Choice Of Regression Model Research Articles

Quantification of alloying elements in steel targets: The LIBS 2022 regression contest

We present the results of the regression contest organized for the LIBS 2022 conference. While the motivation and design of the contest are briefly presented, the work focuses on the methodologies of the three best-performing teams. The employed spectral preprocessing strategies, choice of regression models and its optimization are detailed for each team separately. The aim of the contest reflects the long-term challenges faced by quantitative laser-induced breakdown spectroscopy (LIBS) analysis. Thus, the contest was designed with the purpose of providing a transparent platform for comparing and evaluating the large range of data processing tools available in the LIBS literature. Namely, the contest consisted of the quantification of two major (Cr, Ni) and two minor (Mn, Mo) elements in 15 steel targets. For constructing an appropriate regression model, spectra of 42 targets were provided. The spectra were collected using a commercially available laboratory-based LIBS system and made publicly available. The contest lasted 53 days during which the teams did not receive feedback. In total, 21 teams participated out of which the three best-performing methodologies are presented here. A single linear partial least squares model and two artificial neural network regression models are presented. The corresponding feature selection strategies included emission line selection, spectral range selection, and automatized wavelength selection. Various spectral normalization strategies and data augmentation strategies are also presented.

Exogenous atmospheric variables as wind speed predictors in machine learning

The use of exogenous meteorological variables in wind speed prediction is currently enjoying much attention, particularly with the continued proliferation of wind power onto electricity networks. Typically, the selection of appropriate forecasting regimes or downscaling variables, along with the appropriate domain size, is based on expert knowledge and/or physical principles. There is however little consensus as to which variables are the best predictors. In this paper the wind speed predictive skill provided by 16 exogenous meteorological variables in machine learning algorithms is investigated as a function of: choice of regression model; choice of domain size; forecast period; meteorological variable elevation (i.e. pressure level); and testing site location. The principal components of numeric reanalysis datasets for each of 16 variables, along with lagged winds speeds, were employed as predictors at each of the test sites. The mean best performing wind speed predictors were found to be 950 hPa- vertical velocity; divergence; the u- & v-wind speed components; and geopotential heights. The ability to investigate and rank the forecast skill provided by meteorological predictors is important in gaining insight into physical processes influencing the wind resource and the improvement of wind speed forecasts. Though distinct predictors, domains and approaches were identified to significantly improve forecasting accuracy for a specific site, generalisations were found to be difficult to make, even in the small geographic area investigated. Therefore, it is recommended is that process described in paper is repeated for individual sites in selecting exogenous predictor variables.

Geopolitical risk and China's oil security

This paper aims to make a comprehensive evaluation of China's oil situation from 2000 to 2018. We establish an evaluation framework from three dimensions of oil supply, oil consumption and oil ecology, and calculate the comprehensive score and scores of three dimensions. Results show that the comprehensive score of China's oil security increased from 0.3 to about 0.6 in 2000–2018. After rapid growth from 2003 to 2008, the oil supply security score stabilized at the level of 0.6. In general, China's oil security situation is steadily improving. Further, ADL-MIDAS model is employed to investigate the impact of four types of geopolitical risks (GPRs) on China's oil security. The findings suggest that GPRs have negative effects on China's comprehensive oil security. In the robustness tests, these effects don't change with adjustments to the assessment framework, changes in subjective weights, or the choice of regression models. The impacts of GPRs on China's oil security are mainly realized through the oil supply dimension. GPRs threatening China's oil security are reflected in oil interruption in the international market. Finally, the paper puts forward several policy implications from the perspective of oil security assessment and GPRs.

An Improved ARIMA Method Based on Functional Principal Component Analysis and Bidirectional Bootstrap and Its Application to Stock Price Forecasting

This paper proposes an improved ARIMA method based on functional principal component analysis and bi-directional bootstrap. The proposed method does not require a smoothness assumption, uses intraday prices as auxiliary information and considers their functional characteristics, and effectively performs a bias-variance trade-off in the forecasting model by using a bi-directional bootstrap method. This is achieved by forming a paired sample of ARIMA forecast residuals and functional characteristics, and then fitting the forecast residuals to the regression model using the two-way bootstrap method, thereby improving the forecast accuracy.In addition, the choice of regression model is free. The empirical results show that the proposed method has better predictive performance and is more robust than the ARIMA model. Finally, the proposed method can be extended to environmental science, social science and other fields to help deal with various prediction problems.

