APPLICATION OF MULTIPLE REGRESSION ANALYSIS TO IDENTIFICATION TIME-VARYING LINEAR DYNAMIC SYSTEMS
Dynamic response characteristics of time-varying linear systems
LINEAR SYSTEM↗
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APPLICATION OF MULTIPLE REGRESSION ANALYSIS TO IDENTIFICATION OF TIME-VARYING LINEAR DYNAMIC SYSTEMS
Determining the dynamic response characteristics of time-varying linear systems
LINEAR SYSTEM↗
Digital controllers for VTOL aircraft
Using linear-optimal estimation and control techniques, digital-adaptive control laws have been designed for a tandem-rotor helicopter which is equipped for fully automatic flight in terminal area operations. Two distinct discrete-time control laws are designed to interface with velocity-command and attitude-command guidance logic, and each incorporates proportional-integral compensation for non-zero-set-point regulation, as well as reduced-order Kalman filters for sensor blending and noise rejection. Adaptation to flight condition is achieved with a novel gain-scheduling method based on correlation and regression analysis. The linear-optimal design approach is found to be a valuable tool in the development of practical multivariable control laws for vehicles which evidence significant coupling and insufficient natural stability.
Stengel, R. F.↗
Remote Sensing as a Landscape Epidemiologic Tool to Identify Villages at High Risk for Malaria Transmission
A landscape approach using remote sensing and Geographic Information System (GIS) technologies was developed to discriminate between villages at high and low risk for malaria transmission, as defined by adult Anopheles albimanus abundance. Satellite data for an area in southern Chiapas, Mexico were digitally processed to generate a map of landscape elements. The GIS processes were used to determine the proportion of mapped landscape elements surrounding 40 villages where An. albimanus data had been collected. The relationships between vector abundance and landscape element proportions were investigated using stepwise discriminant analysis and stepwise linear regression. Both analyses indicated that the most important landscape elements in terms of explaining vector abundance were transitional swamp and unmanaged pasture. Discriminant functions generated for these two elements were able to correctly distinguish between villages with high ind low vector abundance, with an overall accuracy of 90%. Regression results found both transitional swamp and unmanaged pasture proportions to be predictive of vector abundance during the mid-to-late wet season. This approach, which integrates remotely sensed data and GIS capabilities to identify villages with high vector-human contact risk, provides a promising tool for malaria surveillance programs that depend on labor-intensive field techniques. This is particularly relevant in areas where the lack of accurate surveillance capabilities may result in no malaria control action when, in fact, directed action is necessary. In general, this landscape approach could be applied to other vector-borne diseases in areas where: 1. the landscape elements critical to vector survival are known and 2. these elements can be detected at remote sensing scales.
Beck, Louisa R.↗
Characterization and Evaluation of Acid Rain in East Central Florida from 1978 to 1995 and Evaluation of Some Chromatographic/Spectroscopic Results from Leachate Samples from CELSS
The results of monitoring the chemical composition of rain in east-central Florida have shown that the rain is moderately acid. The measured acidity of rain is less than that observed in other regions of the U. S., however, it does suggest that the level of acidity is substantial. The annual chemical composition of rain at UCF and at KSC has shown moderate variability. Extreme daily and monthly variations are observed, however these variations are not addressed here. The total ionic composition of rain collected at FL99 is greater than that for rain collected at UCF, however this can be accounted for by site proximity to the ocean with the accompanying marine influence. Difference in acidity data collected from the UCF and FL99 sites which are separated by 50 km may be due in part to the differences that have been observed between laboratory and field pH measurements. Trend assessment for precipitation composition requires evaluation of data that covers some minimum time period. In fact, the subdivision of the multi-year UCF record into individual 10 year records as described above can lead to the conclusion that a significant increase, a significant decrease or no trend exists for acidity depending upon the time period chosen for evaluation. Trend evaluation has also been accomplished by linear and nonlinear regression analysis using monthly volume weighted average concentrations and deposition using the UCF data set and some of the Florida NADP data set.
