropriate image analysis software.

Planetary↗

NASA NTRS1984

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Broussard, J. R.↗

NASA NTRS2004

Fossil Signatures Using Elemental Abundance Distributions and Bayesian Probabilistic Classification

Elemental abundances (C6, N7, O8, Na11, Mg12, Al3, P15, S16, Cl17, K19, Ca20, Ti22, Mn25, Fe26, and Ni28) were obtained for a set of terrestrial fossils and the rock matrix surrounding them. Principal Component Analysis extracted five factors accounting for the 92.5% of the data variance, i.e. information content, of the elemental abundance data. Hierarchical Cluster Analysis provided unsupervised sample classification distinguishing fossil from matrix samples on the basis of either raw abundances or PCA input that agreed strongly with visual classification. A stochastic, non-linear Artificial Neural Network produced a Bayesian probability of correct sample classification. The results provide a quantitative probabilistic methodology for discriminating terrestrial fossils from the surrounding rock matrix using chemical information. To demonstrate the applicability of these techniques to the assessment of meteoritic samples or in situ extraterrestrial exploration, we present preliminary data on samples of the Orgueil meteorite. In both systems an elemental signature produces target classification decisions remarkably consistent with morphological classification by a human expert using only structural (visual) information. We discuss the possibility of implementing a complexity analysis metric capable of automating certain image analysis and pattern recognition abilities of the human eye using low magnification optical microscopy images and discuss the extension of this technique across multiple scales.

Hoover, Richard B.↗

DOE OSTI2025

Coalescence-Induced Spontaneous Shedding of Microdroplets on Superhydrophobic Surfaces Featuring Enclosed Micropillars with Hierarchical Roughness

This study investigated water vapor condensation on superhydrophobic surfaces (SHSs) featuring micropillars enclosed by wall lattices and having three-tier hierarchical roughness. A total of five samples were created with three (NW-J, W200-J and W400-J samples) having large micropillar depth (~6 μm) and two (NW-S and W200-S samples) having small micropillar depth (~1 μm). Two distinct condensate removal modes were observed during condensation: coalescence-induced jumping on samples with large micropillar depth and coalescence-induced shedding on samples with small micropillar depth. The results showed that the diameter of the shedding droplet on the W200-S sample having small micropillar depth could be as small as 107 μm, as compared to the theoretical critical diameter of 267 μm for gravitational shedding on the same sample. The enhanced functionality of the three-tier nanotextures on the W200-S sample could effectively suppress localized pinning of the three-phase contact line and Wenzel neck formation during the growth of condensate droplets. Consequently, during multidroplet coalescence, the released surface energy easily overcomes the solid–liquid adhesion, leading to spontaneous shedding of merged droplets. The inclusion of the wall lattice aids condensate growth by the droplet self-alignment along the walls and promoting coalescence. As a result, the W200-S sample exhibited the highest condensate collection as well. In conclusion, the proposed surface design has great potential for scaling up and implementation in heating, ventilation, and air-conditioning equipment due to the simplicity of the surface morphology and the facile spray-coating method used to achieve hierarchical roughness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2000