Choice of Regression Models in Time Series Data

Time series data possess distinct properties compared to cross section data. They have high temporal dependence, trend component and may have seasonal as well as cyclical patterns. A much-discussed issue in time series data is non-stationarity that highly influences the efficiency and consistency of regression estimates. In addition, time series regressions are most likely to suffer from spurious relationship. Thus, correct choice should be made regarding the regression models to obtain consistent estimates of the parameters and avoid spurious regression. This paper discusses the properties of time series data and the choice of appropriate regression models specifically in the context of finite samples. By discussing the relative strengths and limitations of the regression models that are used in time series data, this paper aims to contribute to the selection framework of regression models in time series analysis.

Investigation of Regression Models of Glycemic Dynamics under Conditions of Measurement Uncertainty

In the course of the research, it was analyzed that there are currently many widespread methods of invasive detection of glycemia. However, such methods can lead to infectious diseases. To minimize the risk of infection, research into the non-invasive method of determining glycemia, which can be used for medical purposes, is gaining popularity. The article describes the most common of these methods currently used.The article deals with the statistical substantiation of procedures for identifying the parameters of the glycemic dynamics model in the uncertainty of the measurement results. The heterogeneity of glycemic dynamics is ensured by the factor stimulating insulin secretion by exogenous glucose (glucose loading). The purpose of the article is to substantiate the choice of regression model of change in the level of glycemia with significant restrictions on the volume of primary measurement information, which cause uncertainty of nonlinear changes of the model at normative glucose loads.For the first time, polynomial regression analysis was applied to identify variants of polynomial regression recovery in incomplete measurement experiments for existing methods of type 2 diabetes, as well as models for the identification of diabetic conditions. Implementation of such dependencies can confirm the presence of stochastic relationships between the factors of influence and response of the organism. Three models are identified that should be prioritized in identifying the diabetic condition. It is shown in the paper that the research problems are reduced to the procedure of polynomial regression restoration as a model of glycemic dynamics depending on the number of possible variants. The analysis of the model shows that the main elements that influence the result are the sum of the regressors with a certain coefficient and the sum of the random remainder of the result of the calculation, which satisfies the conditions of interdependence and normality of probability distribution. One basic model, which is most suitable for the problems of recognizing the parametric model of glycemic dynamics in verifying the validity of statistical hypotheses, was also identified. The paper deals with a polynomial model of function by types of parametric uncertainty regarding the functional relationship between the factors of influence and reaction of the organism. The paper presents, as an example, the estimation of polynomial regressions that model the uncertainty of changes in glycemic levels for alternative conditions.

Enhancing two-stage modelling methodology for loss given default with support vector machines

We propose to incorporate least squares support vector machine technique into a two-stage modelling framework to predict recovery rates of credit cards from a UK retail bank. The two-stage model requires a classification step that discriminates the cases with recovery rate equal to 0 or 1 and a regression step to estimate recovery rates for the cases with recovery rates in (0, 1). The two-stage model with a support vector machine classifier is found to be advantageous on an out-of-time sample compared with other methods, suggesting that a support vector machine is preferred to a logistic regression as the classification technique. We further examine the predictive performances on a subset where recovery rate is bounded in (0, 1) and the empirical evidence demonstrates that support vector regression yields significant but modest improvement compared with other statistical regression models. When modelling on the whole sample, the support vector regression does not present any advantage compared with other techniques within the two-stage modelling framework. We suggest that the choice of regression models is less influential in prediction of recovery rates than the choice of classification methods in the first step of two-stage models.