Madsen, Brooks C.↗
Physical Interpretation of the Correlation Between Multi-Angle Spectral Data and Canopy Height
Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally
Schull, M. A.↗
Improved Understanding of the Modeled QBO Using MLS Observations and MERRA Reanalysis
The Quasi-Biennial Oscillation (QBO) dominates the variability of the tropical stratosphere on interannual time scales. The QBO has been shown to extend its influence into the chemical composition of this region through dynamical mechanisms. We have started our analysis using the realistic QBO internally generated by the Goddard Earth Observing System Version 5 (GEOS-5) general circulation model coupled to a comprehensive stratospheric and tropospheric chemical mechanism forced with observed sea surface temperatures over the past 33 years. We will show targeted comparisons with observations from NASAs Aura satellite Microwave Limb Sounder (MLS) and the Modern Era Retrospective-Analysis for Research and Applications (MERRA) reanalysis to provide insight into the simulation of the primary and secondary circulations associated with the QBO. Using frequency spectrum analysis and multiple linear regression we can illuminate the resulting circulations and deduce the strengths and weaknesses in their modeled representation. Inclusion of the QBO in our simulation improves the representation of the subtropical barriers and overall tropical variability. The QBO impact on tropical upwelling is important to quantify when calculating trends in sub-decadal scale datasets.
MERRA↗
Statistical Analysis of Factors Riving Surface Ozone Variability over Continental South Africa
Statistical relationships between surface ozone (O3) concentration, precursor species and meteorological conditions in continental South Africa were examined from data obtained from measurement stations in north-eastern South Africa. Three multivariate statistical methods were applied in the investigation, i.e. multiple linear regression (MLR), principal component analysis (PCA) and –regression (PCR), and generalised additive model (GAM) analysis. The daily maximum 8-h moving average O3 concentrations were considered in these statistical models (dependent variable). MLR models indicated that meteorology and precursor species concentrations are able to explain ~50% of the variability in daily maximum O3 levels. MLR analysis revealed that atmospheric carbon monoxide (CO), temperature and relative humidity were the strongest factors affecting the daily O3 variability. In summer, daily O3 variances were mostly associated with relative humidity, while winter O3 levels were mostly linked to temperature and CO. PCA indicated that CO, temperature and relative humidity were not strongly collinear. GAM also identified CO, temperature and relative humidity as the strongest factors affecting the daily variation of O3. Partial residual plots found that temperature, radiation and nitrogen oxides most likely have a non-linear relationship with O3,while the relationship with relative humidity and CO is probably linear. An inter-comparison between O3 levels modelled with the three statistical models compared to measured O3 concentrations showed that the GAM model offered a slight improvement over the MLR model. These findings emphasise the critical role of regional-scale O3 precursors coupled with meteorological conditions in daily variances of O3 levels in continental South Africa.
multiple linear regression (MLR)↗
THEMIS signal analysis statistics research program - Development and analysis of modified paired comparisons by use of linearized nonlinear regression
Curve fitting for modified paired comparisons using linearized nonlinear regression
Walsh, J. E.↗
Analysis of fractal dimensions of rat bones from film and digital images
OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.
NASA Discipline Musculoskeletal↗
Vegetation spatial variability and its effect on vegetation indices
Landsat MSS data were used to simulate low resolution satellite data, such as NOAA AVHRR, to quantify the fractional vegetation cover within a pixel and relate the fractional cover to the normalized difference vegetation index (NDVI) and the simple ratio (SR). The MSS data were converted to radiances from which the NDVI and SR values for the simulated pixels were determined. Each simulated pixel was divided into clusters using an unsupervised classification program. Spatial and spectral analysis provided a means of combining clusters representing similar surface characteristics into vegetated and non-vegetated areas. Analysis showed an average error of 12.7 per cent in determining these areas. NDVI values less than 0.3 represented fractional vegetated areas of 5 per cent or less, while a value of 0.7 or higher represented fractional vegetated areas greater than 80 per cent. Regression analysis showed a strong linear relation between fractional vegetation area and the NDVI and SR values; correlation values were 0.89 and 0.95 respectively. The range of NDVI values calculated from the MSS data agrees well with field studies.
