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At least 19 records

Logistic Regression in Clinical Studies

• A logistic regression model is used when the outcome of interest is binary. The term “logistic” refers to the underlying “logit” (log odds) function that is used to model the binary outcome. • Odds ratios are produced from a logistic regression model and have a useful interpretation. • Tips, tricks and concepts used to fit logistic regression models are similar to those used in linear regression models. • Modeling building that is knowledge-based rather than automatic is preferred in most applications of logistic regression. • A logistic regression model that is overparameterized (ie, too many variables for too few events) can result in odds ratios that are implausibly large and confidence intervals that are wide and uninterpretable. These types of “overfitted” models should be avoided. • Logistic regression models can be fit using most standard statistical software.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗

Satellite rainfall retrieval by logistic regression

The potential use of logistic regression in rainfall estimation from satellite measurements is investigated. Satellite measurements provide covariate information in terms of radiances from different remote sensors.The logistic regression technique can effectively accommodate many covariates and test their significance in the estimation. The outcome from the logistical model is the probability that the rainrate of a satellite pixel is above a certain threshold. By varying the thresholds, a rainrate histogram can be obtained, from which the mean and the variant can be estimated. A logistical model is developed and applied to rainfall data collected during GATE, using as covariates the fractional rain area and a radiance measurement which is deduced from a microwave temperature-rainrate relation. It is demonstrated that the fractional rain area is an important covariate in the model, consistent with the use of the so-called Area Time Integral in estimating total rain volume in other studies. To calibrate the logistical model, simulated rain fields generated by rainfield models with prescribed parameters are needed. A stringent test of the logistical model is its ability to recover the prescribed parameters of simulated rain fields. A rain field simulation model which preserves the fractional rain area and lognormality of rainrates as found in GATE is developed. A stochastic regression model of branching and immigration whose solutions are lognormally distributed in some asymptotic limits has also been developed.

Chiu, Long S.↗

Nonlinear Logistic Regression Mixture Experiment Modeling for Binary Data Using Dimensionally Reduced Components

This article presents and illustrates an approach using nonlinear logistic regression for modeling binary response data from a mixture experiment when the components can be partitioned into groups used to form dimensionally-reduced pseudocomponents (DRPs). A DRP is a linear combination of the components in a group, where the linear combinations over all groups are normalized so that the DRP proportions sum to unity. Nonlinear logistic regression is required because, after normalization of the linear combinations, the model expressed in terms of the DRPs is nonlinear in the parameters that specify the linear combinations. A method for obtaining nonparametric tolerance limits on the probability of a “success” for the binary response variable using a bootstrap approach is also presented. Having three DRPs enables viewing data and modeling results on a ternary plot even though there may be many more than three mixture components. A real database, involving whether or not nepheline crystals form in simulated nuclear waste glass after cooling, is used to illustrate the nonlinear logistic regression modeling and nonparametric tolerance limit approaches when there are three DRPs.

Waste glass, Nepheline, Mixture experiment, Logist↗

Probabilistic Power Consumption Modeling for Commercial Buildings Using Logistic Regression Markov Chain

The total energy consumed by buildings takes up to 40% of U.S. energy use, in which a large portion is contributed by commercial buildings. Building performance optimization is desirable but requires accurate building models with uncertainties taken into account. This paper proposes a novel probabilistic modeling method using Logistic Regression Markov Chain (LRMC). The LRMC model enhances the performance of traditional Markov Chain (MC) models by adopting time-variant transition matrices calibrated using logistic regression with exogenous inputs. Compared with existing building models, the proposed model produces accurate multi-step modeling results with full probability distribution. The proposed probabilistic building model is tested using actual commercial building measurements and modeling performance is evaluated with two probabilisitc metrics. The results show that the LRMC model has higher accuracy than traditional MC model and Logistic Regression (LR) model in that it yields lower error scores under both evaluation metrics.

Building modeling↗

Estimating the exceedance probability of rain rate by logistic regression

Recent studies have shown that the fraction of an area with rain intensity above a fixed threshold is highly correlated with the area-averaged rain rate. To estimate the fractional rainy area, a logistic regression model, which estimates the conditional probability that rain rate over an area exceeds a fixed threshold given the values of related covariates, is developed. The problem of dependency in the data in the estimation procedure is bypassed by the method of partial likelihood. Analyses of simulated scanning multichannel microwave radiometer and observed electrically scanning microwave radiometer data during the Global Atlantic Tropical Experiment period show that the use of logistic regression in pixel classification is superior to multiple regression in predicting whether rain rate at each pixel exceeds a given threshold, even in the presence of noisy data. The potential of the logistic regression technique in satellite rain rate estimation is discussed.