PRM75 - Use Of Model Averaging Techniques in Cost-Effectiveness Analysis in Oncology

Often in cost-effectiveness analysis (CEA) of oncologic drugs, survival data from a randomized controlled trial are extrapolated to a lifetime horizon using parametric regression techniques. To capture parameter uncertainty in the analysis, regression parameters along with other model parameters are varied in probabilistic sensitivity analysis. However, structural uncertainty in the choice of regression model is rarely investigated. This study discusses the use of model averaging and provides an example to address structural uncertainty in CEA. Using a cohort partition model, the numbers of patients in “progression-free”, “progressed”, and “dead” health states were calculated directly from progression-free survival (PFS) and overall survival (OS) curves. Weibull, exponential, lognormal, log-logistic, generalized gamma, and Gompertz parametric models were used to extrapolated these curves to a lifetime horizon. Total costs, life year (LY), and quality adjusted life year (QALY) for each regression model were estimated. Weighted results across all models were calculated, based on weights that were derived from Akaike’s or Bayesian Information Criterion (AIC or BIC) parameters. Evaluating solely on BIC values, the lognormal distribution was identified as the best model for both survival curves. This resulted in the lowest observed ICERs. When model selection was based on considerations involving the log-cumulative hazard plots, clinical plausibility, and AIC/ BIC for each distribution, the Weibull distribution was selected for both curves, resulting in a 29% and 27% increase in the ICER for QALY and LY, respectively. Similar increases were observed when model averaging was applied using BIC-derived weights. In this case, model averaging produced results that were similar to those where model selection was based on multiple criteria. Choice of parametric models often has the biggest impact on the outcomes in CEAs in oncology. Model averaging takes into account the structural uncertainty surrounding the choice of parametric models.

Impact of Transformation of Negative Values and Regression Models on Differences Between the UK and US EQ-5D Time Trade-Off Value Sets

National EQ-5D value sets are developed because preferences for health may vary in different populations. UK values are lower than US values for most of the 243 possible EQ-5D health states. Although similar protocols were used for data collection, analytic choices regarding how to model values from the collected data may also influence national value sets. Participants in the UK and US studies assessed the same subset of 42 EQ-5D health states using the time trade-off (TTO) method. However, different methods were used to transform negative values to a range bounded by 0 and -1, and values for all 243 health states were estimated using two different regression models. The transformation of negative values is inconsistent with expected utility theory, and the choice of which transformation method to use lacks a theoretical foundation. Our objectives were to assess how much of the observed difference between the UK and US EQ-5D value sets may be explained by the choice of transformation method for negative values relative to the choice of regression model and the differences between elicited TTO values in the respective national studies (datasets). We applied both transformation methods and both regression models to each of the two datasets, resulting in eight comparable value sets. We arranged these value sets in pairs in which one source of difference (transformation method, regression model or dataset) was varied. For each of these paired value sets, we calculated the mean difference between the two matching values for each of the 243 health states. Finally, we calculated the mean utility gain for all possible transitions between pairs of EQ-5D health states within each value set and used the difference in transition scores as a measure of impact from changing transformation method, regression model or dataset. The mean absolute difference in values was 1.5 times larger when changing the transformation method than when using different datasets. The choice of transformation method had a 3.2 times larger effect on the mean health gain (transition score) than the choice of dataset. The mean health gain in the UK value set was 0.09 higher than in the US value set. Using the UK transformation method on the US dataset reduced this absolute difference to 0.02. The choice of regression model had little overall impact on the differences between the value sets. Most of the observed differences between the UK and US value sets were caused by the use of different transformation methods for negative values, rather than differences between the two study populations as reflected in the datasets. Changing the regression model had little impact on the differences between the value sets.

Regression-Guided Clustering: A Semisupervised Method for Circulation-to-Environment Synoptic Classification

AbstractRegression-guided clustering is introduced as a means of constructing circulation-to-environment synoptic climatological classifications. Rather than applying an unsupervised clustering algorithm to synoptic-scale atmospheric circulation data, one instead augments the atmospheric circulation dataset with predictions from a supervised regression model linking circulation to environment. The combined dataset is then entered into the clustering algorithm. The level of influence of the environmental dataset can be controlled by a simple weighting factor. The method is generic in that the choice of regression model and clustering algorithm is left to the user. Examples are given using standard multivariate linear regression models and the k-means clustering algorithm, both established methods in synoptic climatology. Results for southern British Columbia, Canada, indicate that model performance can be made to range between that of a fully unsupervised algorithm and a fully supervised algorithm.