The Scientific Case for Sample Return from a Primitive Near-Earth Asteroid

This paper is predicated on the recent experimental findings that the smallest structural ferromagnesiosilica entities in collected chondritic aggregate interplanetary dust particles (IDPs) have a predictable metastable eutectic composition. Kinetically controlled gas to solid condensation of MgFe-SiO-O2-H2 vapors does NOT produce stoichiometric crystalline solids (i.e. minerals) such as predicted by equilibrium condensation models but instead yields amorphous solids that are chemically ordered at metastable eutectics in the binary phase diagrams. Therefore these condensed dust grains will have a considerable amount of 'internal free energy' that will make them highly responsive to changes in their environments. Their inherent high energy-content 'buys' time and energy for mineralogical modification and chemical readjustment in response to changing environmental conditions. The activation energy barrier for reactions in metastable eutectic solids will be lower than for crystalline solids. As a result the reactions can take place at much lower temperatures and on much shorter time scales. That is, they will also occur much earlier in the evolution of a parent body wherein heat-producing sources may either be immature or inefficient. The ensuing reaction chains from metastable equilibrium to full thermodynamic equilibration with the local environment will be a chaotic 'Ostwald cascade' but from a well defined starting point to a predictable end result. Here we will discuss the implications of metastable eutectic dust as we see them for dust properties in icy and ice-free parent bodies wherein circumstellar dust is still recognizable because of the primitive nature of these parent bodies. We point to potential engineering constraints on sample acquisition and storage during Earth transit. Among the scientific goals of a primitive Near Earth Asteroid (NEA) sample return mission will be verification of the nature of dust forming and modification processes during hierarchical accretion in the earliest protoplanets. We propose sampling an infrared P- or D-class NEA or an object showing cometary activity such as 2201 Oljato that could be an asteroid or evolved comet. Additional information is contained in the original extended abstract.

Rietmeijer, Frans J. M.↗

DOE OSTI2021

Evaluating the Benefits of Bayesian Hierarchical Methods for Analyzing Heterogeneous Environmental Datasets: A Case Study of Marine Organic Carbon Fluxes

Large compilations of heterogeneous environmental observations are increasingly available as public databases, allowing researchers to test hypotheses across datasets. Statistical complexities arise when analyzing compiled data due to unbalanced spatial sampling, variable environmental context, mixed measurement techniques, and other reasons. Hierarchical Bayesian modeling is increasingly used in environmental science to describe these complexities, however few studies explicitly compare the utility of hierarchical Bayesian models to simpler and more commonly applied methods. Here we demonstrate the utility of the hierarchical Bayesian approach with application to a large compiled environmental dataset consisting of 5,741 marine vertical organic carbon flux observations from 407 sampling locations spanning eight biomes across the global ocean. We fit a global scale Bayesian hierarchical model that describes the vertical profile of organic carbon flux with depth. Profile parameters within a particular biome are assumed to share a common deviation from the global mean profile. Individual station-level parameters are then modeled as deviations from the common biome-level profile. The hierarchical approach is shown to have several benefits over simpler and more common data aggregation methods. First, the hierarchical approach avoids statistical complexities introduced due to unbalanced sampling and allows for flexible incorporation of spatial heterogeneitites in model parameters. Second, the hierarchical approach uses the whole dataset simultaneously to fit the model parameters which shares information across datasets and reduces the uncertainty up to 95% in individual profiles. Third, the Bayesian approach incorporates prior scientific information about model parameters; for example, the non-negativity of chemical concentrations or mass-balance, which we apply here. We explicitly quantify each of these properties in turn. We emphasize the generality of the hierarchical Bayesian approach for diverse environmental applications and its increasing feasibility for large datasets due to recent developments in Markov Chain Monte Carlo algorithms and easy-to-use high-level software implementations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

The hierarchical growth of bright central galaxies and intracluster light as traced by the magnitude gap

Using a sample of 2800 galaxy clusters identified in the Dark Energy Survey across the redshift range 0.20 < z < 0.60, we characterize the hierarchical assembly of bright central galaxies (BCGs) and the surrounding intracluster light (ICL). To quantify hierarchical formation we use the stellar mass–halo mass (SMHM) relation, comparing the halo mass, estimated via the mass–richness relation, to the stellar mass within the BCG + ICL system. Moreover, we incorporate the magnitude gap (M14), the difference in brightness between the BCG (measured within 30 kpc) and fourth brightest cluster member galaxy within 0.5 $R_{200,c}$, as a third parameter in this linear relation. The inclusion of M14, which traces BCG hierarchical growth, increases the slope and decreases the intrinsic scatter, highlighting that it is a latent variable within the BCG + ICL SMHM relation. Moreover, the correlation with M14 decreases at large radii. However, the stellar light within the BCG + ICL transition region (30 –80 kpc) most strongly correlates with halo mass and has a statistically significant correlation with M14. Since the transition region and M14 are independent measurements, the transition region may grow due to the BCG’s hierarchical formation. Additionally, as M14 and ICL result from hierarchical growth, we use a stacked sample and find that clusters with large M14 values are characterized by larger ICL and BCG + ICL fractions, which illustrates that the merger processes that build the BCG stellar mass also grow the ICL. Furthermore, this may suggest that M14 combined with the ICL fraction can identify dynamically relaxed clusters.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