Chiu, Long S.↗

An Alternative Flight Software Trigger Paradigm: Applying Multivariate Logistic Regression to Sense Trigger Conditions using Inaccurate or Scarce Information

In late 2014, NASA will fly the Orion capsule on a Delta IV-Heavy rocket for the Exploration Flight Test-1 (EFT-1) mission. For EFT-1, the Orion capsule will be flying with a new GPS receiver and new navigation software. Given the experimental nature of the flight, the flight software must be robust to the loss of GPS measurements. Once the high-speed entry is complete, the drogue parachutes must be deployed within the proper conditions to stabilize the vehicle prior to deploying the main parachutes. When GPS is available in nominal operations, the vehicle will deploy the drogue parachutes based on an altitude trigger. However, when GPS is unavailable, the navigated altitude errors become excessively large, driving the need for a backup barometric altimeter. In order to increase overall robustness, the vehicle also has an alternate method of triggering the drogue parachute deployment based on planet-relative velocity if both the GPS and the barometric altimeter fail. However, this velocity-based trigger results in large altitude errors relative to the targeted altitude. Motivated by this challenge, this paper demonstrates how logistic regression may be employed to automatically generate robust triggers based on statistical analysis. Logistic regression is used as a ground processor pre-flight to develop a classifier. The classifier would then be implemented in flight software and executed in real-time. This technique offers excellent performance even in the face of highly inaccurate measurements. Although the logistic regression-based trigger approach will not be implemented within EFT-1 flight software, the methodology can be carried forward for future missions and vehicles.

Smith, Kelly M.↗

An Alternative Flight Software Trigger Paradigm: Applying Multivariate Logistic Regression to Sense Trigger Conditions Using Inaccurate or Scarce Information

In late 2014, NASA will fly the Orion capsule on a Delta IV-Heavy rocket for the Exploration Flight Test-1 (EFT-1) mission. For EFT-1, the Orion capsule will be flying with a new GPS receiver and new navigation software. Given the experimental nature of the flight, the flight software must be robust to the loss of GPS measurements. Once the high-speed entry is complete, the drogue parachutes must be deployed within the proper conditions to stabilize the vehicle prior to deploying the main parachutes. When GPS is available in nominal operations, the vehicle will deploy the drogue parachutes based on an altitude trigger. However, when GPS is unavailable, the navigated altitude errors become excessively large, driving the need for a backup barometric altimeter to improve altitude knowledge. In order to increase overall robustness, the vehicle also has an alternate method of triggering the parachute deployment sequence based on planet-relative velocity if both the GPS and the barometric altimeter fail. However, this backup trigger results in large altitude errors relative to the targeted altitude. Motivated by this challenge, this paper demonstrates how logistic regression may be employed to semi-automatically generate robust triggers based on statistical analysis. Logistic regression is used as a ground processor pre-flight to develop a statistical classifier. The classifier would then be implemented in flight software and executed in real-time. This technique offers improved performance even in the face of highly inaccurate measurements. Although the logistic regression-based trigger approach will not be implemented within EFT-1 flight software, the methodology can be carried forward for future missions and vehicles.

Smith, Kelly M.↗

An Alternative Flight Software Paradigm: Applying Multivariate Logistic Regression to Sense Trigger Conditions using Inaccurate or Scarce Information

In late 2014, NASA will fly the Orion capsule on a Delta IV-Heavy rocket for the Exploration Flight Test-1 (EFT-1) mission. For EFT-1, the Orion capsule will be flying with a new GPS receiver and new navigation software. Given the experimental nature of the flight, the flight software must be robust to the loss of GPS measurements. Once the high-speed entry is complete, the drogue parachutes must be deployed within the proper conditions to stabilize the vehicle prior to deploying the main parachutes. When GPS is available in nominal operations, the vehicle will deploy the drogue parachutes based on an altitude trigger. However, when GPS is unavailable, the navigated altitude errors become excessively large, driving the need for a backup barometric altimeter to improve altitude knowledge. In order to increase overall robustness, the vehicle also has an alternate method of triggering the parachute deployment sequence based on planet-relative velocity if both the GPS and the barometric altimeter fail. However, this backup trigger results in large altitude errors relative to the targeted altitude. Motivated by this challenge, this paper demonstrates how logistic regression may be employed to semi-automatically generate robust triggers based on statistical analysis. Logistic regression is used as a ground processor pre-flight to develop a statistical classifier. The classifier would then be implemented in flight software and executed in real-time. This technique offers improved performance even in the face of highly inaccurate measurements. Although the logistic regression-based trigger approach will not be implemented within EFT-1 flight software, the methodology can be carried forward for future missions and vehicles

Smith, Kelly↗

Dynamic logistic regression and variable selection: Forecasting and contextualizing civil unrest

Civil unrest can range from peaceful protest to violent furor, and researchers are working to monitor, forecast, and assess such events to allocate resources better. Twitter has become a real-time data source for forecasting civil unrest because millions of people use the platform as a social outlet. Additionally, daily word counts are used as model features, and predictive terms contextualize the reasons for the protest. To forecast civil unrest and infer the reasons for the protest, we consider the problem of Bayesian variable selection for the dynamic logistic regression model and propose using penalized credible regions to select parameters of the updated state vector. This method avoids the need for shrinkage priors, is scalable to high-dimensional dynamic data, and allows the importance of variables to vary in time as new information becomes available. A substantial improvement in both precision and F1-score using this approach is demonstrated through simulation. Finally, we apply the proposed model fitting and variable selection methodology to the problem of forecasting civil unrest in Latin America. Our dynamic logistic regression approach shows improved accuracy compared to the static approach currently used in event prediction and feature selection.