A comparison of case-only designs for detecting gene × gene interaction in rheumatoid arthritis using genome-wide case-control data in Genetic Analysis Workshop 16

We compare and contrast case-only designs for detecting gene x gene (G x G) interaction in rheumatoid arthritis (RA) using the genome-wide data provided by Genetic Analysis Workshop 16 Problem 1. Logistic as well as novel multinomial and proportional odds models that do not depend on the specification of additive or dominant models for susceptibility loci were applied to the case-only sample. We identified 519 significant interactions (p < 1 x 10-4 in at least one test). All methods detected unique significant interactions; 169 were common to more than one model and only 21 were common to all models. Results emphasize that categorization of the genetic variables and choice of regression model are critical and hugely influential in the identification of G x G. Porportional odds and multinomial methods provide new tools for identification of G x G interactions.

Measurement of Retinal Vascular Caliber: Issues and Alternatives to Using the Arteriole to Venule Ratio

The arteriole to venule ratio (AVR) is widely used in studies of the associations of retinal microvascular disease with systemic and ocular outcomes. This is a discussion of the limitations of AVR; a comparison of its predictive information with that of its components, arteriolar and venular caliber; and a description of a suggested alternative method of modeling arteriolar and venular calibers directly. Data from the population-based Blue Mountains Eye Study were used to compare the predictive information in models using AVR with models using arteriolar and venular calibers directly. Determination was made of how the apparent relationship between vessel caliber and two systemic outcomes (blood pressure [BP] and white blood cell count [WBC]) was influenced by the choice of regression model. These findings were interpreted with reference to the known biological relationship among vessel calibers, BP, and WBC. Models using arteriolar and venular calibers directly had more predictive information than models using AVR. The apparent relationship of vessel caliber to BP and WBC differed substantially, depending on the model chosen. For example, after adjustment for age, sex, and other covariates, decreasing venular caliber was associated with higher systolic BP when modeled separately, but was associated with lower systolic BP when modeled simultaneously with arteriolar caliber. The findings suggest AVR provides less information with regards to predicting systemic outcomes than its two components. Modeling arteriolar and venular calibers separately could be biased by confounding, while modeling both simultaneously appears to provide unbiased, biologically plausible results. The use of this approach is recommended in future research relating retinal vascular caliber to systemic or ocular outcomes.

Does The Choice of Muscle Relaxants Really Affect Postoperative Recovery Time?

In Response: In our article [1], we reported the mean and standard error of the mean for length of surgery and recovery time. Although the re-ported mean length of surgery using long-acting muscle relaxants was longer than that using short- and intermediate-acting muscle relaxants, there was actually considerable overlap between the two groups, with the short- and intermediate-acting muscle relaxants ranging from 45 to 780 min, and the long-acting muscle relaxants ranging from 73 to 820 min. For the sake of simplicity, we chose not to include details of all the regression models we explored. We presented linear models comparing the recovery time associated with the two muscle relaxant groups, controlling for different confounders. By plotting the length of surgery and recovery time on a logarithmic scale, we could have misled readers about our choice of regression model. However, there was a strong linear relationship between the length of recovery time and the length of surgery (r = 0.31 with P < 0.001). The issues of problems with extrapolation mentioned by Bronheim et al. are not relevant to our data and analyses because we did not extrapolate. Jane C. Ballantyne, FRCA YuChiao Chang, PhD Department of Anesthesia and Critical Care; Massachusetts General Hospital; Boston, MA 02114

Does The Choice of Muscle Relaxants Really Affect Postoperative Recovery Time?

In Response: In our article [1], we reported the mean and standard error of the mean for length of surgery and recovery time. Although the re-ported mean length of surgery using long-acting muscle relaxants was longer than that using short- and intermediate-acting muscle relaxants, there was actually considerable overlap between the two groups, with the short- and intermediate-acting muscle relaxants ranging from 45 to 780 min, and the long-acting muscle relaxants ranging from 73 to 820 min. For the sake of simplicity, we chose not to include details of all the regression models we explored. We presented linear models comparing the recovery time associated with the two muscle relaxant groups, controlling for different confounders. By plotting the length of surgery and recovery time on a logarithmic scale, we could have misled readers about our choice of regression model. However, there was a strong linear relationship between the length of recovery time and the length of surgery (r = 0.31 with P < 0.001). The issues of problems with extrapolation mentioned by Bronheim et al. are not relevant to our data and analyses because we did not extrapolate. Jane C. Ballantyne, FRCA YuChiao Chang, PhD Department of Anesthesia and Critical Care; Massachusetts General Hospital; Boston, MA 02114