TDCOSMO - XVI. Measurement of the Hubble constant from the lensed quasar WGD 2038–4008

Time-delay cosmography is a powerful technique to constrain cosmological parameters, particularly the Hubble constant (H0). The TDCOSMO Collaboration is performing an ongoing analysis of lensed quasars to constrain cosmology using this method. In this work, we obtain constraints from the lensed quasar WGD 2038−4008 using new time-delay measurements and previous mass models by TDCOSMO. This is the first TDCOSMO lens to incorporate multiple lens modeling codes and the full time-delay covariance matrix into the cosmological inference. The models are fixed before the time delay is measured, and the analysis is performed blinded with respect to the cosmological parameters to prevent unconscious experimenter bias. We obtain DΔ t = 1.68−0.38+0.40 Gpc using two families of mass models, a power-law describing the total mass distribution, and a composite model of baryons and dark matter, although the composite model is disfavored due to kinematics constraints. In a flat ΛCDM cosmology, we constrain the Hubble constant to be H0 = 65−14+23 km s−1 Mpc−1. The dominant source of uncertainty comes from the time delays, due to the low variability of the quasar. Future long-term monitoring, especially in the era of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, could catch stronger quasar variability and further reduce the uncertainties. This system will be incorporated into an upcoming hierarchical analysis of the entire TDCOSMO sample, and improved time delays and spatially-resolved stellar kinematics could strengthen the constraints from this system in the future.Key words: gravitational lensing: strong / cosmological parameters / distance scale⋆ Corresponding author; kcwong19@gmail.com.⋆⋆ NHFP Einstein fellow.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1992

N-point correlation functions in the CfA and SSRS redshift distribution of galaxies

Using counts in cells, we estimate the volume-average N-point galaxy correlation functions for N = 2, 3, and 4, in redshift samples of the CfA and SSRS catalogs. Volume-limited samples of different sizes are used to study the uncertainties at different scales, the shot noise, and the problem with the boundaries. The hierarchical constants S3 and S4 agree well in all samples in CfA and SSRS, with average S3 = 194 +/- 0.07 and S4 = 4.56 +/- 0.53. We compare these results with estimates obtained from angular catalogs and recent analysis over IRAS samples. The amplitudes SJ seem larger in real space than in redshift space, although the values from the angular analysis correspond to smaller scales, where we might expect larger nonperturbative effects. It is also found that S3 and S4 are smaller for IRAS than for optical galaxies. This, together with the fact that IRAS galaxies have smaller amplitude for the above correlation functions, indicates that the density fluctuations of IRAS galaxies cannot be simply proportional to the density fluctuations of optical galaxies, i.e., biasing has to be nonlinear between them.