Ormsby, J. P.↗
Ordinary chondrites - Multivariate statistical analysis of trace element contents
The contents of mobile trace elements (Co, Au, Sb, Ga, Se, Rb, Cs, Te, Bi, Ag, In, Tl, Zn, and Cd) in Antarctic and non-Antarctic populations of H4-6 and L4-6 chondrites, were compared using standard multivariate discriminant functions borrowed from linear discriminant analysis and logistic regression. A nonstandard randomization-simulation method was developed, making it possible to carry out probability assignments on a distribution-free basis. Compositional differences were found both between the Antarctic and non-Antarctic H4-6 chondrite populations and between two L4-6 chondrite populations. It is shown that, for various types of meteorites (in particular, for the H4-6 chondrites), the Antarctic/non-Antarctic compositional difference is due to preterrestrial differences in the genesis of their parent materials.
Lipschutz, Michael E.↗
Multivariate statistical analysis: Principles and applications to coorbital streams of meteorite falls
Multivariate statistical analysis techniques (linear discriminant analysis and logistic regression) can provide powerful discrimination tools which are generally unfamiliar to the planetary science community. Fall parameters were used to identify a group of 17 H chondrites (Cluster 1) that were part of a coorbital stream which intersected Earth's orbit in May, from 1855 - 1895, and can be distinguished from all other H chondrite falls. Using multivariate statistical techniques, it was demonstrated that a totally different criterion, labile trace element contents - hence thermal histories - or 13 Cluster 1 meteorites are distinguishable from those of 45 non-Cluster 1 H chondrites. Here, we focus upon the principles of multivariate statistical techniques and illustrate their application using non-meteoritic and meteoritic examples.
Wolf, S. F.↗
Chemical studies of H chondrites. 4: New data and comparison of Antarctic suites
We report data for the trace elements Au, Co, Sb, Ga, Rb, Ag, Se, Cs, Te, Zn, Cd, Bi, Ti, and In (ordered by putative volatility during nebular condensation and accretion) determined by neutron activation analysis in 13 H5 chondrites from Victoria Land and 20 H4-6 chondrites from Queen Maud Land, Antarctica. These and earlier results provide Antarctic sample suites of 34 chondrites from Victoria Land and 25 from Queen Maud Land. Treatment of data for the most volatile 10 elements (Rb to In) in these studies by multivariate statistical techniques more robust, as well as more conservative, than conventional linear discriminant analysis and logistic regression demonstrates that compositions differ at marginally significant levels. This difference cannot be explained by trivial (terrestrial) causes and becomes more significant, despite the smaller size of the database, when comparisons are limited to data from a single analyst and when all upper limits are eliminated from consideration. The Victoria Land and Queen Maud Land suites have different mean terrestrial ages (approximately 300 kyr and approximately 100 kyr, respectively) and age distributions, suggesting that a time-dependent variation of chondritic sources with different thermal histories is responsible. As a result, these two Antarctic suites are, on average, chemically distinguishable from each other. Since H chondrites serve as a paradigm for other meteorite classes, these results indicate that the near-Earth populations of planetary materials varied with time on the 10(exp 5)-year timescale.
Wolf, Stephen F.↗
Chemical studies of H chondrites. 6: Antarctic/non-Antarctic compositional differences revisited
We report data for the trace elements Au, Co, Sb, Ga, Rb, Ag, Se, Cs, Te, Zn, Cd, Bi, T1, and In (ordered by putative volatility during nebular condensation and accretion) determined by radiochemical neutron activation analysis of 14 additional H5 and H6 chondrite falls. Data for the 10 most volatile elements (Rb to In) treated by the multivariate techniques of linear discriminant analysis and logistic regression in these and 44 other falls are compared with those of 59 H4-6 chondrites from Antarctica. Various populations are tested by the multivariate techniques, using the previously developed method of randomization-simulation to assess significance levels. An earlier conclusion, based on fewer examples, that H4-6 chondrite falls are compositionally distinguishable from the Antarctic suite is verified by the additional data. This distinctiveness is highly significant because of the presence of samples from Victoria Land in the Antarctic population, which differ compositionally from falls beyond any reasonable doubt. However, it cannot be proven unequivocally that falls and Antarctic samples from Queen Maud Land are compositionally distinguishable. Trivial causes (e.g., analyst bias, weathering) cannot explain the Victoria Land (Antarctic)/non-Antarctic compositional difference for paradigmatic H4-6 chondrites. This seems to reflect a time-dependent variation of near-Earth meteoroid source regions differing in average thermal history.
