Estimated Regression Coefficients Research Articles

Clinical potential of pupillary light reflex and heart rate variability parameters as objective indicators of tonsillectomy-induced pain

Objective. Establishing objective indicators of subjective pain intensity is important in pain assessment. Pupillary light reflex (PLR) and heart rate variability (HRV) indicate autonomic nervous system (ANS) activity and may serve as pain indicators because pain can affect ANS activity. In this prospective longitudinal study, we aimed to investigate the potential of PLR/HRV parameters as objective indicators of subjective pain intensity after tonsillectomy. Approach. Sixty-seven patients undergoing tonsillectomy were enrolled. Subjective pain intensity based on a numeric rating scale (NRS) and eight PLR/HRV parameters were assessed at five time points. We investigated the changes in the NRS values over time. We estimated regression coefficients reflecting parameter changes per unit change in the NRS score using linear mixed-effects models. Main Results. The mean NRS score was 0 at two pre-surgery time points, 5 on postoperative days (PODs) 1 and 2, and 0 at postoperative week 3. Two parameters (initial pupil size [INIT] and constriction latency [LAT]) showed significant changes on POD1 and POD2 in comparison to baseline data measured at the pre-surgery time point. Among these parameters, only LAT showed no significant changes between POD1 and POD2. Significant regression coefficients with the narrowest 95% confidence intervals were observed for INIT and LAT. Increased NRS scores were associated with decreased INIT and shortened LAT. Significance. LAT was a robust indicator of subjective pain intensity. Our patients showed decreased INIT with increased NRS scores, indicating the predominance of the parasympathetic, not sympathetic, tone in pupils. Further studies are required to investigate factors causing this predominance.

Regularized regression on compositional trees with application to MRI analysis.

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees handle more complex relationships among random variables and appear in many disciplines, such as brain imaging, genomics and finance. We consider the problem of sparse regression on data that are associated with a compositional tree and propose a transformation-free tree-based regularized regression method for component selection. The regularization penalty is designed based on the tree structure and encourages a sparse tree representation. We prove that our proposed estimator for regression coefficients is both consistent and model selection consistent. In the simulation study, our method shows higher accuracy than competing methods under different scenarios. By analyzing a brain imaging data set from studies of Alzheimer's disease, our method identifies meaningful associations between memory decline and volume of brain regions that are consistent with current understanding.

A Comparison of Weighted Least Square and Quantile Regression for Solving Heteroscedasticity in Simple Linear Regression

Regression analysis is the study of the relationship between dependent variable and one or more independent variables. One of the important assumption that must be fulfilled to get the regression coefficient estimator Best Linear Unbiased Estimator (BLUE) is homoscedasticity. If the homoscedasticity assumption is violated then it is called heteroscedasticity. The consequences of heteroscedasticity are the estimator remain linear and unbiased, but it can cause estimator haven‘t a minimum variance so the estimator is no longer BLUE. The purpose of this study is to analyze and resolve the violation of heteroscedasticity assumption with Weighted Least Square(WLS) and Quantile Regression. Based on the results of the comparison between WLS and Quantile Regression obtained the most precise method used to overcome heteroscedasticity in this research is the WLS method because it produces that is greater (98%).

Associations of Wearable Sensor Measures With Feed Intake, Production Traits, Lactation, and Environmental Parameters Impacting Feed Efficiency in Dairy Cattle

Feed efficiency is an important trait to dairy production because of its impact on sustainability and profitability. Measuring individual cow feed intake on commercial farms would be unfeasibly costly at present. Thus, developing cheap and portable indicators of feed intake would be highly beneficial for genetic selection and precision feeding management tools. Given the growing use of automated sensors on dairy farms, the objective of this study was to determine the relationship between measurements recorded from multiple wearable sensors and feed intake. A total of three different wearable sensors were evaluated for their association with dry mater intake (DMI). The sensors measured activity (sensors = 3), rumination (sensors = 1), ear temperature (sensors = 1), rumen pH (sensors = 1) and rumen temperature (sensors = 1). A range of 56–340 cows with assorted sensors from 24 to 313 days in milk (DIM) were modeled to evaluate associations with DIM, parity, and contemporary group (CG; comprised of pen and study cohort). Models extending upon these variables included known energy sinks (i.e., milk production, milk fat/protein and metabolic body weight), to characterize the association of sensors measures and DMI. Statistically significant (i.e., P < 0.05) regression coefficients for individual sensor measures with DMI ranged from 9.01E-07 to −3.45 kg DMI/day. When integrating all measures from a single sensor in a model, estimated regression coefficients ranged 8.83E-07 to −3.48 kg DMI/day. Significant associations were also identified for milk production traits, parity, DIM and CG. Associations tended to be highest for timepoints around the time of feeding and when multiple measurements within a sensor were integrated in a single model. The findings of this study indicate sensor measures are associated with feed intake and other energy sink traits and variables impacting feed efficiency. This information would be helpful to improve feed and feeding efficiency on commercial farms as proxy measurements for feed intake.