07 On the choice of regression model for censored Survival data

07 On the choice of regression model for censored Survival data

Effect of Pedal Cadence on Parameters of the Hyperbolic Power - Time Relationship

The purpose of this study was to evaluate the effect of pedal cadence methodology on the relationship between power output and time to exhaustion. Twenty-four subjects each performed 12 all-out cycle ergometer tests (four at a constant 60 rpm, four at a constant 100 rpm, and four where they were allowed to select and, within each test, vary their cadence). The parameters of the hyperbolic power-time relationship, AWC (anaerobic work capacity) and CP (critical power), were estimated for each pedal cadence methodology using three regression models: nonlinear power-time, linear work-time, and linear power-time-1. In all cases, R2 was high and standard errors of the estimate of AWC and CP were low. With the two constant rpm methodologies, the estimates of AWC and CP were influenced by the choice of regression model. The estimates of AWC and CP were also influenced by the pedal cadence in the all-out tests. For example, the CP derived from the 100 rpm tests (mean +/- SD: 195 +/- 50 W) was lower (p < 0.05) than the CP from the other methodologies (207 +/- 50 W and 204 +/- 48 W), and the AWC from the variable cadence methodology (16.1 +/- 6.2 kJ) was greater than the AWC from constant rpm trials (14.5 +/- 5.9 kJ and 14.6 +/- 5.7 kJ). It is concluded that pedal cadence methodology influences the parameters of the power-time relationship.

Sedimented Diatoms in Northern New England Lakes and Their Use as pH and Alkalinity Indicators

Gradient analyses of 29 chemical and physical (C–P) variables and diatom remains in surface sediments of 63 New England lakes (pH 4.4–7.9) indicate a primary C–P gradient of pH, alkalinity, Ca, Mg, conductance, and Al; diatom distributions are most strongly related to that gradient (especially to pH and alkalinity) and also reflect secondary gradients (oceanic–inland, lake morphology, and regional chemistry). The primary relationship supports the calibration of regression models for paleolimnological inference of pH and alkalinity based on diatoms. To optimize inference models for the region's most acidic lakes, a second set of calibrations was run after culling the seven least acidic lakes. Diatom distributions on the restricted pH and alkalinity gradients are of two types: roughly uniclinal and variously unimodal. Models assuming each type were calibrated: CLUSTER (linear), DCA (unimodal), and CCA (unimodal). Log-transformation of alkalinity improved the 63-lake DCA and CLUSTER regressions, but worsened or left the others unchanged. Postulated causes of incongruous diatom assemblages and outlier pH and alkalinity inferences are sediment mixing, focusing time lag, growth of epipelic diatoms at the core site, and atypical lake morphology. Careful selection of calibration lakes is at least as important as the choice of regression models.

An improved processing of radioimmunoassay data by means of a desk-top calculator (1) comparison of regression procedures applied to selected kinds of radioimmunoassay

By means of a programmable desk-top calculator, goodness-of-fit of 3 regression models, four-parameter logistic, quadratic logit-log and linear logit-log models, were evaluated by analysis of variance ( F test) for data of 6 kinds of radioimmunoassays (RIA); thyroid stimulating hormone (TSH), luteinizing hormone (LH), follicle-stimulating hormone (FSH), insulin (IRI), cortisol, triiodothyronine (T 3). Scatchard plot analyses were made with the representative data of these RIAs in order to find the best choice of regression model in relation to the characteristics of antigen-antibody reaction. The analysis of goodness-of-fit of the regression models by means of an F test disclosed the relation between the choice of regression models and the kinds of RIA, which could be grouped into 3 types: (1) almost identical degree of fit with any of 3 regression models (FSH and T 3), (2) more or less equal degree of satisfactory fit with the logistic and quadratic logit-log models (TSH and cortisol), (3) best degree of fit with the quadratic logit-log model among 3 (LH and IRI). The analysis of data with Scatchard plot discriminated 3 general types of curves; (1) linear (FSH) and T 3), (2) linear with tail (TSH and cortisol) and (3) hyperbola (LH and IRI). From these findings, the following tentative conclusions were reached: RIA with linear pattern on Scatchard plot can be satisfactorily regressed with either of 3 models, RIA with linear with tail pattern regressed with either the logistic or quadratic logit-log model, and RIA with hyperbolic pattern regressed best with the quadratic logit-log model.