Gaztanaga, Enrique↗

NASA NTRS1989

A system architecture for a planetary rover

Each planetary mission requires a complex space vehicle which integrates several functions to accomplish the mission and science objectives. A Mars Rover is one of these vehicles, and extends the normal spacecraft functionality with two additional functions: surface mobility and sample acquisition. All functions are assembled into a hierarchical and structured format to understand the complexities of interactions between functions during different mission times. It can graphically show data flow between functions, and most importantly, the necessary control flow to avoid unambiguous results. Diagrams are presented organizing the functions into a structured, block format where each block represents a major function at the system level. As such, there are six blocks representing telecomm, power, thermal, science, mobility and sampling under a supervisory block called Data Management/Executive. Each block is a simple collection of state machines arranged into a hierarchical order very close to the NASREM model for Telerobotics. Each layer within a block represents a level of control for a set of state machines that do the three primary interface functions: command, telemetry, and fault protection. This latter function is expanded to include automatic reactions to the environment as well as internal faults. Lastly, diagrams are presented that trace the system operations involved in moving from site to site after site selection. The diagrams clearly illustrate both the data and control flows. They also illustrate inter-block data transfers and a hierarchical approach to fault protection. This systems architecture can be used to determine functional requirements, interface specifications and be used as a mechanism for grouping subsystems (i.e., collecting groups of machines, or blocks consistent with good and testable implementations).

Smith, D. B.↗

DOE OSTI2024

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Lens Model Accuracy in the Expected LSST Lensed AGN Sample

Strong gravitational lensing of active galactic nuclei (AGN) enables measurements of cosmological parameters through time-delay cosmography (TDC). With data from the upcoming LSST survey, we anticipate using a sample of O(1000) lensed AGN for TDC. To prepare for this dataset and enable this measurement, we construct and analyze a realistic mock sample of 1300 systems drawn from the OM10 (Oguri & Marshall 2010) catalog of simulated lenses with AGN sources at $z<3.1$ in order to test a key aspect of the analysis pipeline, that of the lens modeling. We realize the lenses as power law elliptical mass distributions and simulate 5-year LSST i-band coadd images. From every image, we infer the lens mass model parameters using neural posterior estimation (NPE). Focusing on the key model parameters, $θ_E$ (the Einstein Radius) and $γ_{lens}$ (the projected mass density profile slope), with consistent mass-light ellipticity correlations in test and training data, we recover $θ_E$ with less than 1% bias per lens, 6.5% precision per lens and $γ_{lens}$ with less than 3% bias per lens, 8% precision per lens. We find that lens light subtraction prior to modeling is only useful when applied to data sampled from the training prior. If emulated deconvolution is applied to the data prior to modeling, precision improves across all parameters by a factor of 2. Finally, we combine the inferred lens mass models using Bayesian Hierarchical Inference to recover the global properties of the lens sample with less than 1% bias.

Venkatraman, Padmavathi [Illinois U., Urbana; KIPA↗

DOE OSTI2023

Hierarchical reconstruction of 3D well-connected porous media from 2D exemplars using statistics-informed neural network

The relationships between porous microstructures and transport properties are of fundamental importance in various scientific and engineering applications. Due to the intricacy, stochasticity and heterogeneity of porous media, reliable characterization and modeling of transport properties often require a complete dataset of internal microstructure samples. However, it is often an unbearable cost to acquire sufficient 3D digital microstructures by purely using microscopic imaging systems. Herein this paper presents a machine learning-based technique to hierarchically reconstruct 3D well-connected porous microstructures from one isotropic or several anisotropic low-cost 2D exemplar(s). To compactly characterize the large-scale microstructural features, a Gaussian image pyramid is built for each 2D exemplar. Local morphology patterns are collected from the Gaussian image pyramids, and then they serve as the training data to embed the 2D morphological statistics into feed-forward neural networks at multiple length levels. By using a specially-developed morphology integration scheme, the 3D morphological statistics at different levels can be inferred from the statistics-informed neural networks. Gibbs sampling is adopted to hierarchically reconstruct 3D microstructures by using multi-level 3D morphological statistics, where the large-scale, regional and local morphological patterns are statistically generated and successively added to the same 3D random field. The proposed method is tested on a series of porous media with distinct morphologies, and the statistical equivalence between the reconstructed and the real microstructures is systematically evaluated by comparing morphological descriptors and transport properties. The results demonstrate that the proposed 2D-to-3D microstructure reconstruction method is a universal and efficient approach to generating morphologically and physically realistic samples of porous media.