Wolf, Stephen F.↗
Time-on-task decrements in "steer clear" performance of patients with sleep apnea and narcolepsy
Loss of attention with time-on-task reflects the increasing instability of the waking state during performance in experimentally induced sleepiness. To determine whether patients with disorders of excessive sleepiness also displayed time-on-task decrements indicative of wake state instability, visual sustained attention performance on "Steer Clear," a computerized simple RT driving simulation task, was compared among 31 patients with untreated sleep apnea, 16 patients with narcolepsy, and 14 healthy control subjects. Vigilance decrement functions were generated by analyzing the number of collisions in each of six four-minute periods of Steer Clear task performance in a mixed-model analysis of variance and linear regression equations. As expected, patients had more Steer Clear collisions than control subjects (p=0.006). However, the inter-subject variability in errors among the narcoleptic patients was four-fold that of the apnea patients, and 100-fold that of the controls volunteers; the variance in errors among untreated apnea patients was 27-times that of controls. The results of transformed collision data revealed main effects for group (p=0.006), time-on-task (p=0.001), and a significant interaction (p=0.022). Control subjects showed no clear evidence of increasing collision errors with time-on-task (adjusted R2=0.22), while apnea patients showed a trend toward vigilance decrement (adjusted R2=0.42, p=0.097), and narcolepsy patients evidenced a robust linear vigilance decrement (adjusted R2=0.87, p=0.004). The association of disorders of excessive somnolence with escalating time-on-task decrements makes it imperative that when assessment of neurobehavioral performance is conducted in patients, it involves task durations and analyses that will evaluate the underlying vulnerability of potentially sleepy patients to decrements over time in tasks that require sustained attention and timely responses, both of which are key components in safe driving performance.
NASA Discipline Space Human Factors↗
Time-periodic variations in stratospheric ozone from satellite observations
The time-periodic variations in stratospheric zonal mean ozone number density are examined with emphasis on annual and semi-annual oscillations. The data base for this analysis is the ozone observation from the SAGE II satellite instrument. A multiple linear regression method is adopted for the analysis. The results show that the amplitudes and phases of the time-periodic ozone variations are functions of altitude and latitude.
Wang, Pi-Huan↗
Missing Data and Multiple Imputation: An Unbiased Approach
The default method of dealing with missing data in statistical analyses is to only use the complete observations (complete case analysis), which can lead to unexpected bias when data do not meet the assumption of missing completely at random (MCAR). For the assumption of MCAR to be met, missingness cannot be related to either the observed or unobserved variables. A less stringent assumption, missing at random (MAR), requires that missingness not be associated with the value of the missing variable itself, but can be associated with the other observed variables. When data are truly MAR as opposed to MCAR, the default complete case analysis method can lead to biased results. There are statistical options available to adjust for data that are MAR, including multiple imputation (MI) which is consistent and efficient at estimating effects. Multiple imputation uses informing variables to determine statistical distributions for each piece of missing data. Then multiple datasets are created by randomly drawing on the distributions for each piece of missing data. Since MI is efficient, only a limited number, usually less than 20, of imputed datasets are required to get stable estimates. Each imputed dataset is analyzed using standard statistical techniques, and then results are combined to get overall estimates of effect. A simulation study will be demonstrated to show the results of using the default complete case analysis, and MI in a linear regression of MCAR and MAR simulated data. Further, MI was successfully applied to the association study of CO2 levels and headaches when initial analysis showed there may be an underlying association between missing CO2 levels and reported headaches. Through MI, we were able to show that there is a strong association between average CO2 levels and the risk of headaches. Each unit increase in CO2 (mmHg) resulted in a doubling in the odds of reported headaches.
Foy, M.↗