Optimal model averaging estimator for multinomial logit models

In this paper, we study optimal model averaging estimators of regression coefficients in a multinomial logit model, which is commonly used in many scientific fields. A Kullback–Leibler (KL) loss-based weight choice criterion is developed to determine averaging weights. Under some regularity conditions, we prove that the resulting model averaging estimators are asymptotically optimal. When the true model is one of the candidate models, the averaged estimators are consistent. Simulation studies suggest the superiority of the proposed method over commonly used model selection criterions, model averaging methods, as well as some other related methods in terms of the KL loss and mean squared forecast error. Finally, the website phishing data is used to illustrate the proposed method.

Spatial statistics and soil mapping: A blossoming partnership under pressure

For the better part of the 20th century pedologists mapped soil by drawing boundaries between different classes of soil which they identified from survey on foot or by vehicle, supplemented by air-photo interpretation, and backed by an understanding of landscape and the processes by which soil is formed. Its limitations for representing gradual spatial variation and predicting conditions at unvisited sites became evident, and in the 1980s the introduction of geostatistics and specifically ordinary kriging revolutionized thinking and to a large extent practice. Ordinary kriging is based solely on sample data of the variable of interest—it takes no account of related covariates. The latter were incorporated from the 1990s onward as fixed effects and incorporated as regression predictors, giving rise to kriging with external drift and regression kriging. Simultaneous estimation of regression coefficients and variogram parameters is best done by residual maximum likelihood estimation. In recent years machine learning has become feasible for predicting soil conditions from huge sets of environmental data obtained from sensors aboard satellites and other sources to produce digital soil maps. The techniques are based on classification and regression, but they take no account of spatial correlations. Further, they are effectively ‘black boxes’; they lack transparency, and their output needs to be validated if they are to be trusted. They undoubtedly have merit; they are here to stay. They too, however, have their shortcomings when applied to spatial data, which spatial statisticians can help overcome. Spatial statisticians and pedometricians still have much to do to incorporate uncertainty into digital predictions, spatial averages and totals over regions, and to take into account errors in measurement and spatial positions of sample data. They must also communicate their understanding of these uncertainties to end users of soil maps, by whatever means they are made.

Recursive and Non-Recursive Generalized Least-Squares Methods for Estimation of Time Series Models with Exogenous Variables

We present in this paper two generalized least-squares (GLS) methods for estimating regression coefficients of time series models with exogenous variables. The non-recursive GLS method is a generalization of the GLS method suggested by Cochrane and Orcutt (1949). The proposed GLS method consists of a sequence of four linear regressions. A first regression is fitted and provides residuals. These residuals are modeled as an autoregressive process and are used in a second regression (or autoregression) for obtaining estimators of autoregressive coefficients. These estimators are used to generate transformed endogenous and exogenous variables. A third regression makes use of the lagged values of these transformed variables to estimate the regression coefficients. The estimators of the regression coefficients are used to determine the true residuals which are modeled as an ARMA process which is finally used for obtaining the estimators of autoregressive and moving average parameters. The second GLS method is a recursive version of the first GLS method where the estimators are updated at each time point on receipt of the additional observations. The Simulation results based on different model structures with varying numbers of observations are used to compare the performance of our methods with that of exact maximum likelihood (EML) estimates.

Regression analysis of additive hazards model with sparse longitudinal covariates.