97 MATHEMATICS AND COMPUTING↗

Predicting fatigue from heart rate signatures using functional logistic regression

Physical fatigue can have adverse effects on humans in extreme environments. Therefore, being able to predict fatigue using easy to measure metrics such as heart rate (HR) signatures has potential to have an impact in real-life scenarios. We apply a functional logistic regression model that uses HR signatures to predict physical fatigue, where physical fatigue is defined in a data-driven manner. Data were collected using commercially available wearable devices on 47 participants hiking the 20.7-mile Grand Canyon rim-to-rim trail in a single day. Fitted model provides good predictions and interpretable parameters for real-life application.

60 APPLIED LIFE SCIENCES↗

classLog: Logistic regression for the classification of genetic sequences

Introduction Sequencing and phylogenetic classification have become a common task in human and animal diagnostic laboratories. It is routine to sequence pathogens to identify genetic variations of diagnostic significance and to use these data in realtime genomic contact tracing and surveillance. Under this paradigm, unprecedented volumes of data are generated that require rapid analysis to provide meaningful inference. Methods We present a machine learning logistic regression pipeline that can assign classifications to genetic sequence data. The pipeline implements an intuitive and customizable approach to developing a trained prediction model that runs in linear time complexity, generating accurate output rapidly, even with incomplete data. Our approach was benchmarked against porcine respiratory and reproductive syndrome virus (PRRSv) and swine H1 influenza A virus (IAV) datasets. Trained classifiers were tested against sequences and simulated datasets that artificially degraded sequence quality at 0, 10, 20, 30, and 40%. Results When applied to a poor-quality sequence data, the classifier achieved between >85% to 95% accuracy for the PRRSv and the swine H1 IAV HA dataset and this increased to near perfect accuracy when using the full dataset. The model also identifies amino acid positions used to determine genetic clade identity through a feature selection ranking within the model. These positions can be mapped onto a maximum-likelihood phylogenetic tree, allowing for the inference of clade defining mutations. Discussion Our approach is implemented as a python package with code available at https://github.com/flu-crew/classLog .

Zeller, Michael A.↗

Basic Diagnosis and Prediction of Persistent Contrail Occurrence using High-resolution Numerical Weather Analyses/Forecasts and Logistic Regression. Part I: Effects of Random Error

Straightforward application of the Schmidt-Appleman contrail formation criteria to diagnose persistent contrail occurrence from numerical weather prediction data is hindered by significant bias errors in the upper tropospheric humidity. Logistic models of contrail occurrence have been proposed to overcome this problem, but basic questions remain about how random measurement error may affect their accuracy. A set of 5000 synthetic contrail observations is created to study the effects of random error in these probabilistic models. The simulated observations are based on distributions of temperature, humidity, and vertical velocity derived from Advanced Regional Prediction System (ARPS) weather analyses. The logistic models created from the simulated observations were evaluated using two common statistical measures of model accuracy, the percent correct (PC) and the Hanssen-Kuipers discriminant (HKD). To convert the probabilistic results of the logistic models into a dichotomous yes/no choice suitable for the statistical measures, two critical probability thresholds are considered. The HKD scores are higher when the climatological frequency of contrail occurrence is used as the critical threshold, while the PC scores are higher when the critical probability threshold is 0.5. For both thresholds, typical random errors in temperature, relative humidity, and vertical velocity are found to be small enough to allow for accurate logistic models of contrail occurrence. The accuracy of the models developed from synthetic data is over 85 percent for both the prediction of contrail occurrence and non-occurrence, although in practice, larger errors would be anticipated.

Duda, David P.↗

Basic Diagnosis and Prediction of Persistent Contrail Occurrence using High-resolution Numerical Weather Analyses/Forecasts and Logistic Regression. Part II: Evaluation of Sample Models

Previous studies have shown that probabilistic forecasting may be a useful method for predicting persistent contrail formation. A probabilistic forecast to accurately predict contrail formation over the contiguous United States (CONUS) is created by using meteorological data based on hourly meteorological analyses from the Advanced Regional Prediction System (ARPS) and from the Rapid Update Cycle (RUC) as well as GOES water vapor channel measurements, combined with surface and satellite observations of contrails. Two groups of logistic models were created. The first group of models (SURFACE models) is based on surface-based contrail observations supplemented with satellite observations of contrail occurrence. The second group of models (OUTBREAK models) is derived from a selected subgroup of satellite-based observations of widespread persistent contrails. The mean accuracies for both the SURFACE and OUTBREAK models typically exceeded 75 percent when based on the RUC or ARPS analysis data, but decreased when the logistic models were derived from ARPS forecast data.

Duda, David P.↗