42 ENGINEERING↗

DOE OSTI2023

Comparison of nanocomposite dispersion and distribution for several melt mixers

Breakup (dispersion) and distribution of nanoparticles are the chief hurdles towards taking advantage of nanoparticles in polymer nanocomposites for reinforcement, flame retardancy, conductivity, chromaticity, and other properties. Microscopy is often used to quantify mixing, but it has a limited field of view, does not average over bulk samples, and fails to address nano-particle hierarchical structures. Ultra-small-angle X-ray scattering (USAXS) can provide a macroscopic statistical average of nanoscale dispersion (breakup) and emergent hierarchical structure, as well as the distribution on the nanoscale. Here, this work compares several common mixer geometries for carbon black-polystyrene nanocomposites. Two twin-screw extruder geometries, typical for industrial processing of melt blends, are compared with a laboratory-scale single screw extruder and a Banbury mixer. It is found that for a given mixer, nanoscale distribution increases following a van der Waals function using accumulated strain as an analogue for temperature while macroscopic distribution/dispersion, using microscopy, does not follow this dependency. Breakup and aggregation in dispersive mixing follow expected behavior on the nanoscale. Across these drastically different mixing geometries an unexpected dependency is observed for nanoscale distributive mixing (both nano and macroscopic) as a function of accumulated strain that may reflect a transition from distributive turbulent to dispersive laminar mixing as the mixing gap is reduced.

36 MATERIALS SCIENCE↗

DOE OSTI2020

TDCOSMO - IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 km s−1 Mpc−1. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.Key words: gravitational lensing: strong / galaxies: general / galaxies: kinematics and dynamics / distance scale / cosmological parameters / cosmology: observations⋆ The full analysis is available at https://github.com/TDCOSMO/hierarchy_analysis_2020_public.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRSDate not supplied

Particle-Based Fiber Models of Woven Materials for Earth Entry Thermal Protection

Applications requiring materials with layer-to-layer strength, from basketry to thermal protection systems, use interlaced, three-dimensional woven materials. NASA is developing and deploying woven material heat shields for missions, including Artemis I (3D-MAT for compression pads) and potentially Mars Sample Return - Earth Entry System. These materials are complex, hierarchical and must protect from extreme environments and phenomena, such as deformation, impact and high-enthalpy heating. Woven material performance depends on microstructure, damage and weave geometry. Therefore, fiber-specific models are needed to simulate fiber contacts within the weave hierarchical geometry (fiber to tow to yarn to weave) and the inherent directionality of fibers. Explicit fiber models can simulate how weave microstructure evolution affects thermal and mechanical properties. We parameterize a discrete element bonded particle models (DEM-BPM) of fibers to capture thermal and mechanical behavior within and between fibers, with bonded and contact forces, respectively. We study the proportion of heat transfer and stress via the contact network, fiber bonds and the weave geometry, for example, with respect to yarn warp-weft identity (whether it interlaces weave layers). Our results demonstrate the importance of explicit fiber modeling for connecting microstructure with thermal and mechanical properties.

woven material↗

NASA NTRSDate not supplied

Particle-Based Fiber Models of Woven Materials for Earth Entry Thermal Protection

woven material↗

NASA NTRS2020

Bayesian Statistical Models for Community Annoyance Survey Data

This paper demonstrates the use of two Bayesian statistical models to analyze single-event sonic boom exposure and human annoyance data from community response surveys. Each model is fit to data from a NASA pilot study.Unlike many community noise surveys, this study used a panel sample to collect multiple observations per participant instead of a single observation. Thus, a multilevel (also known as hierarchical or mixed-effects) model is used to account for the within-subject correlation in the panel sample data. This paper describes a multilevel logistic regression model and a multilevel ordinal regression model. The paper also proposes a method for calculating a summary dose-response curve from the multilevel models that represents the population. The two models’ summary dose-response curves are visually similar. However, their estimates differ when calculating the noise dose at a fixed percent highly annoyed.

Musical instruments↗