Additive hazards model is often used to complement the proportional hazards model in the analysis of failure time data. Statistical inference of additive hazards model with time-dependent longitudinal covariates requires the availability of the whole trajectory of the longitudinal process, which is not realistic in practice. The commonly used last value carried forward approach for intermittently observed longitudinal covariates can induce biased parameter estimation. The more principled joint modeling of the longitudinal process and failure time data imposes strong modeling assumptions, which is difficult to verify. In this paper, we propose methods that weigh the distance between the observational time of longitudinal covariates and the failure time, resulting in unbiased regression coefficient estimation. We establish the consistency and asymptotic normality of the proposed estimators. Simulation studies provide numerical support for the theoretical findings. Data from an Alzheimer's study illustrate the practical utility of the methodology.

Has Omicron Changed the Evolution of the Pandemic?

BackgroundVariants of the SARS-CoV-2 virus carry differential risks to public health. The Omicron (B.1.1.529) variant, first identified in Botswana on November 11, 2021, has spread globally faster than any previous variant of concern. Understanding the transmissibility of Omicron is vital in the development of public health policy.ObjectiveThe aim of this study is to compare SARS-CoV-2 outbreaks driven by Omicron to those driven by prior variants of concern in terms of both the speed and magnitude of an outbreak.MethodsWe analyzed trends in outbreaks by variant of concern with validated surveillance metrics in several southern African countries. The region offers an ideal setting for a natural experiment given that most outbreaks thus far have been driven primarily by a single variant at a time. With a daily longitudinal data set of new infections, total vaccinations, and cumulative infections in countries in sub-Saharan Africa, we estimated how the emergence of Omicron has altered the trajectory of SARS-CoV-2 outbreaks. We used the Arellano-Bond method to estimate regression coefficients from a dynamic panel model, in which new infections are a function of infections yesterday and last week. We controlled for vaccinations and prior infections in the population. To test whether Omicron has changed the average trajectory of a SARS-CoV-2 outbreak, we included an interaction between an indicator variable for the emergence of Omicron and lagged infections.ResultsThe observed Omicron outbreaks in this study reach the outbreak threshold within 5-10 days after first detection, whereas other variants of concern have taken at least 14 days and up to as many as 35 days. The Omicron outbreaks also reach peak rates of new cases that are roughly 1.5-2 times those of prior variants of concern. Dynamic panel regression estimates confirm Omicron has created a statistically significant shift in viral spread.ConclusionsThe transmissibility of Omicron is markedly higher than prior variants of concern. At the population level, the Omicron outbreaks occurred more quickly and with larger magnitude, despite substantial increases in vaccinations and prior infections, which should have otherwise reduced susceptibility to new infections. Unless public health policies are substantially altered, Omicron outbreaks in other countries are likely to occur with little warning.

Regression of exchangeable relational arrays

Summary Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators, and ideally the coefficient estimators themselves, must account for dependence between elements of the array, e.g., relations involving the same actor. Existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. We leverage an exchangeability assumption to derive standard error estimators that pool information across actors, and are substantially more accurate than existing estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a dataset involving international trade.

Optimal sampling for design-based estimators of regression models.

Two-phase designs measure variables of interest on a subcohort where the outcome and covariates are readily available or cheap to collect on all individuals in the cohort. Given limited resource availability, it is of interest to find an optimal design that includes more informative individuals in the final sample. We explore the optimal designs and efficiencies for analyses by design-based estimators. Generalized raking is an efficient class of design-based estimators, and they improve on the inverse-probability weighted (IPW) estimator by adjusting weights based on the auxiliary information. We derive a closed-form solution of the optimal design for estimating regression coefficients from generalized raking estimators. We compare it with the optimal design for analysis via the IPW estimator and other two-phase designs in measurement-error settings. We consider general two-phase designs where the outcome variable and variables of interest can be continuous or discrete. Our results show that the optimal designs for analyses by the two classes of design-based estimators can be very different. The optimal design for analysis via the IPW estimator is optimal for IPW estimation and typically gives near-optimal efficiency for generalized raking estimation, though we show there is potential improvement in some settings.

Land price polarization and dispersion in Tokyo: a spatial model approach

Intensifying spatial inequality in housing markets is of great concern for urban planners and policymakers. This study employed a year-on-year analysis using universal kriging to fit the official land price data in Tokyo over the period 1997–2021. By comparing estimated regression coefficients with the estimated spatial variogram parameters, we found evidence of rising spatial polarization and dispersion in land prices of Tokyo. This was confirmed via price differences between western and central Tokyo that are becoming larger with each passing year. The determinants of the land price have different impacts on prices in western and central Tokyo. As for the variogram parameter, the nugget effects of the residuals in spatial models are increasing for the non-central region and decreasing in central Tokyo, which indicates that the degree of spatial dispersion is increasing.

Kernel Regression for Matrix-Variate Gaussian Distributed Signals Over Sample Graphs

Recent advances of kernel regression assume that target signals lie over a feature graph such that their values can be predicted with the assistance of the graph learned from training data. In this paper, we propose a novel kernel regression framework whose outputs follow a matrix-variate Gaussian distribution (MVGD) such that the kernel matrix can be viewed as the column covariance matrix of outputs, and the hyperparameters of a chosen kernel can be optimized using gradient methods. Furthermore, in contrast to the state-of-the-art kernel regression algorithms over graph (KRG), a sample graph of target outputs is introduced to work with regression coefficients and hyperparameters of a chosen kernel in our algorithms. The proposed KRG framework is decomposed into two stages, including the estimation of row and column covariance matrices of MVGD and graph learning along with the estimation of regression coefficients. Numerical approaches are developed to tackle the corresponding optimization problems. Experimental results over synthetic and real-world datasets demonstrate that the performance of the proposed algorithms is superior to that of the state-of-the-art methods.

Investigation of potential descriptors of chemical compounds on prevention of nephrotoxicity via QSAR approach

Drug-induced nephrotoxicity remains a common problem after exposure to medications and diagnostic agents, which may be heightened in the kidney microenvironment and deteriorate kidney function. In this study, the toxic effects of fourteen marked drugs with the individual chemical structure were evaluated in kidney cells. The quantitative structure–activity relationship (QSAR) approach was employed to investigate the potential structural descriptors of each drug-related to their toxic effects. The most reasonable equation of the QSAR model displayed that the estimated regression coefficients such as the number of ring assemblies, three-membered rings, and six-membered rings were strongly related to toxic effects on renal cells. Meanwhile, the chemical properties of the tested compounds including carbon atoms, bridge bonds, H-bond donors, negative atoms, and rotatable bonds were favored properties and promote the toxic effects on renal cells. Particularly, more numbers of rotatable bonds were positively correlated with strong toxic effects that displayed on the most toxic compound. The useful information discovered from our regression QSAR models may help to identify potential hazardous moiety to avoid nephrotoxicity in renal preventive medicine.

A Modern Gauss–Markov Theorem

This paper presents finite‐sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss–Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label “linear estimator” from the pedagogy of the Gauss–Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators).

DIRECT SOLUTION OF POLYNOMIAL REGRESSION OF ORDER UP TO 3

This article presents results related to the direct solution of the polynomial regression parameters based on the analytical solving of regression equations. The analytical solution is based on the normalization of the values of independent quantity with equidistance steps. The proposed solution does not need to directly solve a system of polynomial regression equations. The direct expressions to calculate estimators of regression coefficients, their standard deviations, and also standard and expanded deviation of polynomial functions are given. For a given number of measurement points, the parameters of these expressions have the same values independently of the range of input quantity. The proposed solution is illustrated by a numerical example used from a literature source.

A New Rapid Approach for Predicting Death in Coronavirus Patients: The Development and Validation of the COVID-19 Risk-Score in Fars Province (CRSF).

Background:Patients who are identified to be at a higher risk of mortality from COVID-19 should receive better treatment and monitoring. This study aimed to propose a simple yet accurate risk assessment tool to help decision-making in the management of the COVID-19 pandemic.Methods:From Jul to Nov 2020, 5454 patients from Fars Province, Iran, diagnosed with COVID-19 were enrolled. A multiple logistic regression model was trained on one dataset (training set: n=4183) and its prediction performance was assessed on another dataset (testing set: n=1271). This model was utilized to develop the COVID-19 risk-score in Fars (CRSF).Results:Five final independent risk factors including gender (male: OR=1.37), age (60–80: OR=2.67 and >80: OR=3.91), SpO 2 (≤85%: OR=7.02), underlying diseases (yes: OR=1.25), and pulse rate (<60: OR=2.01 and >120: OR=1.60) were significantly associated with in-hospital mortality. The CRSF formula was obtained using the estimated regression coefficient values of the aforementioned factors. The point values for the risk factors varied from 2 to 19 and the total CRSF varied from 0 to 45. The ROC analysis showed that the CRSF values of ≥15 (high-risk patients) had a specificity of 73.5%, sensitivity of 76.5%, positive predictive value of 23.2%, and negative predictive value (NPV) of 96.8% for the prediction of death (AUC=0.824, P<0.0001).Conclusion:This simple CRSF system, which has a high NPV, can be useful for predicting the risk of mortality in COVID-19 patients. It can also be used as a disease severity indicator to determine triage level for hospitalization.

A Taylor Expansion Algorithm for Spatial Downscaling of MODIS Land Surface Temperature

Land surface temperature (LST) with fine spatiotemporal resolution is a much-needed parameter in the earth surface system. The LST downscaling is an efficient way to improve the spatiotemporal resolution of LST and has been developed rapidly in recent years. Due to the simple operations and discernable effects of statistical regression and its extension algorithms, these algorithms have been widely researched. However, most statistical regression models assume scale invariance, which makes the downscaled LST inaccurate. This study analyzed the scale effect in the process of LST upscaling/downscaling, then proposed a new algorithm based on Taylor expansion for Moderate Resolution Imaging Spectroradiometer (MODIS) LST downscaling. The Taylor expansion algorithm estimates regression coefficients between LST and auxiliary parameters in the consistent scale. It is tested in three typical areas of different landscape with different auxiliary parameters, and the results are significantly improved compared to the traditional algorithm. However, the new algorithm may introduce the temporal discrepancy between MODIS LST and empirical concavity factor (S), which is estimated with Landsat 8 data, into the downscaling procedure in some circumstances. To discuss the influence of temporal discrepancy, we designed three schemes for pairing MODIS and S and analyzed the downscaled results. The results show that the proposed algorithm got the best downscaled results when the MODIS LST acquired time is consistent with the time of S. When the time is inconsistent, the pairing scheme of a similar season gives better results than that of different seasons. The algorithm performs generally well so long as the spatial distribution of auxiliary parameters in the date of Landsat 8 acquisition is similar to the date of MODIS acquisition.

Modelling old‐age retirement: An adaptive multi‐outcome LAD‐lasso regression approach

AbstractUsing unique administrative register data, we investigate old‐age retirement under the statutory pension scheme in Finland. The analysis is based on multi‐outcome modelling of pensions and working lives together with a range of explanatory variables. An adaptive multi‐outcome LAD‐lasso regression method is applied to obtain estimates of earnings and socioeconomic factors affecting old‐age retirement and to decide which of these variables should be included in our model. The proposed statistical technique produces robust and less biased regression coefficient estimates in the context of skewed outcome distributions and an excess number of zeros in some of the explanatory variables. The results underline the importance of late life course earnings and employment to the final amount of pension and reveal differences in pension outcomes across socioeconomic groups. We conclude that adaptive LAD‐lasso regression is a promising statistical technique that could be usefully employed in studying various topics in the pension industry.

Solutions to problems of nonexistence of parameter estimates and sparse data bias in Poisson regression.

Poisson regression can be challenging with sparse data, in particular with certain data constellations where maximum likelihood estimates of regression coefficients do not exist. This paper provides a comprehensive evaluation of methods that give finite regression coefficients when maximum likelihood estimates do not exist, including Firth’s general approach to bias reduction, exact conditional Poisson regression, and a Bayesian estimator using weakly informative priors that can be obtained via data augmentation. Furthermore, we include in our evaluation a new proposal for a modification of Firth’s approach, improving its performance for predictions without compromising its attractive bias-correcting properties for regression coefficients. We illustrate the issue of the nonexistence of maximum likelihood estimates with a dataset arising from the recent outbreak of COVID-19 and an example from implant dentistry. All methods are evaluated in a comprehensive simulation study under a variety of realistic scenarios, evaluating their performance for prediction and estimation. To conclude, while exact conditional Poisson regression may be confined to small data sets only, both the modification of Firth’s approach and the Bayesian estimator are universally applicable solutions with attractive properties for prediction and estimation. While the Bayesian method needs specification of prior variances for the regression coefficients, the modified Firth approach does not require any user input.